Article

Assessing Game Theory, Role Playing, and Unaided Judgment

Abstract and Figures

Green's study (Int. J. Forecasting (forthcoming)) on the accuracy of forecasting methods for conflicts does well against traditional scientific criteria. Moreover, it is useful, as it examines actual problems by comparing forecasting methods as they would be used in practice. Some biases exist in the design of the study and they favor game theory. As a result, the accuracy gain of game theory over unaided judgment may be illusory, and the advantage of role playing over game theory is likely to be greater than the 44% error reduction found by Green. The improved accuracy of role playing over game theory was consistent across situations. For those cases that simulated interactions among people with conflicting roles, game theory was no better than chance (28% correct), whereas role-playing was correct in 61% of the predictions.  2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.
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1
Is the Evidence on Forecasting Conflicts
Based on Proper Science?
J. Scott Armstrong
The Wharton School, University of Pennsylvania, Philadelphia, PA
November 13, 2001
Abstract
Green's (2002) study on the accuracy of forecasting methods for conflicts does
well against traditional scientific criteria. Moreover, it is useful, as it examines
actual problems by comparing forecasting methods as they would be used in
practice. Some biases exist in the design of the study and they favor game
theory. As a result, the accuracy gain of game theory over unaided judgment
may be illusory, and the advantage of role playing over game theory is likely
to be greater than the 44% error reduction found by Green. The improved
accuracy of role playing over game theory was consistent across situations.
In Armstrong (1997a), I reviewed Co-opetition by Nalebuff and Brandenburger (1996).
Their use of game theory to analyze real-world situations seemed compelling. I concluded that it
was unfortunate that the decision makers had not engaged the help of game theorists before they
made their decisions. I had some misgivings about the book, however. For example, was there
any evidence that game theory had led to better decisions or predictions in conflicts? So I
contacted the authors. Brandenburger responded that he was not aware of any studies of the
predictive validity of game theory and I was unable to find any such studies.
Many hundreds of academics have been working on game theory for half a century. Thus,
it seems strange that it is difficult to find evidence on its predictive validity. Imagine that
hundreds of medical researchers spent half a century developing drugs without testing whether
they worked as predicted. They would not be allowed to put their drugs on the market.
Green sent me an early draft of his paper in July 2000. I thought that it was an important
contribution. Here was (1) an important problem that (2) challenged existing beliefs, (3)
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contained surprising results, (4) used simple methods, (5) provided full disclosure, and (6)
explained it all clearly. In short, Green violated all rules in the “Author's Formula” (Armstrong
1982). That formula, based on a review of empirical research, was updated in Armstrong
(1997b). Given the violations, I concluded that reviewers would reject the paper. As a result,
with the permission of the Editor of the International Journal of Forecasting, Jan deGooijer, I
informed the author that his paper would be accepted, subject to reasonable responses to any
substantive reviewer concerns that might arise.
Before launching into my analysis, it is worth noting that Green was systematic about his
own evaluation of his study. He rated the study on the 32 principles for the evaluation of
forecasting methods from Armstrong (2001c). His study did well on 28 of the principles, poor on
three, with one being judged as not relevant. I have reviewed these ratings and am in agreement.
The rating are summarized at http://decision.co.nz/ratings.pdf.
I discuss whether 1) the problem is important, 2) the findings are important, and 3) the
study was done in a scientific manner. I then provide suggestions for further research.
Important Problem?
Green's problem can be stated in two parts: Is it useful to accurately forecast decisions by
parties involved in conflicts? If so, which method can best improve upon the way that people
currently forecast such decisions?
With respect to the first question, it seems that by better predicting the decisions by the
other party in a conflict, one can make better decisions. For example, in 1975, Britain refused to
sell the Falkland Islands to a group of Argentine investors backed by the Argentine government.
As a result, they had to fight a war, which was clearly a less profitable alternative for Britain as it
destroyed resources and people. The three Argentine generals involved did not anticipate
Britain's response once Argentine troops occupied the Falkland Islands. Thus, they lost a war and
their jobs.
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Predictions of decisions might also be of interest to parties outside the conflict. For
example, in the case involving the negotiations between the National Football League owners
and the Players Association, an insurance company offered strike insurance to the players. To do
so, they had to forecast the likelihood that the players would decide to strike.
With respect to the second question, Green examined some of the more important ways
that have been recommended for such situations. For example, game theory is often suggested as
a way to predict the behavior of rational decision makers, and we have ample evidence from
economics that predictions of rational responses are often accurate, even when surprising.
Consider for example the predictions of negative consequences by economists for programs to
provide economic assistance to single mothers who have young children; many people, including
the leading policy makers in some countries, were surprised that people responded to economic
incentives in that situation.
I conclude that the problem is important.
Important Findings?
Green's results show substantial differences in accuracy. On average, the best method,
role playing, had half the error rate of the worst method, unaided judgment, in predicting actual
decisions. Improvements were found in each of the six situations. These findings were obtained
from over 1,100 participants. Seldom in studies of forecasting does one encounter such large
improvements in accuracy. For example, combining, which is regarded as one of the more
important techniques in forecasting, reduces error by about 12% (Armstrong 2001b). I conclude
that the findings are important.
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Competent Science?
I examined aspects of the scientific method in Green's study. Partly these are standard
issues in scientific methods, and partly they are in response to issues raised by reviewers.
Design objective?
Green used the method of multiple hypotheses. I believe this to be one of the most
important procedures in striving for objectivity.
Green tried to avoid biases. Due to practical considerations this was not always possible,
as discussed below. As it turned out, the design favored game theory relative to unaided
judgment and role playing.
Literature review complete and objective?
Green used literature reviews published by others. He also used references in the papers
published in key papers. These procedures offer protection against the claim that he might have
been biased in his search. However, he also used the SSCI and Internet searches, so there is the
potential for bias in screening the papers. Finally, he sent e-mail messages to 474 game theorists
to determine whether relevant research might have been overlooked. Given that researchers often
become advocates of their approach, this later procedure was biased in favor of finding results
favorable to game theory versus the other methods.
Samples of participants large enough?
Some of the reviewers claimed that the study was flawed because the sample of
participants was too small. This criticism is unfounded because the participants based their
judgments about the behavior of others, not about their own decision in such a case. Such “expert
opinion surveys” need only five to 20 experts, depending on such things as the need for
precision, level of expertise, and variability of knowledge among the experts (Ashton 1986;
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Hogarth 1978; and Libby and Blashfield 1978). Green obtained forecasts from 21 game theory
experts.
Samples of participants representative?
Because the experts are assessing the behavior of others, there is no need to have
representative experts. Indeed, one would prefer to have the most capable, experienced, and
interested experts. Self selection can help in selecting such experts. (For example, studies of
survey research have shown that those who are more interested in a topic are more likely to
respond; Armstrong & Overton, 1977). All of the game theory experts were self-selected,
whereas, role-players and unaided judges were often captive participants in classes. Self-
selection would seem to favor game theory.
Most of the unaided judges had little expertise. Since they must draw in part upon their
knowledge of similar situations, they would seem to be at a disadvantage relative to the game
theorists.
Sample of situations large enough?
Green's study was based on six situations. Additional situations would improve the
confidence that one might have in the results. Still, using the Wilcoxon signed-ranks test
(one-tail), the probability of getting such results would be only .03 if there were no real
difference between the accuracies of game theory and role playing.
In Armstrong (2001a), I suggested that role playing was most appropriate when the
interactions in a conflict are examined. Because the Panabla did not involve interactions, I
recalculated the percentage of correct responses with it excluded. A striking picture emerges.
Chance, unaided judgment, and game theory produce virtually identical results with about 28%
correct predictions, compared with 61% for role playing.
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To assess the sensitivity of these results to the selection of the situations, I then excluded
each of the other situations. This allowed for a comparison of the average accuracy with each
combination of the remaining four situations. Again, the results were consistent, as shown in
Table 1. In addition, as noted in the last column, the error reductions of role playing over game
theory is similar across these analyses. The error reduction is calculated as 100 X (GT"s wrong
predictions minus RP's wrong decisions)/ GT's wrong predictions.
Table 1: Average Percentage of Correct Forecasts with Some Situations Excluded
Error reduction
Excluded situations Chance Unaided judgment Game theory Role playing RP vs. GT
Panalba 28 27 28 61 46
Also excluding:
Artists 31 32 33 69 54
Distribution 27 32 27 58 42
55% 29 27 27 61 47
Zenith 27 26 29 62 46
Nurses 27 17 22 56 43
Sample of situations representative?
One possibility is that the selection of situations are more likely to include "interesting"
cases, and that they might have been considered to be interesting because they were hard to
assess judgmentally. This would constitute a bias against unaided judgment, thus favoring game
theory and role playing. To assess this, I examined the extent of the error reductions of role
playing relative to unaided judgment versus the degree of difficulty for unaided judgment. The
results, shown in Table 2, show no evidence of bias with respect to easy versus difficult
situations. For example, the error reduction was 48% for the three easiest and 50% for the three
most difficult. This analysis does not rule out other sources of bias, however.
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Table 2: Were the situations biased against judgment?
Situations
Correct
by Judgment
Correct by
Role playing
% Error
Reduction
Artists' reprieve 5 29 25
Distribution plan 5 75 74
55% plan 27 60 45
Zenith 29 59 42
Panalba 34 76 64
Nurses 68 82 44
Instructions followed?
Green was studying a practical issue. Assume that you have a conflict situation. Does it
help to appeal to leading game theorists to make predictions by using game theory? In a real
situation, the extent to which game theorists are successful would depend not only on the value
of game theory, but on whether analysts can successfully match the situation to their knowledge
of game theory, and the extent to which game theory gives them a better understanding of the
situation. One would expect that those with more experience in game theory would be more
skillful at applying game theory to these situations. However, Green found that those with more
experience in game theory were no more accurate in their predictions. He also found that those
spending more time were not more likely to be correct.
The instructions for unaided judgment were easy to follow. However, the role playing
was done by people who had little prior experience with this approach. Most were students, so it
seems likely that some might not have taken the exercise seriously. As a result, game theory had
an advantage over role playing.
External incentives provided to the participants were minimal. Would the result have
changed had there been financial incentives? Remus, O’Connor and Griggs (1998) examined the
evidence on this issue. Based on ten studies, they conclude that there is little evidence that
financial incentives would improve accuracy for judgmental forecasting
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Intrinsic incentives would seem to favor the game theorists, as they were asked to use
game theory in making predictions. Presumably, they would want to see game theory do well,
whereas the other participants had no attachment to their method.
Biased administration?
The experiments were conducted by those who had a prior hypothesis. Might this have
produced an unintended bias that might lead the participants to act as the researchers expected?
This has been referred to as “demand effects.” Sigall, Aronson and van Hoose (1970), examined
the evidence and found little support for the theory that participants are cooperative with the
experimenters. Rather, their concern seems to be to present themselves in a favorable light,
which would suggest a bias in favor of game theorists.
As with any study, bias might occur for other reasons. Thus, it would be useful if the
studies could be replicated or extended by those who might believe that game theory is superior
to role playing.
Biases from variations in administration?
One reviewer claimed that the design was faulty because there were variations in the
administrative procedures. For example, different times were allowed for different
administrations. In my opinion, variations are useful when there is a potential for bias. Thus, for
example, researchers are typically advised to vary the order of the presentation of materials to
participants (as Green did). Variations also allow one to assess whether administrative
procedures have any effect. On the whole, I saw the variations as a benefit to Green's design.
Full disclosure?
Green reported on all of his procedures. Some of the details are provided on the Internet.
This includes information about the participants and explanations of how they made their
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predictions. For description of the reasoning used by the game theorists, see
decision.co.nz/approach.pdf
He was responsive to reviewers when they asked for additional explanation. As nearly as
I can judge, he has met the requirements for full disclosure.
Other criteria examined?
The use of a forecasting method also depends on the cost, acceptability, and other factors.
Green provides some details on costs and game theory was the most expensive approach. As for
acceptability, it seems reasonable to hypothesize that role playing, by showing a vivid and
detailed prediction of the decisions, would be compelling to decision makers. It would be useful
to make empirical comparisons on the acceptability of unaided judgment, game theory, and role
playing forecasts.
Green's study focused primarily on predictive validity. Game theory may have other uses
such as improving the search for alternative solutions although I expect that formal idea
generation procedures, such as brainstorming, will prove superior to game theory. Can game
theory substantially improve the way managers think about problems in comparison, say, to
someone instructed to calculate net present values for alternatives? In short, I have been unable
to find evidence that game theory has any practical value for managers.
Clearly written?
An important aspect of good research is that it be clearly written. Green's paper has a
Flesch-Kinkaid readability index equal to 12th grade. This is much more readable than typical
scientific papers.
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Further Research
While a single study is vastly superior to no studies, it cannot be expected to resolve all
of the issues. To date, the level of research effort devoted to game theory is thousands of times
that devoted to alternative procedures for analyzing conflicts. My primary recommendation is
that game theorists should adopt the method of multiple hypotheses such that it embraces
procedures other than game theory.
Does game theory add to an analyst's way of making predictions in real situations? As
noted above, the procedures were biased in favor of game theory. What if 474 non-game theorist
adults of similar background as the game theorists were contacted, and the same situations were
presented. Assume then that those most interested made unaided judgmental predictions. Would
their accuracy be equal to that provided by the game theorists? If so, one could conclude that the
superiority of the game theorists in Green's study was due to their experience rather than to their
knowledge of game theory.
Conflicts vary, so it would be useful to study the conditions under which each approach is
most effective. This would be aided by examining more situations, especially if substantially
different from those in Green's study. Note, for example, that game theory was better than role
playing for the one situation that did not have active interactions between two groups. Goodwin
(2002) discusses various types of situations. It would be useful to study real situations that have
been suggested by game theorists. To date, however, my appeals to game theorists to supply such
situations have gone unanswered.
Experts who have experience with conflict situations might be able to make good
forecasts at a lower cost than role playing. This seems especially likely if they identify analogous
situations in a structured manner. Research on analogies might help to determine whether it is
possible to identify relevant experts, how one should structure the forecasting task, and whether
analogies can lead to low-cost predictions that are as accurate as those by role playing.
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Green's study has focused on forecasting. One might extend the study to decision making.
For example, has game theory led to better decisions than those that could be obtained by other
methods, such as evaluating the net present value of alternative strategies? Can game theory
produce a better set of strategies than one might achieve by using brainstorming or other creative
techniques? To date, despite the enormous efforts that researchers have devoted to research on
game theory, I have been unable to find evidence that game theory will improve decision
making.
Conclusions
An examination of threats to validity supports Green's comparative study of forecasting
methods. The game theorists’ predictions were slightly more accurate than those from the use of
unaided judgment, though the advantage might have been due to biases in the design, such as the
lack of experience on the part of the participants using unaided judgment. Role playing was
substantially more accurate than game theory despite biases favoring game theory.
References
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(ed.): Principles of Forecasting: A Handbook for Researchers and Practitioners.
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Armstrong, J. S. (2001b), "Combining forecasts," in J. S. Armstrong (ed.): Principles of
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Armstrong, J. S. (2001c), "Evaluating methods," in J. S. Armstrong (ed.): Principles of
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Armstrong, J. S. (1997a), "Why can't a game be more like a business? A review of Co-opetition
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... Conquanto o conceito de cooperação num contexto de competição seja bastante claro e importante para a compreensão das relações entre os indivíduos (Axelrod, 1987(Axelrod, , 1988Axelrod & Dion, 1988;Axelrod & Hamilton, 1981) e também na teoria dos jogos (Armstrong, 2002;Brandenburger & Nalebuff, 1996;Rabin, 1993;Zhong, Zheng, Zheng, Xu, & Hui, 2006), na literatura de Administração, as relações de cooperação e competição concomitantes apenas relatam relacionamentos em um contexto meso (Schillo et al., 2000), ou seja: no nível das organizações. ...
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EBIs/ESOs substantially change the traditional production/service function because ESOs/EBIs can have different psychological effects(motivation or de-motivation), and can create intangible capital and different economic payoffs. Although Game Theory is flawed, it can be helpful in describing interactions in ESO/EBIs transactions. ESOs/EBIs involve two-stage games and there are no perfect Nash Equilibria for the two sub-games. The large number of actual and potential participants in these games significantly complicates resolution of equilibria and increases the dynamism of the games given that players are more sensitive to other peoples moves in such games. This article: a) analyzes how ESOs/EBIs affect traditional assumptions of production functions (in both the manufacturing and service sectors), b) analyzes ESOs/EBIs transactions using game theory concepts, c) illustrates some of the limitations of game theory.
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In this book, Brandenburger and Nalebuff use game theory to develop a set of guidelines that will "make it easier to explain the reasoning behind a proposed strategy." The games that they use as analogies do not involve sports with their zero-sum outcomes; instead, they consider a variety of games that allow for mutual benefit, as well as harm, for the players. They use the term co-opetition, which is consistent with their message that cooperation pays off in some situations, competition in others. They encourage readers to think about not only how to play the game, but also how to change the rules. Examination of these games leads them to make recommendations for managers, many of which are relevant to marketing managers. So, to the extent that a game is like a business, this book should be useful. My aims in reviewing the book are to ask: (1) Is it new? (2) Is it useful? and (3) Is it supported? The book has flaws, particularly in the area of supporting evidence, but it is an important book.
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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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Role-playing and unaided opinions were used to forecast the outcome of three negotiations. Consistent with prior research, role-playing yielded more accurate predictions. In two studies on marketing negotiations, the predictions based on role-playing were correct for 53% of the predictions while unaided opinions were correct for only 7% (p < 0.001).
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Valid predictions for the direction of nonresponse bias were obtained from subjective estimates and extrapolations in an analysis of mail survey data from published studies. For estimates of the magnitude of bias, the use of extrapolations led to substantial improvements over a strategy of not using extrapolations.
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I reviewed the published empirical evidence concerning journal peer review, which consisted of 68 papers, all but three published since 1975. Peer review improves quality, but its use to screen papers has met with limited success. Current procedures to assure quality and fairness seem to discourage scientific advancement, especially important innovations, because findings that conflict with current beliefs are often judged to have defects. Editors can use procedures to encourage the publication of papers with innovative findings such as invited papers, early-acceptance procedures, author nominations of reviewers, results-blind reviews, structured rating sheets, open peer review, and, in particular, electronic publication. Some journals are currently using these procedures. The basic principle behind the proposals is to change the decision from whether to publish a paper to how to publish it
Book
Principles of Forecasting: A Handbook for Researchers and Practitioners summarizes knowledge from experts and from empirical studies. It provides guidelines that can be applied in fields such as economics, sociology, and psychology. It applies to problems such as those in finance (How much is this company worth?), marketing (Will a new product be successful?), personnel (How can we identify the best job candidates?), and production (What level of inventories should be kept?). The book is edited by Professor J. Scott Armstrong of the Wharton School, University of Pennsylvania. Contributions were written by 40 leading experts in forecasting, and the 30 chapters cover all types of forecasting methods. There are judgmental methods such as Delphi, role-playing, and intentions studies. Quantitative methods include econometric methods, expert systems, and extrapolation. Some methods, such as conjoint analysis, analogies, and rule-based forecasting, integrate quantitative and judgmental procedures. In each area, the authors identify what is known in the form of `if-then principles', and they summarize evidence on these principles. The project, developed over a four-year period, represents the first book to summarize all that is known about forecasting and to present it so that it can be used by researchers and practitioners. To ensure that the principles are correct, the authors reviewed one another's papers. In addition, external reviews were provided by more than 120 experts, some of whom reviewed many of the papers. The book includes the first comprehensive forecasting dictionary.
This note examines the number of experts to be included in a prediction group where the criterion of predictive ability is the correlation between the uncertain event and the mean judgment of the group members. It is shown that groups containing between 8 and 12 members have predictive ability close to the “optimum” under a wide range of circumstances but provided (1) mean intercorrelation of experts' opinions is not low (<.3, approximately) and/or (2) mean expert validity does not exceed mean intercorrelation. Evidence indicates these exceptions will not be common in practice. The characteristics needed by an additional expert to increase the validity of an existing group are also derived.
In decision situations where relevant variables cannot be easily measured, mathematical aggregation of individual judgments may prove to be a useful decision aid. A wide variety of studies indicate that composite judgments formed by equal-weighting aggregation models outperform the average individual judge making up the composite. However, the use of these composite judgments in actual decision making situations has not been suggested because of inefficiencies caused by the need to include the judgments of a large number of individuals in the formation of the composite. If composites formed by pooling judgments of fewer decision makers produce similar incremental performance, these inefficiencies would be substantially reduced, making use of such a technique more practical. This study empirically tested the effects of group size upon the incremental accuracy of an equal-weighted composite judge in three different judgment tasks. The results indicate that on average the majority of the increment gained by aggregating large numbers of judges can be obtained by aggregating three judges.
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It has been suggested that cooperativeness on the part of Ss in supporting the hypotheses of Es, yields artifactual data in some social psychological experiments. An experiment was conducted to examine the nature of this cooperation. It was predicted that cooperativeness would not manifest itself when the Ss own ends would be better satisfied by not cooperating. 40 Ss were randomly assigned to 1 of 3 experimental conditions or a control condition. In the experimental conditions, Ss were told that they knew the E's specific hypothesis. In 2 of these conditions the S could confirm the E's hypothesis and also "look good." In the 3rd experimental condition these outcomes were mutually exclusive. Results indicate that Ss in the 3rd condition choose to look good, thereby disconfirming the E's "hypothesis." Results support the prediction. The control condition was later replicated and a condition in which Ss knew the broad nature, but not the specifics of the E's hypothesis, was added. Results again support the hypothesis that Ss try to look good. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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I present evidence to suggest that studying the use of game theory in prediction is a legitimate area of research and suggest ways in which game theory might be used to make or support predictions. Green’s study predominately assesses the accuracy of predictions by game theorists (who may have made informal use of game theory concepts) rather than predictions obtained from formal game theory models. I argue that the accuracy of predictions derived from such models is likely to be contingent on the characteristics of the conflict and provide a partial taxonomy of these characteristics, together with their hypothesised effects. I also argue that it would be worth investigating the potential use of game theory as an aid to obtaining probabilistic predictions.