An Experimental Study of Conventions and Norms
ABSTRACT Although it is now recognized that norms play an important role in many economic decisions, compliance with conventions is generally considered to be driven by rational self-interest only. We report instead experimental data showing that (1) ‘external’ norms of fairness sustain social conventions that have emerged from repeated play of simple coordination games; and (2) with repetition such conventions acquire an ‘intrinsic’ normative power of their own. This creates pressure towards conformity, and patterns of regular behaviour that are far stronger and more stable than those that would be generated by mere self-interest and rationality.
- SourceAvailable from: Luigi Mittone[Show abstract] [Hide abstract]
ABSTRACT: According to a tradition that goes back to David Hume, social conventions have a natural tendency to turn into norms. Normativity increases compliance and stabilizes individual behaviour in spite of changes in incentives. In this paper we report experimental data that confirm this insight and encourage mildly optimistic conclusions regarding human sociality: habits provide extra glue that keeps individuals together, and prevents them from succumbing to anti-social temptation even when punishment is unlikely.Journal of Economic Psychology. 01/2010;
Article: The normativity of Lewis Conventions[Show abstract] [Hide abstract]
ABSTRACT: David Lewis famously proposed to model conventions as solutions to coordination games, where equilibrium selection is driven by precedence, or the history of play. A characteristic feature of Lewis Conventions is that they are intrinsically non-normative. Some philosophers have argued that for this reason they miss a crucial aspect of our folk notion of convention. It is doubtful however that Lewis was merely analysing a folk concept. I illustrate how his theory can (and must) be assessed using empirical data, and argue that it does indeed miss an important aspect of real-world conventions.Synthese 10/2013; · 0.70 Impact Factor
Article: Esistono le convenzioni di Lewis?[Show abstract] [Hide abstract]
ABSTRACT: Una convenzione, secondo David Lewis, è la soluzione di un gioco di coordinazione il cui equilibrio è determinato dalla storia del gioco. Un elemento importante delle Convenzioni di Lewis è il loro carattere intrinsecamente non-normativo. Per questo motivo alcuni filosofi hanno sostenuto che esse ignorano un aspetto cruciale del concetto ordinario di convenzione. È improbabile, tuttavia, che Lewis volesse analizzare una nozione del senso comune. In questo articolo intendo mostrare che la sua teoria può (e deve) essere valutata utilizzando dati empirici, e che effettivamente essa non cattura un importante elemento delle convenzioni. Che le Convenzioni di Lewis esistano o meno dipende dalla misura nella quale esse riescono ad approssimare il reale comportamento degli individui, e dalla presenza di teorie alternative che spiegano meglio i fenomeni empirici. Sei seduto di fronte allo schermo di un computer. Utilizzando il mouse, puoi scegliere fra due bottoni di colore (da sinistra a destra) Rosso e Blu. Nel frattempo altri due giocatori stanno affrontando la stessa decisione. Se sceglierete lo stesso colore, guadagnerete * La ricerca riportata in questo articolo è stata finanziata dal progetto RES-000-22-1591 dell'Economic and Social Research Council e dal Computable and Experimental Economics Laboratory dell'Università di Trento. Versioni precedenti sono state presentate alle Università di Amsterdam, Cambridge, e Trento, a un seminario della British Society for Philosophy of Science, e alle conferenze annuali della SIFA e della STOREP. Ringrazio i partecipanti a questi eventi e in particolare Elena Casetta, Mario Gilli, Philippe Mongin, Ivan Moscati e Achille Varzi per avermi aiutato a migliorare il testo dell'articolo. Gli errori rimanenti sono, come al solito, tutti a mio carico.01/2009;
An Experimental Study of Conventions and Norms*
(Department of Sociology and Philosophy, University of Exeter and CEEL, University of Trento)
(Department of Economics and CEEL, University of Trento)
Although it is now recognized that norms can play an important role in economic
decisions, behaviour in coordination games is generally considered to be driven by
rational self-interest. We report instead experimental data showing that (1)
‘external’ norms of fairness sustain social conventions that have emerged from
repeated play of simple coordination games; and (2) with repetition such
conventions acquire an ‘intrinsic’ normative power of their own. This creates
pressure towards conformity, and patterns of regular behaviour that are far stronger
and more stable than those that would be afforded by mere self-interest and
Economists and psychologists generally agree that norms of equality and reciprocity play
an important role in many socio-economic contexts, for instance by helping subjects to
achieve Pareto-superior outcomes or fairer allocations of goods than is predicted by
standard rational choice theory (Fehr and Fischbacher 2002). In many other areas,
however, individualistic instrumental rationality or some close variant thereof is
considered to be prevalent. Consider conventions, for example: following David Lewis
(1969), it has become customary to model conventions as solutions to repeated
coordination games with multiple equilibria. Thomas Schelling (1960) convincingly
argued that the problem of equilibrium selection in several coordination games is solved
by the existence of ‘salient’ solutions or ‘focal points’. In the case of conventions,
salience is provided by precedence: the strategy followed by the majority of players up
until now becomes a focal point that we can all use to successfully coordinate from now
on. When this is the case, an equilibrium becomes established as the convention in a
given population and the coordination problem is solved (Lewis 1969).
* Research for this paper was financed by the ESRC grant RES-000-22-1591 and the Computable and
Experimental Economics Laboratory of the University of Trento. Early drafts were presented at the
universities of Amsterdam and Cambridge, a seminar of the British Society for Philosophy of Science, and
a conference of the Italian Society for the History of Economic Thought. We are grateful to members of
these audiences, Ivan Moscati, Mario Gilli, Matteo Ploner, Marco Failla and two anonymous ESRC
reviewers for their constructive feedback. Tim Miller and Marco Tecilla provided invaluable help in
designing the software and running the experiments. The usual disclaimers apply.
Repeated coordination games constitute the vast majority of social interactions that we
face in everyday life. The Lewis-Schelling approach therefore seems to vindicate the
analytical power of the rational choice approach: individual self-interest cum a theory of
induction and focal points may go a long way towards explaining this ubiquitous feature
of social life. This reading, however, is not entirely correct. Lewis (1969) explicitly
highlighted the importance of social norms in sustaining conventions by proscribing
deviations from established behavioural regularities. Other theorists, like Margaret
Gilbert (1989), have gone even further and questioned the very distinction between
norms and conventions. They have argued that conventions are intrinsically normative
phenomena, and that a standard rational-choice analysis based on individual rationality
and narrow self-interest is unable to capture their essential features.
In order to adjudicate between these different views, we report a series of experiments
that investigate for the first time the relation between norms and conventions. The
evidence, as we shall see, largely confirms Lewis’ insights concerning the importance of
norms in sustaining coordination, but also points in the direction of an intrinsic normative
element in conventions.
2. Conventions and norms
The idea that norms and conventions play an important role in the functioning of markets
(and society as a whole) is as old as economics itself, and in various guises this insight
seems to have re-emerged periodically in the history of economic theory. In the
contemporary debate it sits at the core of the so-called ‘social capital’ theory and the
‘new’ institutional economics, but also drives the work of many experimental and
behavioural economists. But what, exactly, are conventions and norms? The standard
approach in contemporary rational choice theory has been to model these important
institutions as solutions to coordination and social-dilemma problems, respectively (e.g.
Ullmann-Margalit 1977, Schotter 1981, Sugden 1986). In this section we briefly review
the standard analysis of conventions and norms, and lay out some hypotheses for
A simple coordination problem is represented in Table 1. As usual, the first number in
each cell represents the payoff of the row player, the second one of the column player.
Each Nash equilibrium (Left-Left and Right-Right) is a possible solution of this game. A
perfectly rational calculator cannot do better in this game than by flipping a coin and
choosing a strategy at random. Schelling (1960) however noticed that in many real-life
situations human beings seem to be much more successful at coordinating than purely
rational calculators. He argued that seemingly irrelevant features of the environment,
such as the position of the objects of choice or the way they are labelled, can function as
‘cues’ that help us to converge on a common solution. A strategy that is made ‘salient’ by
such features is called a ‘focal point’, and in the course of repeated interaction is likely to
become a point of attraction for the individuals in a given population (see also Sugden
Right 0, 0 1, 1
Table 1: A simple coordination game
Schelling’s hypothesis was mainly based on anecdotal examples and rudimentary
experiments, but recent more systematic studies have confirmed its validity (Mehta et al.
1994). The first important application of focal points theory dates back to 1969, with the
publication of an important book on Convention by the philosopher David Lewis. Lewis,
who was mainly interested in the conventional nature of language, introduced the idea
that a given strategy may be made salient simply by precedence, or the fact that it was
played by a sufficiently large number of people in previous rounds of the game. When
this happens, we shall say that a convention has emerged in a given population.
In one important respect Lewis’ theory sits firmly in the rational choice tradition. Our
main motivation to follow a convention is strictly selfish: we drive on the left because we
want to avoid accidents; we say ‘cat’ rather than ‘tac’ because we want to be understood
by our interlocutors; we wear black at funerals because we want to communicate our
grief. Lewis’ approach thus leads naturally to a neat separation between social norms and
conventions. A social norm always comes with an intrinsic ‘ought’, and is usually backed
up by a system of sanctions. The sanctions are meant to change the payoffs of the game:
for example, to change a mixed-motives game (like a prisoner’s dilemma) into a
coordination game (Figure 1).1
Left 2, 2 0, 3
Right 3, 0 1, 1
Figure 1: Transforming a Prisoner’s Dilemma game into a Coordination game.
The transformation of (3, 0) and (0, 3) into (0, 0) may take place in different ways. If the
payoffs represent utility values, as it is usually the case in game theory, the reduction of
the ‘free-riding’ payoffs (Right-Left and Left-Right) may be due to a feeling of guilt or
shame: the other player had trusted my cooperation and I have let her down, for example.
But in many societies there are external mechanisms that can reduce our payoffs both at
the psychological and the material level: a verbal reproach and ostracism from business
are examples of how normative pressure helps in attaining socially superior equilibria in
the game of life.
Roughly, then, a social norm exists when every individual (1) prefers to conform to the
norm provided that (almost) everybody else does the same; (2) it is common knowledge
1, 1 0, 0
Right 0, 0 1, 1
2, 2 0, 0
1 For a seminal game-theoretic account of social norms along these lines, see Ullmann-Margalit (1977).
that one ought to conform; and (3) this normative expectation is backed up by sanctions.2
Lewis somewhat misleadingly claims that ‘conventions are a species of norms’. But it is
important to realize that Lewis-Conventions are not norms in the sense specified by
conditions (1)-(3). Rather, conventions are supported by extrinsic normative
considerations: one follows a convention because (a) it is individually rational to do so,
and (b) deviance from conventions is usually sanctioned by other independent social
norms. 3 Although a convention does not per se imply a commitment to conformity, in
other words, normative pressure to abide is exercised by a set of ‘external’ social norms
that tend to reduce deviance from an established regularity.
Suppose, for example, that two players have been playing repeatedly the coordination
game in Table 1. With repetition, Left-Left has emerged as a convention, and both
players expect the other to continue to comply with it. Imagine that the situation were to
change in such a way that one of the players now has an incentive to deviate from the
established convention.4 By doing that she would damage the other player, an action that
is sanctioned by various norms in our society. The social consequences of violating these
norms may be serious enough to compensate for the gain, and thus deter the player from
deviating. In this sense, ‘external’ norms play an important role in sustaining social
Norms therefore play an important role in Lewis’ theory, by enhancing the resilience of
social conventions in the presence of potential deviants. Given that repeated coordination
is the prevalent form of social interaction, this analysis attributes much more importance
to the existence of social norms than is commonly recognised by rational choice theorists.
The importance of norms in sustaining coordination however has never been empirically
investigated so far. The first question we will try to answer in our experiments is:
(Q1) Do ‘external’ social norms help sustaining conventions in the way envisaged
Some authors however have argued that Lewis’ theory underestimates the normativity of
convention. Margaret Gilbert (1969) has argued forcefully that social conventions and
related concepts (customs, tradition, rules) must be analysed in terms of a more primitive
notion of collective agency. In particular, conventions result from a “quasi-agreement”
among members of a group to pursue a certain line of action that will attain a specific
collective goal. Such quasi-agreements need not be formulated explicitly, but are often
2 Although Lewis does not analyze social norms in depth, ‘Ludovician’ theories of norms can be found e.g.
in Pettit (1990) and Bicchieri (2006).
3 See in particular Lewis (1969, p. 98). A detailed discussion of this aspect of Lewis’ theory can be found in
Gilbert (1989, especially p. 354).
4 Notice that the new incentives need not be material: in some cases a mere change in one’s preference
structure creates the temptation to defect from a convention. A suicidal person, for example, may be
tempted to kill herself by driving on the wrong side of the road. The pressure of moral norms however will
induce her to find an alternative way of committing suicide that does not cause harm to others. It is also
possible that an individual may simply fail to conform to a convention by mistake. In such cases
(‘trembling hands’), the ‘external’ norms and associated sanctions will make sure that occasional deviants
pay more attention in the future.
inferred from the mere observation that people do pursue a certain line of action that
serves the goals of the relevant group. Collective intentions result in a joint commitment
that cannot be unilaterally breached by an individual group member. This is why,
according to Gilbert, we usually feel the need to excuse and justify a breach of
convention in front of other group members. 5
Gilbert’s theory blurs the very distinction between conventions and norms that is at the
core of the standard rational choice approach. Conventions are not only supported by
external norms that sanction deviance for independent reasons, but are themselves norms.
Failure to conform thus violates a normative principle that stands at the core of
conventional behaviour. This view is not implausible, in the light of what we know about
human tendencies towards conformity. Classic experiments in social psychology show
that deviance from conventional behaviour is psychologically costly, to such an extent
that people prefer to give false perceptual reports to going against a group’s majority
(Sherif 1936, Asch 1951, 1956). Thus in the context of coordination problems the mere
formation of a majority and the collective repetition of a task may create a normative
pressure on members of a group to conform to a behavioural regularity, even when they
have an individualistic incentive to deviate.
Evolutionary game theorists and cultural anthropologists also assign an important role to
conformity in their models. Consider the phenomenon of altruistic punishment, for
example: there is extensive evidence that many experimental subjects are willing to
punish deviations from established norms of fairness by destroying the earnings of free
riders, even if this act is costly for the punishing individuals (Fehr and Gachter 2000,
2002; Gintis 2000). This form of ‘strong reciprocity’ can be used to stabilize pro-social
norms of fairness and cooperation. Such norms, in turn, may confer a fitness advantage to
a group of cooperators, and take over an entire population via processes of group
selection. Group selection works only under relatively strict conditions, though: it is
crucial in particular that variation among groups is maintained in spite of migration.
Henrich and Boyd (2001) have shown that a moderate amount of conformist learning can
sustain the effect of group selection, by making sure that homogeneity of behaviour is not
threatened by new immigrants.
5 There are by now several theories of collective agency in the scientific and philosophical literature. The
labels vary from discipline to discipline, from ‘collective intentionality’ in philosophy (Searle 1990,
Bratman 1993, Tuomela 1995), to ‘group identity’ in social psychology (Tajfel and Turner 1989), and
‘team reasoning’ in economics (Sugden 2000, Bacharach 2006). Here we focus on Gilbert’s version
because of its contractualist aspect and its accent on the intrinsic normativity of convention. The unifying
trait of theories of all theories of collective agency is the claim that both individuals and groups can be
legitimately taken as units of agency. These theories however are still individualistic in the sense that
collective preferences and beliefs are supposed to be ‘stored’ in the minds of the individual members of the
group. The idea is that each individual carries different preference/beliefs profiles that are put at use in
different circumstances. Depending on the context, one can act either on the basis of her own
individualistic preferences and beliefs, or on the basis of collective preferences and beliefs qua group
Although conformity may hold the key to understanding the evolution of human
cooperation,6 this hypothesis has never been directly tested so far. The second question
we try to answer in our experiments then is the following:
(Q2) Do conventions tend to evolve into social norms? Or, in other words, does
repeated convergence on a coordination solution create an intrinsic normative
pressure to conform that may override individual incentives to deviate?
We investigated these two questions using the standard methods of experimental
economics. In the next two sections we describe the design of each experimental study
and the main results obtained.
3. Study 1
Our first study was run at the University of Exeter (UK) and was designed to answer the
first question (Q1) outlined above. Subjects were recruited using email lists from the
population of graduate and undergraduate students. Volunteers registered for one of the
experimental sessions and, as they arrived at the lab, were seated randomly at one of 18
computer terminals separated by partitions. After signing a consent form, they were asked
to read the experimental instructions illustrating the main features of the task. The task
varied depending on the experimental condition. Each subject participated in one
condition only, and all comparisons took place across subjects. Our first study consisted
of a comparison between two conditions, labelled ‘Baseline’ and ‘Norms’ respectively. In
both conditions subjects played in groups of three players, with random selection of
group membership, anonymity, and without the possibility of communication. They
received a show-up fee, and on top of that received whatever they earned in the
experimental task. Individual payoffs were calculated in terms of ‘experimental tokens’
which were converted into real money at the exchange rate of 3 p per token (or £1 = 33
The main task in the Baseline condition was a repeated coordination game with two
options labelled ‘Red’ and ‘Blue’. At each round each subject chose an option by clicking
a button on the screen and then receives feedback regarding the choices of the other two
group members. If all members chose the same option, they earned 10 tokens each;
otherwise, they received nothing. The payoffs of this game are represented in Table 2.
For simplicity, we use a 2 x 2 matrix were the row player is ‘You’, and the column player
6 See also Richerson and Boyd (2005: 203-206), Gintis et al. (2003).
7 Average earnings ranged between £9 and £11, depending on the condition, for less than one hour of
Blue 0, 0
Table 2: Coordination task
After a few rounds the overwhelming majority of the groups converged on a common
strategy, and continued to coordinate for the rest of the game.8 Subjects were told in the
instructions that the game would last for ten rounds. They were also told that the payoffs
may change during the course of the game, and that not all players may be informed in
advance when this happens (although they will all be fully briefed after one of these
‘special rounds’ has taken place). No specific details were provided regarding the payoff
structure of these special rounds.
As a matter of fact, in the tenth and last round all groups faced a special task with the
payoff structure represented in Table 3. Within each group, only one player (that we will
call the ‘potential deviant’) was made aware in advance of this change in payoff
structure. In Table 3 the potential deviant is the row player, and again for simplicity the
other two group members are represented as the column player. The potential deviant
expects that the other group members will continue to coordinate on the established
convention, lacking any reason to do otherwise. She knows, however, that the other
players will be told at the end of this round that the payoff structure had changed, and that
she was aware of this change.
Red 200, 200 300, 0
Blue 300, 0 200, 200
Table 3: Incentive to deviate in the 10th round
Notice that the game in Table 3 is not a coordination game. Since the other two players
are going to continue to play the convention (‘Red-Red’, say), the potential deviant faces
a straightforward choice between maximizing the earnings of the group vs. her own
income. With this design we can detect the effect of norms on individual behaviour by
observing whether the experimental subjects are willing to forego individual earnings in
order to conform to the regularity that has evolved during the previous rounds of group
play. The normativity of convention is the (normative) expectation that you ought to bear
the possible costs of non-deviance, because I am planning my choices based on the
(plain) expectation that you will conform. It is thus manifested in the decision to ‘leave
some money on the table’ and privilege the group’s earnings with respect to one’s own
8 For curiosity: the dominant convention emerging from these early stages was Red (played 66% of the
time). A possible explanation suggested by recent neuroeconomic studies is that when faced with a choice
between two indifferent options, we tend to choose the one upon which our sight fixated first, and it’s twice
as likely that we fixate on the left-hand side than on the right-hand side object. (Rangel 2007).
10, 10 0, 0
As a matter of fact, in our experiment the majority of potential deviants decided to
conform to the established convention and thus maximize the group’s earnings.9 The
mere fact that some subjects are willing to conform to the convention and forego
individual gains however merely tells us that there is some norm at work, but does not
indicate exactly what kind of norm we are observing. In the previous section we have
distinguished among two possible source of normativity: (i) ‘external’ norms of fairness,
altruism, or cooperation that prescribe to play cooperatively in a situation such as the one
represented in Table 3; and (ii) the ‘intrinsic’ normativity of convention, that is, the
pressure to conform to collective group behaviour that has emerged from repeated team
play over the first nine rounds of the game. Our two experimental studies are designed to
separate these effects as observed in the Baseline condition.
3.2. Norms condition
In the ‘Norms’ condition we tried to manipulate the ‘external’ norms that may help to
sustain convention-abiding behaviour. Intuitively, three ‘external’ considerations may
prompt subjects to seek the maximization of group rather than individual earnings:
altruistic considerations prescribing to increase the earnings of the other players, fairness
considerations prescribing to avoid inequitable outcomes, and/or utilitarian
considerations prescribing to maximize the sum of the individual payoffs of group
members. In either case, such considerations encourage a conformist behaviour with
respect to the established convention: altruist, egalitarian, and utilitarian players should
all choose Red-Red or Blue-Blue in round ten of the Baseline condition. To observe the
force of these ‘external’ norms at work, we decided to compare behaviour in the Baseline
condition with behaviour in a ‘Norms’ condition when one of these factors (fairness,
intended as inequality aversion) has been controlled for by design.
The Norms condition is in all respects identical to the Baseline, except that the payoffs in
the 10th (‘special’) round are those represented in Table 4. The main difference between
this payoff structure and the one in Table 3 is that following the convention now carries a
higher cost for the potential deviant. The choice therefore is not between collective and
individual gain, but between others’ gain and my gain. Since ‘my loss is your gain’ (and
vice-versa), the decision to stick to the convention can be supported only by a norm of
altruism or a utilitarian norm, but not by a norm of fairness (or inequality-aversion) as in
Table 3. If external norms of fairness do play a role in sustaining conventions, we expect
to observe lower compliance with the convention in the Norms than in the Baseline
Red 0, 200 300, 0
Blue 300, 0 0, 200
Table 4: Payoffs 10th round of the Norms condition
9 We provide a more detailed data-analysis in 3.3 below.
Experiment 1 was designed to answer the question:
(Q1) Do egalitarian, altruistic, and utilitarian norms provide ‘external’ support to
If the answer to this question were positive, we would expect to observe more deviance in
Norms than in the Baseline condition. If, in contrast, the answer was negative, there
should be no significant difference both in deviance and in punishment rates across the
The data were collected at the Financial and Experimental Economics Laboratory of the
University of Exeter (FEELE) between October 2006 and February 2007. In total 273
subjects participated in the experiment (141 in the Baseline and 132 in the Norms
condition). In each condition we obtained one observation regarding potential deviants
per each group of three players. A first process of data-analysis was run to identify and
discard those subjects who had misunderstood the nature of the experimental task, based
on their answers in the pre-experimental questionnaire and/or failure to coordinate during
the first nine rounds of the coordination game. This left us with 72 observations regarding
potential deviants (38 in Baseline, 34 in Norms).
The deviation data for each condition are summarized in Table 5. Overall, out of 72
potential deviants, 33 (45.8%) decided to maximize their own monetary gains instead of
coordinating with the other members of their group. Although 54.2% may seem a
relatively high proportion of players displaying ‘socially-oriented’ or ‘norm-abiding’
behaviour, these figures are consistent with highly replicated results in experimental
Public Goods, Dictator, and similar games.10 Conformity to the convention however is
distributed unevenly across the two conditions. While in the Baseline only 28.9% of
subjects deviate, when egalitarian concerns are removed by design (in the Norms
condition) the rate of deviance surges to 64.7% of the sample.
Condition N Deviants %
Baseline 38 11 28.9
Norms 34 22 64.7
Total 72 33 45.8
Table 5: Experiment 1: deviation rates
Comparison between the Baseline and the Norms condition therefore indicates that (1)
‘external’ social norms of fairness and cooperation do sustain conventions, and can be
manipulated experimentally by changing the relative payoffs of the game. Statistical
analysis confirms that the null hypothesis (H0: ‘there is no effect from manipulating
payoffs in the Norms condition’) is rejected using an ordinary chi-square test (χ2 = 9.242,
10 Charness and Rabin (2002) provide data from a wide range of settings.
df = 1, p = .002) as well as more demanding non-parametric tests (Mann-Whitney Z = -
3.019, p = .003; Kolmogorov-Smirnov Z = 1.515, p = .020).
4. Study 2
Our second study was designed to test whether conventions impose an intrinsic
normative obligation, independently of the influence of external norms. To discriminate
between external norms and the intrinsic normativity of conventions, we compared
behaviour in the Baseline condition with behaviour in a structurally similar one-shot
game, where subjects face a similar payoff structure to the one of Table 3, but without
being exposed to a history of successful coordination in the previous rounds of the game.
In the ‘One-shot’ condition subjects again play in groups of three, anonymously and
without communication. The payoff structure is transparent to all players this time, and
the game is played in two stages as follows: in the first stage, two players must choose
simultaneously between two options (Red and Blue); if they choose the same option, the
game proceeds to stage two; if in contrast they fail to coordinate, the game ends and all
players earn zero tokens. In the second stage of the game, the third player (the potential
deviant) faces a choice between: (a) playing the same colour chosen by the other players
in the previous round, or (b) playing a different colour. The payoff structure is
represented in Figure 2, as seen from the viewpoint of the potential deviant (or ‘Self’
300, 0 200, 200 300, 0 200, 200
Figure 2: The One-shot condition
Although the One-shot condition and the final round of the Baseline condition are not
strictly speaking isomorphic from a game-theoretic point of view, the choice faced by the
potential deviant becomes identical if the potential deviants in the Baseline condition
expect the other players to play the established convention in the 10th round of the game
(as confirmed by the behavioural data). In either condition, then, the potential deviant
must take the choices of the other players as given, and faces a straightforward dilemma
between an individualistic and a cooperative choice. The relevant difference, for our
purposes, lies in the fact that in the Baseline the potential deviant may be influenced by
precedence – a history of repeated convergence on a common strategy – whereas in the
One-shot condition (which is similar to a Dictator game) this element has been removed
by design. If individualistic behaviour is more common in the One-shot than in the
Baseline condition, then, we would obtain direct evidence that repeated group play
generates an independent, intrinsic normative pressure on individuals to conform to the
group’s conventions. This normativity, combined with external norms of altruism and
fairness, should increase the resilience of conventions to changes in individual incentives.
For reasons to be explained shortly, we ran this study twice: at the University of Exeter
during the winter of 2006-07 and at the Computable and Experimental Economics
laboratory of the University of Trento in June 2008. We report for completeness the
Exeter data first, and explain why we felt that a replication with a slightly modified
design was required.
Overall 207 observations were collected in the Exeter run of the One-shot condition;
since several players failed to coordinate in the first stage of the game, the proportion of
useful data-points concerning potential deviants was lower here than in the other
conditions (46 out of a total maximum of 69). The relevant data can be found on the left-
hand side of Table 6. Recall that the study aimed at answering the following question:
(Q2) Are conventions endowed with intrinsic normative power that significantly
reduces deviance rates, independently of these external norms?
If the answer were positive, we would expect to observe more deviance in One-shot than
in the Baseline condition. If the answer were negative, in contrast, there should be no
significant difference both in deviance and in punishment rates across the two conditions.
Comparison between the One-shot and Baseline conditions suggests that mere repetition
of a collective task may enhance the conformity to a convention. Statistical testing
however provides a weak result, with the null hypothesis (H0: ‘there is no effect from
repeated group play’) coming close only to rejection at the 10% level in a chi-square (χ2
= 2.463, df = 1, p = .116) and in a Mann-Whitney test (Z = -1.560, p = .119), but failing
by a good margin in a Kolmogorov-Smirnov non-parametric test (Z = .762, p = .607).
Condition N Deviants % N Deviants %
Baseline 38 11 28.9 29 9
One-shot 46 21 45.6 28 19
Total 84 32 38.0 57 28
Table 6: Study 2: deviation rates
The One-shot condition as implemented in the Exeter experiments however was flawed
in one important respect. In the first stage of the game the first two members of the group
have the option of ending the game immediately by failing to coordinate, which would
result in an equal payoff of zero tokens to each player. By deciding not to derail the game
(that is, by successfully coordinating on either Red or Blue), the first two players thus
send an implicit message to the potential deviant that may be read as an offer of
cooperation. There is extensive evidence from the experimental literature that ‘nice’
moves of this kind can trigger norms of reciprocation.11 It is possible, then, that some
third players would respond ‘nice’ with ‘nice’ and choose to conform to the first two
Intentions in contrast cannot play a similar role in the Baseline. Here the first two players
cannot see the opportunity of ending the game by failing to coordinate. On the contrary,
they stick to the convention because they think that this is the best course of action for all
members of the group. Their success in coordinating, therefore, cannot be read by the
potential deviant as a ‘nice’ intentional move to be reciprocated by conforming. It can be
argued then that our original design failed to control for one important motivation. This
convinced us to run a new, improved experiment where intentions and reciprocity have
been properly shielded by design. In this replication we simply eliminated the
opportunity for the first two players to end the game after the first stage: instead of
making their choice, a computer programme assigned a colour to both of them before
proceeding to the second stage of the game. As in the Baseline condition, the third player
now could not read their moves as a ‘nice’ intentional offer but only as an accident of the
Our first task consisted in replicating the evidence obtained in the Baseline condition at
Exeter, so as to compare it with the newly designed One-shot condition. In order to make
comparison possible, we kept the design of the Baseline condition as well as the general
procedures as close as possible to those implemented in the British part of the
experiment. In total 171 subjects participated in two sessions (84 in the Baseline and 87
in the One-shot condition).
The deviation data for each condition are summarized on the right-hand side Table 6.
Notice, first of all, that the results of the Baseline condition replicate those obtained at
Exeter. Comparison between the One-shot and Baseline conditions in Trento suggests
that mere repetition of a collective task does enhance the conformity to a convention. The
null hypothesis (H0: ‘there is no effect from repeated group play’) is rejected in a two-
tailed chi-square test (χ2 = 6.33, df = 1, p = .0119), as well as in a Mann-Whitney (Z = -
2.649, p = .008) and in a Kolmogorov-Smirnov non-parametric test (Z = 1.336, p = .056).
These data confirm our insight that the original design was indeed flawed. While
qualitatively we observed in Trento the same surge in deviance rates in the One-shot
condition that we had observed in Exeter, the effect was much stronger once reciprocal
motives had been controlled for by design. On the basis of these data we feel confident to
11 See e.g. Charness and Rabin (2002), Falk et al. (2003), McCabe et al. (2003), Cox (2004).
conclude that repeated coordination play leads to the emergence of a convention that is
normatively binding for the members of the group.
Coordination games are a ubiquitous form of social interaction, and understanding their
functioning should be a priority in the foundations of social science. The evidence
presented in this paper confirms the hypothesis that (contrary to the received view) social
norms play an important role not only in the solution of mixed-motives games, but also in
sustaining conventional behaviour in coordination games. Lewis’ (1969) claim that
norms of fairness and altruism provide ‘external’ support to conventions is vindicated by
our experimental data. The data also suggest that conventions have a tendency to turn
into social norms, acquiring an intrinsic normative power that further reduces deviation
rates from an established behavioural regularity. This result goes well beyond the
expectations of those social scientists who have highlighted conformity as an important
element in the evolution of pro-social behaviour. Richerson and Boyd, for example, have
claimed that conformity is likely to play a role ‘only if individuals have difficulty
evaluating the costs and benefits of alternative cultural variants’ (2005: 206). If this were
true, we should expect pressure towards conformity to be rather weak in presence of
well-defined individual incentives. As we have seen, in contrast, the effect of conformity
is strong even with clearly stated payoffs and immediate rewards. The texture of norms
that keeps societies together is probably far stronger than traditionally recognized by
rational choice theorists, and the study of norms and their functioning is surely the next
important task in economics and social science more generally.
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