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Forecasting decisions in conflict situations: A comparison of game theory, role playing and unaided judgment (conflictforecasting.com)

July 2002

DOI:10.1016/S0169-2070(02)00025-0

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RePEc

Authors:

University of South Australia

Can game theory aid in forecasting the decision making of parties in a conflict? A review of the literature revealed diverse opinions but no empirical evidence on this question. When put to the test, game theorists’ predictions were more accurate than those from unaided judgement but not as accurate as role-play forecasts. Twenty-one game theorists made 99 forecasts of decisions for six conflict situations. The same situations were described to 290 research participants, who made 207 forecasts using unaided judgement, and to 933 participants, who made 158 forecasts in active role-playing. Averaged across the six situations, 37 percent of the game theorists’ forecasts, 28 percent of the unaided-judgement forecasts, and 64 percent of the role-play forecasts were correct.

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Electronic copy available at: http://ssrn.com/abstract=1159537

International Journal of Forecasting 18 (2002) 321–344 www.elsevier.com/locate /ijforecast

F orecasting decisions in conﬂict situations: a comparison of game

theory, role-playing, and unaided judgement

Kesten C. Green

School of Business and Public Management

Victoria University of Wellington

and Decision Research Ltd

Box

5530,

Wellington

New Zealand

Abstract

Can game theory aid in forecasting the decision making of parties in a conﬂict? A review of the literature revealed diverse

opinions but no empirical evidence on this question. When put to the test, game theorists’ predictions were more accurate

than those from unaided judgement but not as accurate as role-play forecasts. Twenty-one game theorists made 99 forecasts

of decisions for six conﬂict situations. The same situations were described to 290 research participants, who made 207

forecasts using unaided judgement, and to 933 participants, who made 158 forecasts in active role-playing. Averaged across

the six situations, 37 percent of the game theorists’ forecasts, 28 percent of the unaided-judgement forecasts, and 64 percent

of the role-play forecasts were correct. 2002 International Institute of Forecasters. Published by Elsevier Science B.V.

Keywords

Conﬂict; Expert opinion; Forecasting; Game theory; Judgement; Role-playing; Simulation

1 . Introduction gers in a series of electricity trading simulations.

The role-play behaviour was so at odds with the

In 1996 the New Zealand government trans- executives’ own beliefs about how the market

ferred some of the assets of its monopoly participants should and would behave, that they

electricity generator to a new private sector ignored the forecast. Turning to game theory for

electricity-generating company, Contact Energy help, Contact management found it to be ‘‘no

Ltd. It further split the residual into three help at all . . . the role-playing exercise had

entities in 1999. Wishing to know how particip- already foretold the future, as we were to ﬁnd

ants in the new competitive market for out to our cost.’’

wholesale electricity would behave following This anecdote suggests that role-playing may

the second split, Contact organised its execu-

tives to role-play the generator company mana-

Interview with Toby Stevenson, General Manager Elec-

*Tel.: 164-4-499-2040; fax: 164-4-499-2080. tricity Trading, Contact Energy Limited, 7 December

E-mail address

kesten.green@vuw.ac.nz (K.C. Green). 2000.

PII: S0169-2070(02)00025-0

Electronic copy available at: http://ssrn.com/abstract=1159537

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be an effective approach to predicting decisions biases. Indeed, Nalebuff and Brandenburger

made in conﬂicts among small numbers of (1996, p. 8) wrote ‘‘by presenting a more

decision makers with much at stake. The pri- complete picture of each . . . situation, game

mary purpose of the research described in this theory makes it possible to see aspects of the

paper was to investigate the relative accuracy of situation that would otherwise have been ig-

methods used to forecast decisions made in real nored. In these neglected aspects, some of the

conﬂicts. For this purpose, I deﬁned accuracy as greatest opportunities . . . are to be found’’. The

the proportion of forecasts that match the actual entry on game theory in Bullock and Trom-

decision. Accuracy is commonly regarded as the bley’s (1999) dictionary states that game theor-

most important criterion for judging the worth ists ‘‘hope to produce a complete theory and

of a forecast (Armstrong, 2001b). The methods I explanation of the social world’’. Given these

examined were unaided judgement, game claims and the fact that game theory is used by

theory, and role-playing. I deﬁned game theory forecasting practitioners and is recommended by

as what game theorists do when faced with experts, it is legitimate to ask whether the

practical forecasting problems. It was not the method can help forecasters make useful predic-

purpose of the study to investigate other aspects tions for real conﬂicts.

of the methods, such as their value for generat- Opinions on the value of game theory for

ing strategic ideas. forecasting real conﬂicts are diverse. In contrast

While unaided judgement is commonly used to the optimistic claims made by Nalebuff and

to forecast decisions in conﬂicts, game theory Brandenburger (1996) and in Bullock and

and role-playing are not. Armstrong, Brodie, Trombley (1999), Shubik (1975, p. xi) de-

and McIntyre (1987) surveyed 59 practitioner scribed the assumptions behind formal game

members of the International Institute of Fore- theory as ‘‘peculiarly rationalistic’’. He con-

casters. The practitioners were asked about the tinued: ‘‘It is assumed that the individuals are

use, by their respective organisations, of meth- capable of accurate and virtually costless

ods for forecasting competitive actions. The computations. Furthermore, they are assumed to

authors found that the organisations of 85 be completely informed about their environ-

percent of practitioners used the opinions of ment. They are presumed to have perfect per-

experts with domain knowledge, the organisa- ceptions. They are regarded as possessing well-

tions of 8 percent of practitioners used formal deﬁned goals. It is assumed that these goals do

game theory, and the organisations of 7 percent not change over the period of time during which

of practitioners used role-playing. The same the game is played’’. He concluded that while

study found expert opinion on the relative value game theory may be applicable to actual games

of the methods to be at odds with the reported (such as backgammon or chess), and even be

frequency of use by practitioners’ organisations. useful for constructing a model to approximate

Both marketing and forecasting experts ranked an economic structure, such as a market, ‘‘It is

game theory and role-playing more highly than much harder to consider being able to trap the

practitioners, although they disagreed about the subtleties of a family quarrel or an international

relative value of the two methods—forecasting treaty bargaining session’’ (p. 14).

experts preferred role-playing over game theory. The usefulness and realism of role-playing

Game theory may help practitioners provide are often contrasted with the limitations of game

more accurate forecasts than unaided judgement theory in the game-theory literature. For exam-

because, for example, the discipline of the ple, Nalebuff and Brandenburger (1996, p. 62)

approach should tend to counter judgemental emphasised the importance and difﬁculty of

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323

appreciating the perceptions of other parties. In give ‘‘insufﬁcient consideration of the contin-

a brief note, they suggested that one way for gent decisions of others’’, as evidenced by such

managers to do this is to ‘‘ask a colleague to phenomena as winner’s curse and non-rational

role-play by stepping into [another] player’s escalation of commitment (Zajac & Bazerman,

shoes’’ (p. 63). 1991, p. 43).

Shubik (1975) dealt with role-playing more Babcock, Loewenstein, Issacharoff, and Ca-

comprehensively. He stated that ‘‘an extremely merer (1995) demonstrated that judgement

valuable aspect of operational gaming is the tends to be biased by the role of the judge. They

perspective gained by viewing a conﬂict of asked participants to provide an estimate of a

interests from the other side. Experience gained fair judgement in a dispute between two parties.

in playing roles foreign to one’s own interests Before being presented with identical brieﬁng

may provide insights hard to obtain in any other material, half the participants were told they

manner’’ (p. 9). Shubik further suggested that were to take the role of a lawyer for the

game theory is less realistic than role-playing complainant and the other half were told they

(gaming): ‘‘In summary we should suggest that were to represent the defendant. Estimates of a

many of the uses of gaming are not concerned fair judgement diverged between the two groups

with problems which can be clearly and narrow- of ‘lawyers’ and the authors show that the two

ly deﬁned as belonging to game theory. En- groups interpreted the brieﬁng material in dif-

vironment-poor experimental games come clos- ferent (self-serving) ways. Similarly, Cyert,

est to being strict game theory problems. Yet March, and Starbuck (1961) found that role-

even here, features such as learning, searching, players produced divergent forecasts from

organising, are best explained by psychology, identical sets of numbers depending on whether

social-psychology, management science, and they were told they were ‘cost analysts’ or

other disciplines more relevant than game ‘sales analysts’. Statman and Tyebjee (1985)

theory’’ (p. 17). replicated the study, and obtained results con-

Schelling (1961) stated that ‘‘part of the sistent with the earlier research.

rationale of game organization [role-play ex- Given the foregoing evidence, a manager

perimentation] is that no straightforward ana- wanting to forecast a decision in a conﬂict may

lytical process will generate a ‘solution’ to the consider asking someone not involved in the

problem, predict an outcome, or produce a conﬂict for his or her considered opinion on

comprehensive map of the alternative routes, what decision is most likely. Yet independent

processes, and outcomes that are latent in the judges are also subject to inﬂuences that lead to

problem’’ (p. 47). In contrast, role-plays ‘‘do inaccurate forecasts. For example, they may be

generate these complexities and, by most re- subject to biases arising from the use of com-

ports, do it in a fruitful and stimulating way’’. mon judgemental heuristics, or to overconﬁ-

dence. Bazerman (1998, p. 6) identiﬁed three

broad classes of heuristic (availability, repre-

sentativeness, anchoring) that can engender

2 . Prior evidence judgemental biases. Arkes (2001) examined the

Although judgement may be adequate for evidence and concluded that experience often

predicting decisions made in routine conﬂicts, leads forecasters using unaided judgement to

decision makers can be subject to serious ignore base rate data and shun decision aids to

judgemental biases or blind spots. Decision the detriment of forecast accuracy. Evidence on

makers who are involved in a conﬂict tend to the forecasting accuracy of independent judges

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is provided by Armstrong (2001a) who found asking for empirical evidence on the predictive

that research participants exercising their un- validity of game theory for real conﬂicts. I had

aided judgement performed no better than previously used the addresses to recruit game-

chance when predicting decisions made in con- theorist research participants. Included in the

ﬂicts. letter was a URL for a draft of this paper. I

There is little evidence on the predictive received 18 responses, none of which provided

validity of game theory for real conﬂicts. Reis- substantive evidence on predictive validity.

man, Kumar, and Motwani (2001) reviewed all One response was an automatic message from

game-theory articles published in the leading an ISP informing of an invalid address and ﬁve

US OR/MS journals and found that an average were automatic messages generated for addres-

of less than one article per year addressed a sees who were on leave or otherwise unavail-

real-world application. Armstrong (1997) stated able. A single respondent claimed to have no

‘‘I have reviewed the literature on the effective- relevant expertise, and a further four either

ness of game theory for predictions and have asked for the draft paper in another format or

been unable to ﬁnd any evidence to directly stated that they would look at the material later.

support the belief that game theory would aid Six respondents provided comments on the

predictive ability’’ (p. 94). paper or information on game theory. One of

Such evidence as there is tends to be indirect these referred to ‘‘the huge literature on ex-

and incomplete, typically comparing game- perimental economics that shows under what

theory predictions with decisions made in role- conditions game theory with the ‘rational actor

play experiments rather than with those from assumptions’ works, and where it does not’’.

actual conﬂicts. For example, Armstrong and The second of these respondents pointed to his

Hutcherson (1989) found two studies (Neslin & own work on the civil conﬂict in Northern

Greenhalgh, 1983; Eliashberg, LaTour, Sangas- Ireland as offering evidence of predictive va-

wamy, & Stern, 1986) that involved the use of lidity for a variety of game theory (Brams &

game theory to predict decisions made in Togman, 2000). He stated ‘‘I think our

negotiations. In both studies the negotiations predictions . . . have for the most part been

were role-plays rather than actual negotiations, borne out by events’’. Brams and Togman

with the implication that the role-play decisions suggested that game theory and the theory of

(which game theory predicted imperfectly) were moves (an extension of game theory) give

equivalent to actual negotiation agreements. insights that ‘‘can help political leaders predict

Similar approaches have been widely used by both the dynamics of conﬂict and the conditions

game theorists. Shubik (1975) notes that ‘‘ex- that can provide an escape from it’’ (p. 337).

perimental gaming’’ is employed to examine the The book in which their paper appears also

‘‘validity of various solution concepts’’ de- contains claims of accuracy for a forecasting

veloped by game theorists (p. 20). Rapoport and model using game-theory and decision-theory

Orwent (1962) conducted a comprehensive analysis of the civil conﬂict over Jerusalem

review of the use of experimental games to test (Organski, 2000). A third respondent pointed to

game-theory hypotheses. They concluded this his own work on analysing play in an interna-

review with a suggestion that ‘‘game theory is tional sporting competition. His paper was not

not descriptive and will not predict human relevant to this research. Finally, four of the

behavior, especially in games with imperfect

information about the payoff matrices’’ (p. 34). Personal communication from Steven Brams, 13 June

I sent an e-mail letter to 474 e-mail addresses 2001.

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respondents who had offered comment or in- Three of the articles mentioned the predictive

formation did not address the question of pre- accuracy of game theory for real conﬂicts.

dictive validity. Ghemawat and McGahan (1998) used historical

A search of the Social Science Citation Index market data to examine price competition be-

(SSCI) for the period 1978 to 7 July 2001 using tween electricity generating companies. The

the phrases ‘game theory’ and ‘forecasting’ authors found that game-theory models had

yielded two articles. Substituting ‘prediction’ greater explanatory power than ‘nonstrategic

for ‘forecasting’ yielded a further 14 articles. analysis’. They suggested that game theory is

Jehiel (1998) turned up in both searches, but the most likely to provide accurate forecasts of

article was purely speculative and theoretical. conﬂicts when there is concentrated competition

Of the remainder, one concerned a behavioural (few players), mutual familiarity, and repeated

pharmacology study using mice (Parmigiani, interaction. Gruca, Kumar, and Sudharshan

Ferrari, & Palanza, 1998), a second was a (1992) proposed a game-theory model of exist-

review of research on strategic decision making ing players’ responses to a new entrant to a

(Schwenk, 1995), and a third concerned the market. They compared the predictions from

predictive validity of agency theory (Ghosh & their game-theory model with empirical evi-

John, 2000). dence on actual behaviour in conﬂicts of this

Aside from Henderson (1998), which offered type and with the predictions of an alternative

only opinions on the usefulness of game theory, model. They found that their model provided

the remaining 11 articles all provided evidence forecasts that were more consistent with the

for the predictive accuracy of game theory empirical evidence for more combinations of

relative to another method, relative to a decision competitive situation than did the alternative

made in a real conﬂict, or both. Predictions model, but did not provide enumeration. Keser

were compared to the outcomes of experiments and Gardner (1999) found that the Nash equilib-

in six of the articles, and this was the only rium failed to predict the behaviour of particip-

comparison that was made in two of these ants in a common-pool resource game experi-

articles (Diekmann, 1993; Sonnegard, 1996). ment. They suggested that ‘‘policies based on

Batson and Ahmad (2001) compared the predic- that equilibrium’s predictions are suspect’’. The

tions of classic game theory with predictions participants were students experienced in game

from the theory of rational choice and the theory, and the researchers expected the design

empathy–altruism hypothesis. Gibbons and Van of the experiment to favour Nash equilibrium

Boven (2001) compared game-theory predic- decisions.

tions with the outcomes of experiments and the Finally, Sandholm (1998) compared the pre-

stated preferences of role-players. McCabe and dictions of three classes of ‘evolutionary game

Smith (2000) compared game-theory predic- theory’ models of social convention on the basis

tions with the outcomes of experiments and of reasonableness.

with predictions based on theories of ‘social Although the 11 articles did not provide

exchange’. Suleiman (1996) conducted experi- formal evidence on the accuracy of forecasts by

ments to test hypotheses about why classic game theorists relative to reasonable non-game-

game theory fails to predict the behaviour of theoretic alternatives, they did support the con-

participants in ‘ultimatum’ game experiments. tention that game theory is considered to be a

The experiments involved comparing the game forecasting method by some authors.

outcomes with the predictions of the particip- A search of the Internet using the Google

ants. search engine and the same terms I used for the

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SSCI search on July 17, 2001 (‘game theory’ (2001a) found that role-playing provided more

and ‘forecasting’) produced too many hits to accurate forecasts than chance and unaided

investigate. Using the three phrases ‘compara- judgement.

tive’, ‘forecasting accuracy’, and ‘game theory’ Role-playing and game theory depend on

yielded 17 hits, including one duplicate. Eleven contrasting assumptions about modelling con-

of the hits were lists of courses or papers—the ﬂict situations. Those who adopt a game-theory

three search terms were dispersed among unre- approach must assume that they can radically

lated course summaries and abstracts of papers. reduce the complexity of a conﬂict without

Four of the hits were of single documents, predictive validity being lost. The role-play

rather than lists. None of the four offered any approach, on the other hand, incorporates com-

evidence on the forecasting accuracy of game plexity and emotion into a simulation.

theory for real conﬂicts. One URL returned an Armstrong (2001c) has suggested that the

‘access denied’ message. accuracy of different approaches to predicting

Bennett (1995, p. 27) listed four missing decisions made in conﬂicts is related to the

dimensions of classic game-theory models: dif- realism with which they allow forecasters to

fering perceptions, dynamics, combinatorial model the situation: the more realistic the

complexity, and linked issues. Two extensions representation, the more accurate the predictions

of game theory that set out to address its are likely to be (Principle 7.2). This hypothesis

shortcomings have been ‘hypergame analysis’ implies that the use of game-theory knowledge

(Bennett & Huxham, 1982), and ‘drama theory’ should result in more accurate forecasts than the

(Howard, 1994a,b). While hypergames are in- use of unaided judgement and that the use of

tended to take players’ divergent perceptions role-playing should produce more accurate fore-

into account by describing and analysing a set casts than the use of game-theory knowledge.

of subjective but linked games, drama theory

moves further away from the sparseness of

game theory by attempting to incorporate emo- 3 . Methods

tion into the analysis of conﬂict situations. On

the face of it, these developments should deliver

3 .1.

Selection of conﬂicts

greater realism—and perhaps also greater pre-

dictive accuracy—than classic game theory. I chose six real conﬂicts to assess the relative

Nevertheless, to test hypotheses about behaviour accuracy of forecasts from unaided judgement,

generated by drama theory, Bennett and game theory, and role-playing. The conﬂicts

McQuade (1996), for example, resorted to role- each occurred between small numbers of de-

playing to provide the behavioural benchmark. cision-makers with much at stake. They were

Role-playing is the third and last of the three diverse in the parties that were involved, the

forecasting methods considered. It is ‘‘a tech- level of conﬂict, and the type of decision that

nique whereby people play roles and enact a was to be made. Furthermore, the conﬂicts were

situation in a realistic manner. Role-playing can all unlikely to be recognised by participants. I

be used to predict what will happen if various neither sought nor deliberately avoided conﬂict

strategies are employed. It is especially relevant situations that resembled familiar game-theory

when trying to forecast decisions made by two models. Neutral but informed observers wrote

parties who are in conﬂict’’ (Armstrong, 2001d, the descriptions of the situations.

p. 807). Role-playing is used to simulate rather Three of the situations (‘Artists’ Protest’,

than analyse conﬂict situations. Armstrong ‘Distribution Channel’, and ‘55% Pay Plan’)

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were ﬁrst used in research by Armstrong based my description on a Grenada Television

(1987). Artists’ Protest was a conﬂict between documentary about a British Steel investment

artists and government over ﬁnancial support— decision that was complicated by conﬂicting

Armstrong based his description of it on a interests among the decision makers (Graef,

report in The Wall Street Journal (Newman, 1976). I disguised the situation, but did not alter

1982). Distribution Channel was a proposal by it in any substantive way. I sought advice from

Philco Corporation for commercial cooperation a professor who had used the documentary in

requiring decision makers to trade off conﬂict- his teaching for many years. He had also

ing interests—Armstrong took a description of worked at British Steel for one of the managers

it from a book of marketing case histories who played a major part in the investment

(Berg, 1970). The 55% Pay Plan was a conﬂict decision portrayed in the documentary. The

between National Football League owners and professor considered the description to be an

players over revenue shares—Armstrong based accurate representation of the situation.

his description of it on two reports in Sports I also wrote the description of the sixth

Illustrated published prior to the start of situation, ‘Nurses Dispute’. The situation was a

negotiations (Boyle, 1982; Kirshenbaum, 1982). dispute over pay between nursing staff and

A fourth situation, ‘Panalba Drug Policy’, was management. The nurses went on strike angry

ﬁrst used in experiments conducted by Arm- that they were being offered a much lower pay

strong (1977) on the inﬂuence of role on increase than management had already given to

managers’ behaviour. Panalba was a conﬂict intensive care nurses and junior doctors. A

between the board members of a pharmaceutical mediator was appointed by a government

company and the consumers of one of the agency. The principal negotiators for the two

company’s drugs. Unlike the other conﬂicts in parties co-operated with the research and, after

this research, one party to the conﬂict (the they had reached an agreement, some members

consumers) was absent except in the abstract. of the nurses’ negotiation team role-played the

Armstrong wrote: ‘‘The description was based dispute in a debrieﬁng session using the materi-

upon the true case of Panalba as reported by al I had prepared for this research. Asked how

Mintz (1969). Information was also taken from the description could be improved, the principal

Upjohn’s Annual Reports. I made up details for negotiator did not have any suggestions and

this case ...tomakethe extreme nature of this considered the material a fair and accurate

case obvious. Attempts were made to obtain representation. I used two versions of the situa-

further information from the Upjohn Co. to tion description that were the same in all

ensure the facts were accurately presented, but respects other than the names of the people and

they refused to answer’’ (p. 196). organisations involved. In the ﬁrst version I

Prior research using these four situations used actual names. In the second, I changed the

provided information on the accuracy of role- names of the people and organisations after one

playing and judgemental forecasts. These data potential participant said he was unhappy play-

were collected by Armstrong and colleagues ing the role of a real person and withdrew from

and were summarised in Armstrong (2001a). In his session.

all, 147 judgemental forecasts made by 230 The descriptions of the six situations are

participants, and 119 role-play forecasts from available on the Internet at www.kestencgreen.

653 participants were obtained from this source. com. I used the same situation descriptions,

I wrote the description of the ﬁfth situation, role descriptions, and exhaustive list of deci-

‘Zenith Investment’ for this research project. I sions from which the participants were asked to

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choose for all three forecasting methods: un- Volunteers from one third-year university

aided judgement, role-playing, and game theory. class provided 10 Zenith predictions. I asked

I discuss an exception to the uniform treatment participants to leave the lecture theatre with the

below. material I had given them and to return the

For any forecasting method to be useful, it completed questionnaires no more than one

must be more accurate than chance. I use the hour after having received their instructions.

term ‘chance’ to refer to the probability of Volunteers from two third-year classes pro-

selecting, at random, the decision that was vided 20 predictions. I used 10 minutes of class

actually made, from the exhaustive list of time to distribute material on ﬁve situations

potential decisions provided to participants. (Nurses was not included) and to brief the

students. I instructed them to return their com-

pleted questionnaires to their lecturer, or to fold

3 .2.

Unaided judgement them (so that ‘Freepost’ information and address

The participants using unaided judgement were displayed) and post them.

read the description of a conﬂict and then I had offered ﬁve marketing students, one

selected the decision they thought most likely information-technology student, one environ-

from a list. I recruited these judges on the basis mental-planning consultant, and one medical

of convenience. They had no special knowledge doctor $NZ25 (about $US10) to participate in a

of the situations nor of the class of problem I role-playing session, but I did not need them for

asked them to consider. that purpose. Instead, they provided eight pre-

Except for predictions for the Zenith and dictions for the Zenith situation. I asked them to

Nurses situations, I took most of the predictions adjourn to a room away from the role-players

using unaided judgement that are used in this with the material I had given them and to return

research from studies reported by Armstrong completed questionnaires to me no more than

(2001a). Role descriptions were not provided to one hour after getting their instructions. In a

all the judges who took part in the research situation similar to the one just described,

reported by Armstrong, but Armstrong and students who were not needed for role-playing

Hutcherson (1989) have shown that providing provided predictions for the Nurses situation

role descriptions to judges has no effect on their instead.

forecasting accuracy. In some cases, the judges

were paired off to discuss the problem before

3 .3.

Role-playing

making their predictions. In other cases, they

acted alone. I gave each role-play participant a single role

I provided all participants in the new research description to read and told participants to adopt

with a full set of information for a single the role they had been given for the duration of

situation (including roles for both parties) and a their simulation. When they had adopted their

questionnaire. I told them that the material roles, I asked the role-players to read a descrip-

included a description of a conﬂict that had tion of the conﬂict. I then told them to form

occurred in the past. I asked them to read the groups, with each group comprising one role-

material and, without conferring with others or player for each role. For example, in the Nurses

referring to other sources of information, use situation there were ﬁve roles: two management

their judgement to predict the decision that had roles, two union roles, and one mediator role.

actually been made, and then complete and Once the role-players were in their groups, I

return the questionnaire. told them to role-play the conﬂict from the time

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329

speciﬁed in the description until they arrived at characters’ names and positions. I told them to

a decision or ran out of time. When they meet in their groups, wearing their name

ﬁnished, each role-player recorded the decision badges, and to introduce themselves to each

the group had made or, if they had run out of other while in character.

time, the decision he or she thought would have I told the Zenith Investment role-players that

been made had the group been free to continue. the chairman of Zenith would set a time and

With the exception of six groups of Nurses place for a meeting and that they should prepare

Dispute role-players, the role-players were, like for the meeting in a manner consistent with

the judges, recruited on the basis of convenience their printed brieﬁng material. In the verbal

rather than because they resembled the charac- brieﬁngs, I emphasised that it was appropriate to

ters they were to play or were familiar with the hold informal discussions with other members

roles they were to play or were knowledgeable of their group (the Zenith Policy Committee)

about the situation. Most of the role-players prior to the meeting. I told Nurses Dispute

were university students. I conducted role-play role-players that, after introductions, the two

simulations for the Zenith and Nurses situations parties to the dispute should agree to a time and

as part of this research, and took role-play place for their ﬁrst meeting and that subsequent

results for the other four situations from Arm- meetings could be held at the discretion of the

strong (2001a). parties. I told participants who had been given

I brought the participants for the Zenith and the mediator roles, one from each group at the

Nurses simulations together in lecture theatres session, to meet at a designated place. I told

or similar settings for their brieﬁngs. I gave them to discuss mediation and its application to

each participant an information sheet, which the dispute among themselves until the parties

provided basic information on the research in their own groups called upon them, or 30

project and on role-playing, and a consent form. minutes had elapsed. If the contesting parties

I told them it was very important that they take failed to agree within 30 minutes, they were

the role-playing seriously. Additional space, obliged to accept the services of their gov-

such as a second lecture theatre, meeting rooms, ernment-appointed mediator. This measure was

or lobby areas, was available for role-playing. I intended to simulate the effect of employment

encouraged the role-players to make good use relations legislation that had just taken effect at

of the available space for holding both formal the time of the dispute.

meetings and private discussions. At the end of No efforts were made to increase the realism

the brieﬁngs, I told them that they were free to of the simulations beyond what has been de-

improvise provided that they remained in scribed here. There were no theatrical or tech-

character and true to the situation description. nological devices, nor were any confederate

They were allowed to retain their printed role role-players used.

and situation descriptions for the duration of the The procedures I adopted in this research

session. This material included the questionnaire were similar to those Armstrong and Hutcher-

that the role-players were to ﬁll in at the end of son adopted for Artists’ Protest, Distribution

their role-plays. I drew their attention to the Channel, and 55% Pay Plan (Armstrong, 1987;

decision options presented in the questionnaires Armstrong & Hutcherson, 1989). Although

and told them that they would be expected to similar in other respects, the role-plays of

match one of these with their own group’s Panalba Drug Policy (Armstrong, 1977) in-

role-play decision. I also gave role-players volved people belonging to a single party (the

printed self-adhesive badges showing their members of the Upjohn Board) who had a

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common purpose—neither representatives of Nurses sessions whether they would tend to

consumers nor of the Food and Drug Adminis- identify more with union or management in a

tration were present. pay dispute. I then allocated them according to

A total of 170 university students role-played their preferences, with the more equivocal par-

the Zenith situation in 17 groups. I conducted ticipants given the mediator role. I allocated

these role-plays in three sessions with different participants in the third session to roles on the

participants. Five groups role-played the situa- basis of my assessment of the compatibility of

tion in an organisational behaviour class and their experience with the demands of the roles.

four in a conﬂict-of-laws class. I recruited the

eight groups of role-players in the third session

3 .4.

Prediction by game theorists

from among students attending mathematics and

computer science lectures. I offered the students The initial sample of 558 game theorists was

who attended the third session $NZ25 to take composed of the members of the Game Theory

part.Whereas participants in earlier sessions had Society, recipients of the International Society

been assigned randomly to roles, in the third of Dynamic Games E-Letter, and a small

session I asked ‘natural leaders’ and ‘quantita- number of prominent game-theory experts who

tive analysis experts’ to come to the front of the were not members of the other two groups. I

theatre. I allocated ‘natural leaders’ to the expected that a large initial sample would be

Chairman roles and ‘quantitative experts’ to the necessary because the task was demanding and I

roles of either Finance Director or Chief Plan- was offering no extrinsic rewards.

ner. I assigned the remaining participants ran- I sent everyone in the sample of experts an

domly to the seven other roles. e-mail message and material on ﬁve situations,

I told all participants that their taking part excluding the Nurses Dispute (Appendix A). I

would help with research on decision making in personalised the messages when this was pos-

conﬂict situations and was likely to be both sible. Although the Game Theory Society mem-

enjoyable and (in the case of the ﬁrst two bership list contained only e-mail addresses,

sessions) relevant to their studies. I told particip- names were included in most of the e-mail

ants that the situation they were to role-play had addresses. I conducted Internet searches when

occurred in the past and that it involved a group they were not and ended up with names for all

of senior managers making an important invest- but 57 e-mail addresses in the sample.

ment decision. I made recipients aware of the purpose of the

A total of 110 participants role-played the research with the e-mail message’s subject line:

Nurses situation in 22 groups. I conducted three ‘Using Game Theory to predict the outcomes of

sessions. In the ﬁrst session, 10 students with conﬂicts’. Moreover, in the ﬁrst paragraph I

work experience who were enrolled in courses wrote ‘‘I am engaged on a research project

on dispute resolution role-played in two groups. which investigates the accuracy of different

In the second session, 90 students recruited with methods for predicting the outcomes of con-

an offer of $NZ25 cash role-played in 18 ﬂicts’’.

groups. In the third session, 10 participants I attached MS-Word ﬁles containing the

selected for experience relevant to the situation material on the situations to the messages. I

(union negotiators, managers, management varied the order of the ﬁve situation ﬁles across

negotiators, and professional mediators) role-

played in two groups.

I asked participants in the ﬁrst and second http: //www.hut.ﬁ/Units/SAL/isdg/issue23.txt.

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331

the sample to reduce the risk that respondents reminders one week apart to those who had not

who predicted decisions for only some of the already responded.

situations would do so for similar subsets. In

addition, I hoped that varying the order of the

situations in the e-mail messages would counter 4 . Findings

any effect that might have arisen had the experts

4 .1.

Unaided-judgement replication and

changed their processes of deriving predictions extension

in some systematic way as they worked through

the situations.

4 .1.1.

Participation

The material on each of the situations in- Participants provided one forecast each for

cluded descriptions of all of the roles, a descrip- Artists’ Protest (eight forecasts), Distribution

tion of the situation, and a questionnaire. In the Channel (ﬁve), Panalba Drug Policy (four),

questionnaires, I asked respondents to select the Zenith Investment (21), and Nurses Dispute

most likely from a list of possible decisions. I (22).

also asked them how long they took to derive Students from the two classes who undertook

the prediction and how many years’ experience the task in their own time reported taking

they had working with game theory. I repeated between 2 and 120 minutes to derive their

the question on experience for each situation in individual predictions. The mean time was 30

case the recipient of the e-mail message asked minutes and the median was 25 minutes. I gave

other people to respond to one or more of the the participants making predictions for Zenith

problems. In anticipation of some respondents and Nurses an hour to do so. Zenith judges took

being willing to participate in the research but an average of 15 minutes to derive a prediction.

unwilling to make a prediction for particular I did not ask the Nurses judges to record the

situations, I included a question with each time they actually spent on the task.

situation asking those who did not make predic- One Nurses Dispute respondent claimed to

tions to give a reason for not doing so. I also know more about the situation than was con-

asked them to identify any situations they tained in the material provided but gave no

thought they recognised. I asked respondents to indication of knowing anything about the actual

complete and return their questionnaires elec- agreement, and so I included the response in the

tronically or to print them out and return the analysis. None of the other respondents admit-

completed forms by fax or post. ted to recognising any of the situations they had

After 13 and 14 days, I sent individualised been given.

e-mail reminders to the 413 addressees in the Fewer than 10 percent of the participants I

original sample who had not responded. The asked to undertake the task in their own time

reminder included a copy of the original letter returned completed questionnaires. I received

and the attached ﬁles in the same order as in the responses for four of the ﬁve situations pro-

original e-mail message. vided—none was received for the 55% Pay

I sent individual replies to all those who Plan.

responded, irrespective of the nature of their

responses.

A year after the ﬁrst appeal to game theorists,

4 .1.2.

Predictions

I sent material on the Nurses situation to those The unaided-judgement predictions new to

who had provided predictions in response to the this research were (in an unweighted average

ﬁrst appeal. I followed this with up to two across the situations) correct for 31 percent of

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predictions. This rate is little different from hted average for the role-plays of the four

chance (27 percent) for the ﬁve situations for situations reported by Armstrong (2001a),

which I received responses. New predictions for which was 60 percent. Chance for these four

situations that were also reported by Armstrong situations is, on average, somewhat lower at 26

(2001a) (Artists, Distribution, and Panalba) were percent, however. The forecasting accuracy of

correct for 19 percent of predictions. This the eight groups with ‘natural leaders’ and

ﬁnding is consistent with Armstrong (2001a), ‘quantitative analysis experts’ allocated to roles

who reported 13 percent correct for the same was similar to that of the other nine groups—

situations. there were ﬁve correct forecasts from each

treatment.

For the Nurses Dispute situation, role-play

4 .2.

Role-playing extension agreements matched the actual agreement be-

4 .2.1.

Participation tween management and union in 18 of the 22

For the Zenith Investment situation, roughly groups (82 percent). This is better than chance.

half the students in the two classes that were not Although neither of the groups in the two-group

offered payment stayed to take part in role- (third) session reached an agreement in the

plays. After their brieﬁng, the organisational course of their role-plays, both groups chose the

behaviour class had little more than 30 minutes actual decision when asked what decision they

remaining for role-playing and completing ques- thought would have occurred had their role-

tionnaires. The conﬂict-of-laws class had a full playing continued.

hour available, and all took this long, while the

groups of paid recruits took as long as an hour

4 .3.

Game theorists

for their role-playing alone. Some of the role-

players given only half an hour complained of

4 .3.1.

Participation

not having enough time, as did some who were I received responses of various types from

given an hour. Nevertheless, all 17 groups made 269 addresses (48 percent of the initial sample).

decisions. One of the paid recruits recognised Of these, 78 were invalid-address messages, 18

the situation but did not recall the decision that were automatic rejection messages (typically on

was made or discuss her knowledge with her leave messages), and six were statements that

group. the addressee was not a game-theory expert.

For the Nurses Dispute situation, participants The balance of 167 responses consisted of

in the ﬁrst and second sessions typically took messages from 95 game theorists who stated

between 45 minutes and one hour for their that they did not wish to participate, 51 game

role-playing. The two groups of role-players in theorists who promised to respond or who

the third session took one-and-a-half hours for wanted more information but did not respond

their role-playing and neither group had come to after receiving it, and 21 game theorists who

an agreement when I asked them to stop. each responded with a completed questionnaire

for at least one situation.

4 .2.2.

Predictions

For the Zenith Investment situation, the role-

4 .3.1.1.

Reasons for refusing to participate

play decisions matched the actual decision for Of the 95 people who responded but refused

10 of the 17 groups (59 percent). This was to participate, 90 provided reasons (Appendix

better than chance, which is 33 percent for B). Most (72) stated they were too busy with

Zenith. The ﬁnding was similar to the unweig- other commitments to spend time helping with

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333

this research. Eight maintained that their game-

4 .3.1.4.

Probabilistic forecasts

theory speciality was not applicable to the While the questionnaires instructed respon-

problems provided. Ten wrote either that it was dents to ‘check one—✓’ or something similar,

not appropriate to apply game theory to the the e-mail message stated ‘‘you may assign

problems given (six) or that there was insufﬁ- probabilities to possible outcomes, rather than

cient information for them to derive predictions picking a single outcome, if you consider this to

(four). be appropriate’’. One game theorist who re-

sponded for a single situation (Artists) provided

probabilities rather than choosing a single deci-

4 .3.1.2.

Selective prediction sion. He assigned a zero probability to the

Nine of the 21 experts who returned com- actual decision.

pleted questionnaires did not provide predic-

tions for all of the original ﬁve situations. I

4 .3.2.

Predictions

obtained 85 usable predictions in all from the 21 Overall, the game-theory experts’ predictions

experts out of a potential total of 105 predic- matched the actual decision for 37 percent of

tions. It seems reasonable to assume that they their predictions. This rate is better than chance

made predictions for the situations they consid- (an unweighted average of 27 percent over the

ered themselves most capable of predicting six situations) and better than unaided judge-

accurately. One respondent recognised the Ar- ment (28 percent).

tists’ Protest situation and I excluded his re-

sponse from the analysis.

5 . Discussion

4 .3.1.3.

Further participation

When I appealed again to the 21 game

5 .1.

Relative predictive accuracy

theorists who had responded to the original

appeal, 14 provided usable predictions for the In Table 1, I combined the results from this

Nurses Dispute situation and one sent an unus- research (chieﬂy game-theory experts’ predic-

able response. tions for six situations, and unaided judgement

Table 1

Accuracy of unaided judgement, game theorist, and role-play predictions. Percent correct predictions (number of predictions)

Chance Unaided Game Role-play

judgement theorist

Artists’ Protest 17 5 (39) 6 (18) 29 (14)

Distribution Channel 33 5 (42) 31 (13) 75 (12)

55% Pay Plan 25 27 (15) 29 (17) 60 (10)

Zenith Investment 33 29 (21) 22 (18) 59 (17)

Panalba Drug Policy 20 34 (68) 84 (19) 76 (83)

Nurses Dispute 33 68 (22) 50 (14) 82 (22)

Totals (unweighted ) 27 28 (207) 37 (99) 64 (158)

Results reported in Armstrong (2001a), except Zenith Investment, Nurses Dispute, and 17 predictions for other situations

from this research: Artists (one correct/n58); Distribution (1/5); Panalba (1/4).

Results reported in Armstrong (2001a) except Zenith Investment and Nurses Dispute.

Percentage ﬁgures in this row are unweighted averages of the percentage of correct responses reported for each situation.

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and role-play predictions for Zenith Investment strong & Hutcherson, 1989). Unlike the role-

and Nurses Dispute) with the unaided judge- players, the game theorists were not restricted in

ment and role-play predictions for four situa- the time they had to derive their forecasts nor in

tions from Armstrong (2001a). the resources they could exploit, although my

Role-play forecasts were more accurate than written instructions asked them to avoid confer-

predictions by game theorists, which were, in ring with others.

turn, more accurate than unaided judgement Motivation may have inﬂuenced forecasting

predictions. These ﬁndings are consistent with accuracy. Game theorists had the most reason to

Schelling’s (1961) observation that role play be motivated. I told them that I planned to use

provides more realistic representations of con- their forecasts in a comparison of forecasting

ﬂict than do theoretical models, and with Arm- methods, and that I would publish their names

strong’s (2001b) suggestion that forecasting in the resulting paper (Appendix A). The par-

accuracy for conﬂicts is positively related to the ticipants playing roles or using unaided judge-

realism of the forecasting method. The differ- ment, on the other hand, knew they would

ence in accuracy between prediction by game remain anonymous.

theorists and prediction using unaided judge- The superiority of game theorists’ forecasts

ment is substantial and is statistically signiﬁcant over forecasts based on unaided judgement may

at 95 percent (

54.3, degrees of freedom 1, be due to the game theorists’ greater familiarity

P50.04). The error was about 12 percent with conﬂicts. This possibility does not affect

lower across the six situations, thus supporting the conclusion that those who wish to predict

the claim that game theory can improve the the decisions made in conﬂicts would do better

forecasting of conﬂict situations. The difference to ask game theorists than to rely on judges with

in accuracy between prediction by game theor- no expertise. The relative accuracy of people

ists and prediction by role-play decisions is who are experts on conﬂicts and who use

large and statistically signiﬁcant (

524.6, unaided judgement to predict decisions made in

degrees of freedom 1, P,0.001). I applied the conﬂicts is a matter for further research.

statistical tests to the Table 1 data in the form of

two separate two-by-two contingency tables

5 .2.

Factors that might have disadvantaged

(two accuracy levels by two methods). game theorists

’

predictions

Some participants provided more than one

forecast. These participants may have been able Perhaps the game theorists were not really

to apply what they learned to subsequent fore- experts. I put respondents through a number of

casts. If this were the case, the game-theory ‘ﬁlters’ before asking them for their forecasts—

experts were most likely to beneﬁt because they ﬁlters that would reasonably be expected to

provided an average of ﬁve forecasts each and exclude those who were not experts. These

were free to revise their forecasts. Role-players, ﬁlters were: (a) the composition of the original

on the other hand, generally played a role in a sample (mostly Game Theory Society mem-

single situation, although some were asked for bers); (b) the initial e-mail message, in which I

their opinion on the decision that was made in stated ‘‘I am writing to you because you are a

an unrelated situation (Armstrong, 1987; Arm- game theory expert’’; and (c) the potential

respondents’ own assessments of their ability to

successfully apply a game-theory approach to

Unless otherwise stated, all

tests are of two-by-two the problems.

contingency tables with continuity correction (Siegel &

Castellan, 1988, Eq. (6.3), p. 116). I asked respondents about their experience

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335

with game theory. Their median experience was ‘‘spending more time would have not changed

six and a quarter years. Most of the respondents my answers, except if I had communicated with

had enough experience to merit game-theory- others’’. In response to follow-up e-mail mes-

expert status. More experience as a game theor- sages, nine of the 12 respondents stated that

ist did not, however, lead to more accurate they did not believe that more time would have

predictions (Table 2). changed their predictions. Little or no gain in

Perhaps the respondents did not spend accuracy was associated with spending more

enough time on the tasks to demonstrate the time on the forecasting task (

50.08, degrees

strength of a game-theory approach to predict- of freedom 2, P50.96) (Table 3). Further,

ing decisions made by parties in conﬂict. The only for the Panalba situation was there a

respondents were presumably busy people, and I monotonic increase in accuracy across the three

did not offer to pay them for their work. time categories.

Nevertheless, the respondents responded vol- Perhaps the respondents were unable to dem-

untarily and were, it seems likely, motivated to onstrate the strength of a game-theory approach

perform well having taken on the tasks. If, after to prediction because they lacked adequate

starting on the task, potential respondents began information about the situations. Four experts

to doubt their ability to predict the decisions in cited inadequate information about the situa-

the time they had available, they could have tions as a reason for not participating in the

abandoned the task without risking embarrass- research. Yet these four comprised only four

ment. It seems plausible that the withdrawal of percent of those who provided a reason for not

respondents who doubted their own abilities participating.

would tend to bias responses towards those I designed the research to compare the fore-

from the more capable. The link between conﬁ- casting accuracy of the methods by providing

dence and accuracy is, however, tenuous (Arkes, the same material to the practitioners of all three

2001). methods. I assumed that the material provided

The game theorists reported spending nearly was a fair representation of the type of in-

40 minutes, on average, deriving their predic- formation that could realistically be assembled

tions for each situation, including 10 minutes about an unfolding conﬂict. Perhaps the experts

reading the material. This ﬁgure is in keeping could have produced better forecasts had they

with the up to 45 minutes that Armstrong been provided with different information. Per-

(1977) allowed role-players in his research. One haps, given equivalent resources, game-theory

game theorist respondent, who stated apologeti- experts would have collected different types of

cally that he had spent ‘only’ about 20 minutes Table 3

on each of the situations, went on to write that Game theorists’ predictions: the effect of time spent on

accuracy

Table 2 Time spent on forecast n% Correct

Game theorists’ predictions: the effect of experience on Up to 25 minutes (36) 36

accuracy 26 to 40 minutes (43) 37

Experience n% Correct More than 40 minutes (20) 40

Fewer than 5 years (31) 39 Number of predictions.

Between 5 and 10 years (35) 40

More than 10 years (33) 33

Test of independence in a two-by-nclassiﬁcation (Fisher,

Number of predictions. 1973, p. 87).

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information about the situations and would, as a predictions, ‘‘standard neoclassical models do

consequence, have produced better forecasts. well without the intellectual baggage of game

Further research may address these issues. theory’’ (p. 240).

Perhaps the game theorists would have been While Gintis declared that predicting the

more accurate in forecasting different types of decisions made in individual real conﬂicts is

conﬂicts. The game-theory experts provided the ‘‘not what game theory is good at’’, other

most accurate forecasts for the Panalba Drug researchers seem to think that game theory can

Policy conﬂict, while their accuracy for the be used to provide useful forecasts for some

other conﬂicts was poor. In sympathy with types of conﬂict for which ‘rational actor’

Shubik (1975), Gintis (2000) offered a possible assumptions would seem rather brave. The use

explanation for this dichotomy in the game of methods based on game theory to forecast

theorists’ forecasting accuracy: the rational civil conﬂicts has been mentioned (Brams &

actor model from neoclassical economics. He Togman, 2000; Organski, 2000), as has their

wrote ‘‘.. . when faced with market condi- use for predicting incumbents’ responses to a

tions—anonymous, nonstrategic interactions— new competitor (Gruca et al., 1992), for com-

people behave like self-interested, outcome-ori- mon-pool resource problems (Keser & Gardner,

ented actors . . . In other settings, especially in 1999), and for conﬂicts involving concentrated

the area of strategic interactions, people behave competition, mutual familiarity, and repeated

quite differently’’ (p. 240). The Panalba conﬂict interaction (Ghemawat & McGahan, 1998).

is an ‘anonymous, nonstrategic interaction’, and My research provides some evidence of game

the decision makers in the conﬂict did behave as theorists’ forecasting accuracy for some of these

‘self-interested, outcome-oriented actors’. The types of conﬂicts. While none of the six con-

ﬁve other conﬂicts, on the other hand, involved ﬂicts I used involved sectarian violence, it could

face-to-face strategic interaction and ongoing be argued that the Artists’ Protest was a civil

relationships. This distinction suggests that conﬂict. The game-theory experts, on average,

managers would be sensible to seek forecasts of did no better than chance in forecasting the

conﬂicts from game theorists only if those in decision made in this conﬂict. Any pay dispute

conﬂict are likely to behave as ‘rational actors’. (for example, the 55% Pay Plan and the Nurses

Bennett’s (1995) ‘missing dimensions’ (men- Dispute) meets the conditions listed by

tioned earlier) may also help managers to dis- Ghemawat and McGahan, if they are taken

tinguish between conﬂicts for which game literally, as does the Zenith Investment conﬂict.

theory can provide accurate forecasts and those The game-theory experts averaged 34 percent

for which this is unlikely. For example, these correct for these three conﬂicts. This compares

dimensions are weak or absent in the Panalba with 41 percent for unaided judgement, 67

conﬂict.Whether managers would be able to use percent for role-playing, and 30 percent for

Bennett’s ‘missing dimensions’ or Gintis’s chance. None of the six conﬂicts involved a new

‘market conditions’ to make the distinction competitor or a common pool resource. Game

between conﬂicts that are tractable under game theorists’ predictions may be more accurate for

theory is a matter for further research. Ironical- conﬂicts of these types than they were for the

ly, even if such a distinction could be made in

advance, Gintis (2000) suggested that game

theory may not add value, because, in situations Personal communication from Herbert Gintis, 15 June

in which it is likely to help make accurate 2001.

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337

six I used in this research. Further research may strate their knowledge of game theory or to

answer this question. describe its application in their (typically brief)

responses—after all, I had told them that I

selected them because of their game-theory

5 .3.

Did the game theorists use game theory

expertise. For these reasons, I examine relative

For each of their predictions, I asked game rather than absolute ratings in the following

theorists, ‘‘Broadly, what approach did you use analysis.

to derive your prediction?’’. The answers to this The ratings provide modest support for the

question were diverse. Five university students, contention that a more structured application of

enrolled in an Honours-level economics course game theory would have increased the accuracy

that included game theory, rated the responses. of game theorists’ forecasts. Of the 33 predic-

Each of these student raters had completed tions that were associated with a mean knowl-

between two and ﬁve courses with game-theory edge rating of 3.0 or higher, 48 percent were

content. I told the raters nothing about the correct. This compares with 33 percent correct

research participants or the situations. Speciﬁ- for the 64 predictions associated with lower

cally, they did not know that the participants ratings. The difference between the proportions

were game-theory experts. They each rated up is not signiﬁcant, however (

51.7, degrees of

to 97 of 98 responses both for evidence of freedom 1, P50.20). The proportion correct

game-theory knowledge (implicit or explicit) among the 19 predictions with application rat-

and for the extent to which the responses ings of 3.0 or higher was 42 percent compared

implied that knowledge of game theory had to 37 percent among the 78 with lower ratings.

been applied to making a prediction. The raters Again, the difference is not statistically signiﬁ-

derived their ratings independently using a zero cant (

50.02, degrees of freedom 1, P5

(‘none’) to 10 (‘high’) scale. The rating ques- 0.89). There was no meaningful relationship

tionnaire, which includes the game theorists’ between the situations and the mean ratings for

responses, is available on the Internet at the situations (F(5,92) 50.9; P50.47 for both

www.kestencgreen.com. ratings).

I calculated Cronbach’s Alpha scores to test Ratings aside, what is important for the

interrater reliability for the students’ knowledge purpose of this research is that the respondents

and application ratings. Alphas were 0.69 (n5were aware that I was assessing game-theory

73) and 0.42 (n555), respectively. I averaged forecasts and that I expected them to apply their

the ﬁve raters’ ratings to provide two mean game-theory knowledge and skills to the fore-

ratings for each game-theorist response. The casting problems (Appendix A). The responses

overall average rating for knowledge was 2.6 of the six who considered it inappropriate to

and for application 2.2. Some game-theorist apply game theory to the problems lends further

responses were rated highly: the maximums of support to my contention that respondents knew

the ﬁve-rater means were 8.0 and 8.2, respec- what was expected of them. If some respondents

tively. Ratings were mostly quite low, however. failed to apply game-theory knowledge to the

While I asked the raters to assess the re- problems (and some responses suggested this),

sponses without giving them contextual infor- this implies that these respondents considered

mation, the game theorists knew the context that knowledge not useful for, or applicable to,

when they wrote their responses. It is reasonable these problems, or that the cost of applying it

to assume that they felt no obligation to demon- was too high.

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5 .4.

Alternative assessment of forecast In the case of the Artists’ Protest, the most

accuracy popular choice by game theorists was option C

(42 percent). Option C was a compromise

Despite the relative inaccuracy of game- between the status quo and the actual decision,

theory experts’ forecasts, a manager who ob- which was the government conceding to the

tained several forecasts for a single conﬂict artists’ demands. This forecast could have

might still have been led to expect the decision alerted the parties to the likelihood that the

that actually occurred, or at least have been actual decision would favour the artists. Score:

warned that it might occur. This might be the 0.5.

case if the actual decision made in the conﬂict In the case of the Distribution Channel con-

was the most popular choice of the game ﬂict, most game theorists (54 percent) forecast a

theorists or if the most popular choice of the short-term trial for the scheme, but the actual

game theorists was similar to the actual deci- decision was to make a long-term commitment.

sion. Nevertheless, it seems reasonable to as- The forecast would not have been likely to lead

sume that such a set of forecasts would be less the proposer of the scheme to expect a long-

likely to lead a manager to expect the actual term commitment. Score: 20.5.

decision than a set in which an absolute majori- In the case of the 55% Pay Plan, the great

ty were accurate. A manager is most likely to majority of game theorists (88 percent) forecast

commit to a course of action when provided a strike by the players, but their forecasts were

with an unambiguous forecast and to reap the evenly divided between the three strike op-

beneﬁts of this commitment if the forecast is tions—short, medium, and long. Such a forecast

accurate. I propose the following accuracy-score would have led the parties to expect a strike but

regime to allow comparisons between the fore- not necessarily a long strike, which is what

casting methods based on the likelihood that a occurred. Score: 0.

set of forecasts would lead managers to conﬁ- In the case of the Zenith Investment conﬂict,

dently expect the actual decision: the majority of game theorists (56 percent)

forecast that no new steel production plants

would be purchased. The Board chose to pur-

Accuracy of forecast set Accuracy

score

chase two new plants. The absolute majority

game-theorist forecast was completely wrong in

An absolute majority choose the actual decision 2

Actual decision is the most popular choice ( #50 percent) 1

this instance. Score: 22.

Either popular choice or absolute majority choice is similar

As Table 4 shows, the total accuracy score

to actual decision 0.5

for the game-theorist forecasts for the six con-

No clear choice 0

Either popular choice or absolute majority choice is dissimilar

ﬂicts is 2.0 out of a possible total of 12. Making

to actual decision 20.5

a similar calculation for the role-play forecasts

Popular choice is substantially different from the actual deci- 21

is straightforward: for all conﬂicts except the

sion

Artists’ Protest, an absolute majority of fore-

Absolute majority choice is substantially different

from the actual decision 22

casts was correct and therefore the role-play

forecasts score two points for each of these. The

For both the Panalba and Nurses conﬂicts, the popular role-play decision Artists’ Protest was

game theorists’ absolute majority choice was option B, which was similar to the actual

the actual decision (Table 1). The accuracy

score is therefore 2 for both Panalba and n517, as one game theorist provided a probabilistic

Nurses. forecast.

Green /International Journal of Forecasting

18 (2002) 321

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339

Table 4 less than an hour to produce, in practice it

Accuracy of forecasts: an alternative assessment. Accuracy would be difﬁcult to recruit students or experts

Scores: 22to12for less than one hour at a time for a commer-

Predictions by Role-playing cial forecasting task. On this basis, the marginal

game theorists cost of a game-theory forecast is six times more

Artists’ Protest 0.5 0.5 than the cost of an unaided-judgement forecast

Distribution Channel 20.5 2 by a student. The number of role-players needed

55% Pay Plan 0 2 for a role-play forecast will vary depending on

Zenith Investment 222

the situation and the judgement of the fore-

Panalba Drug Policy 2 2 caster. A two-party conﬂict can be role-played

Nurses Dispute 2 2 using two students to represent each party; four

Totals (unweighted) 2.0 10.5 students in total. The cost of a role-play forecast

in this case would be two-thirds the cost of a

decision. In fact, 13 of the 14 role-play deci- game-theory forecast. The role-plays of the six

sions either matched the actual decision (option situations used in this research involved an

A) or were similar to it (options B and C). This average of six role-players per simulation. With

implies a score of 0.5 for Artists’ Protest and a six role-players per simulation, the marginal

total accuracy score for role-playing of 10.5. cost is similar to that of the game-theory

forecasts: the equivalent of one hour of expert

time. Thus 10 independent role-play or game-

5 .5.

Cost of forecasts theory forecasts for a single conﬂict may cost

Managers deciding between forecasting meth- the equivalent of 50 h of expert time. Ten

ods are often inﬂuenced by the relative costs of unaided-judgement forecasts by domain experts

methods as well as their accuracy. When seek- would have a similar cost, but the cost of using

ing to forecast decisions in a conﬂict, asking a students as judges would be nearer the equiva-

neutral observer to describe the situation is lent of 42 h of expert time.

likely to be a sensible starting point. A week

(40 h) may be enough time for an experienced

person to assemble a concise and accurate 6 . Conclusions

description of a situation. The actual time,

however, will depend upon the importance and The primary purpose of my research was to

complexity of the problem and on any deadlines assess the relative worth of unaided judgement,

inherent in the situation. The time taken to game theory, and role-playing for predicting

compile a situation description is the major part decisions made in real-world conﬂicts involving

of the ﬁxed cost of forecasting. few players and high stakes. To do this, I

The cost per forecast varies across the meth- combined new ﬁndings on the accuracy of

ods. Students were used for unaided judgement game-theory experts’ predictions, role-play pre-

and role-play forecasts in this research. Stu- dictions, and predictions based on unaided

dents’ time is likely to cost, at most, one-sixth judgement with role-play and unaided-judge-

as much as that of experts. Although most of the ment ﬁndings summarised in Armstrong

forecasts reported in this paper took somewhat (2001a). I then compared the accuracy of the

forecasts from the different methods. The results

support the view implied by Schelling (1961)

Personal communication from J. Scott Armstrong, 11

January 2002. and stated directly by Armstrong (2001a) that

340 K

Green /International Journal of Forecasting

18 (2002) 321

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344

role-playing will provide more accurate fore- nology (FRST contract: Vic 903). The contract

casts than other methods for forecasting deci- is administered by Raymond Harbridge and Pat

sions in conﬂicts because it provides more Walsh.

realistic representations.

The predictions of game-theory experts did

offer an improvement over the traditional ap- A ppendix A. E-mail messages to game

proach: their forecasts were more accurate, on theorists

average, than unaided judgement. Role-play

predictions were better than chance and unaided

judgement for all situations, and better than

First e-mail message

game-theory experts’ predictions for all but one Subject: Using game theory to predict the

situation. Game theorists’ forecasts, on the other outcomes of conﬂicts.

hand, varied more widely in their accuracy than

did role-play forecasts. Their forecasts were less Dear Dr X

accurate than the forecasts of people using I am writing to you because you are an expert

unaided judgement for two of six situations and in game theory. I am engaged on a research

were no better than chance for four of the six project which investigates the accuracy of dif-

situations. Game theorists are experts on con- ferent methods for predicting the outcomes of

ﬂicts, whereas the other research participants conﬂicts. What I would like you to do is to read

were not. Further research would be necessary each of the 5 attached descriptions of real

to determine whether game-theory expertise conﬂict situations and to predict the outcomes

confers any advantage over the unaided judge- of each conﬂict. The ﬁles contain both descrip-

ment of experts on conﬂicts who are not famil- tions of the situations and of the individuals or

iar with game theory. The cost of the forecast- parties involved.

ing methods is similar. Each ﬁle includes a short questionnaire.

Space is provided for your prediction, and for a

short description of the method you used to

derive your prediction. You may assign prob-

A cknowledgements abilities to possible outcomes, rather than pick-

I am grateful for the cooperation of the game ing a single outcome, if you consider this to be

theory experts (listed in Appendix C) who appropriate. If you are unable to provide a

contributed their judgements and their helpful prediction for a situation, please state why in the

comments on this research. Without their help, space provided in the questionnaire. The sixth

my research would not have been possible. I ﬁle contains a questionnaire only. Please com-

also thank J. Scott Armstrong, Urs Daellenbach, plete it when you have ﬁnished with the 5

John Davies, six anonymous reviewers who situations.

provided helpful advice and criticism, David I would appreciate it if you do not discuss the

Harte and Shirley Pledger who provided advice situations with other people, as I’d rather each

on statistical methods, and Mary Haight who participant provided an independent response.

made many useful editorial suggestions. This Although I intend to acknowledge all of the

paper is, in part, based on research funded by people, such as yourself, who help me with this

the Public Good Science Fund administered by research, my report will not associate any

the Foundation for Research Science and Tech- prediction with any individual.

Green /International Journal of Forecasting

18 (2002) 321

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344

341

Your prompt response is very important to descriptive’’, and therefore not an appropriate

the successful completion of my project. Please technique for ‘‘predict[ing] actual behaviour’’.

help me to prove the sceptics wrong about the This respondent asserted that ‘‘game theory is a

level of cooperation I get! mediocre predictor of actual behaviour’’, and

that ‘‘I believe that the long-term ambition of

Best regards, Kesten Green (most) game theory to ﬁnd optimal solutions to

School of Business and Public Management, any decision problem is fundamentally mis-

Victoria University of Wellington, PO Box conceived’’. Further, ‘‘ﬁnding a situation that

5530, Wellington, New Zealand. Tel.: 164-4- can be well modelled by a game of chicken tells

499-2040; fax: 164-4-499-2080. e-mail: you a number of interesting things ...it does

kesten.green@vux.ac.nz not give you a prediction of what the outcome

will be with real players . . . nor . . . how ideal-

Second e-mail message ised rational players should react’’.

Subject: Help with research on game theory. A third game theorist stated that he ‘‘did not

see why [predicting decisions] is a game theory

Dear Dr Y question’’. In particular, the respondent objected

About three weeks ago I sent you an email that the request to predict the decision made in

asking for your help with research I am con- the one situation he had looked at, presumably

ducting on game theory. I really need more the Panalba Drug Policy, ‘‘seemed. . . a ques-

responses, and I wonder whether you might tion about my opinions on company ethics’’.

consider responding. In a fourth expert’s opinion ‘‘the role of game

The material I originally sent is repeated theory in practical situations is not so much in

below. If you are unable to read the attach- computing the equilibrium, but rather a useful

ments, please let me know and I will send you help in thinking the situation through’’. His

.txt ﬁles instead. brief outline of what this would involve had a

similar ﬂavour to the approach recommended by

Regards Nalebuff and Brandenburger (1996). The re-

Kesten Green spondent went on to write that ‘‘Game theory

etc. is a tool in understanding complex

situations . . . which forces you to think of the

strategic aspects of the situation, but people do

A ppendix B. Game theorist responses not always behave strategically, and one has to

Not appropriate to apply game theory to the take that into account also’’. In sum: ‘‘The best

problems provided

(

six responses

)

game theory . . . can offer is to explain some

One stated that the aim of what he does is phenomena, but I don’t see how it can predict

‘‘not to predict what shall happen here. This the outcomes of real life situations’’. This

depends on the psychology of the players, response was echoed by a ﬁfth game theorist: ‘‘I

which is not the object of mathematics. It is to am afraid our theoretical knowledge is not

give one of [the players] the quantitative tools straightforwardly applicable to real-life prob-

that will let him act optimally according to his lems’’. A sixth wrote that she was ‘‘a game

perceived interests’’. ‘theorist’ and not a strategic planner’’, and

Another was of the opinion that ‘‘most/many further that she failed to ‘‘see any ‘game theory’

theorists see GT as prescriptive rather than in [the] project’’.

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Bereket Kebede Andre Rossi de Yelena Yanovskaya

Insufﬁcient information to derive a prediction

Oliveira

(

four responses

)

Somdeb Lahiri Ronald Peeters Shmuel Zamir

One stated: ‘‘You have not provided sufﬁ-

Massimiliano Landi Alex Possajennikov Jose Zarzuelo

Andy McLennan Eleuterio Prado Anthony Ziegelmeyer

cient information about preferences and institu-

tions for me to identify a game-theoretic model

Peter Bennett Vito Fragnelli Harold Houba

Pierre Bernhard Herbert Gintis Marc Kilgour

and make a prediction from that’’. The respon-

Steven Brams

dent was concerned that in order to ‘‘predict

what ‘really’ might happen (rather than what a

theoretical model would predict), I would need R eferences

to know a lot more about the context in which

the problems arose’’. Arkes, H. R. (2001). Overconﬁdence in judgmental fore-

casting. In Armstrong, J. S. (Ed.), Principles of forecast-

ing

a handbook for researchers and practitioners.

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Jan 1982
J OPER RES SOC

Nash's Theory of Cooperative Games as a Predictor of the Outcomes of Buyer-Seller Negotiations: An Experiment in Media Purchasing

Article

Nov 1983

The authors report an experimental investigation of the ability of Nash's theory of cooperative games to predict the outcomes of buyer-seller negotiations, using the purchase of media time as an example. Previous theoretical work has identified conflict, power, and influence as central elements of buyer-seller negotiations. Nash's theory provides a framework for understanding conflict resolution. A role-playing experiment tests Nash's theory, while controlling for the potential effects of situational power and negotiator influence. Results support Nash's theory.

History-independent prediction in evolutionary game theory

Article

Aug 1998
RATION SOC

William H. Sandholm

Three classes of models from evolutionary game theory are studied, which make history-independent predictions: stochastic stability, stochastic stability with local interaction and cheap talk. It is argued that of the three, only local interaction models yield credible history-independent predictions.

Statistical Methods for Research Workers

Article

Sep 1972

The prime object of this book is to put into the hands of research workers, and especially of biologists, the means of applying statistical tests accurately to numerical data accumulated in their own laboratories or available in the literature.

Modelling Decisions in International Relations: Game Theory and Beyond

Article

Apr 1995

Peter G. Bennett

Renewed interest in Game Theory and its extensions comes at a time when richer models than ever before are on offer. This paper starts with a non-technical introduction to game models, arguing that they can best be used to provide an understanding of decisions, rather than prescriptions. It then examines some common criticisms of the approach, in particular those surrounding the concept of "rational choice." Extensions to the basic model are then illustrated: for example, approaches stressing differences in perception or introducing "internal" and "external" games. Rather than being restricted to rational choice in a narrow sense, these approaches offer a richer picture of decision-making as "reflective choice." More radical possible developments include replacing the "game" metaphor by that of "drama," and combining formal analysis with empirical theory to create "knowledge-based" modelling methods.

Cooperation Through Threats: The Northern Ireland Case

Article

Mar 1998
PS-POLIT SCI POLIT

On February 9, 1996, after a seventeen-month cease-fire, the Irish Republican Army (IRA) set off a bomb in East London. Less than a week later, the London police found and destroyed a bomb that the IRA had left in a telephone booth in the West End. A few days later, another IRA bomb went off on a doubledecker bus. The British government, under the leadership of John Major, asserted that it would have no official contact with Sinn Féin, the political arm of the IRA, until the paramilitary activities stopped. The government also deployed 500 additional troops in Northern Ireland. In October 1996, the IRA detonated two bombs at the British Army's headquarters in Lisburn, bringing the violent conflict back to Northern Ireland for the first time since the cease-fire. On May 1, 1997, Tony Blair was elected Great Britain's prime minister. His election brought a renewed sense of optimism and good will to the conflict in Northern Ireland. Responding to Blair's overtures, including his warning that “the settlement train is leaving, with or without them” (Hoge 1997a, A7), the IRA announced on July 19, 1997, that they had “ordered the unequivocal restoration of the cease-fire” (Clarity 1997c, 1). Soon thereafter, Sinn Féin was invited to participate in the peace talks, which reconvened on September 15, 1997.

Forecasting decisions in conflict situations: A comparison of game theory, role playing and unaided judgment (conflictforecasting.com)

Abstract

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