On the origin of conventions: evidence from coordination games

On the Origin of Convention: Evidence From Coordination Games

John B. Van Huyck, Raymond C. Battalio, and Frederick W. Rankin

Revised June 1996

Abstract: We report the results of a coordination game experiment. The experiment carefully distinguishes between conventions based on labels and conventions based on populations. Our labels treatments investigate the abstraction assumptions that underlie the concept of a strategy, while our population treatments investigate the attraction of alternative mutually consistent ways to play under adaptive behavior. We observe conventions emerging in communities with one population and labels and with two populations and no labels, but the most effective treatment is two labeled populations. A final section investigates individual subject behavior. Specifically, we estimate logistic response learning models. Of the models considered, a version of exponential fictitious play fits our data best.

Key words: convention, labels, populations, coordination, dynamical systems, adaptive learning, exponential fictitious play, human behavior.

Introduction

Two related problems exist in the theory of equilibrium points. First, the mutual consistency requirement of an equilibrium assignment is not an implication of individual rationality, because individual rationality does not restrict the subjective beliefs a player may hold. Rather, individual rationality means internal consistency and internally consistent beliefs and actions of different players may not be mutually consistent. Second, there is often more than one mutually consistent strategy combination, which results in an indeterminant analysis. Consequently, understanding the origin of mutually consistent behavior is an essential complement to the theory of equilibrium points. [1]

It is possible to construct a deductive equilibrium selection theory by introducing abstraction assumptions that go beyond individual rationality and mutual consistency: assumptions like efficiency, symmetry, and security. Deductive selection principles select equilibrium points based on thinking about the description of the game. However, if the deductive approach is to provide an accurate theory of observable games, the selection principles of efficiency, symmetry, and security must formalize characteristics that are commonly known to be psychologically salient.

Van Huyck, Battalio, and Beil (1990; 1991) and Van Huyck, Cook, and Battalio (forthcoming) present evidence against the psychological salience of efficiency. [2] Van Huyck et al. (1995) present evidence against the psychological salience of symmetry in symmetric bargaining games. [3] In these experiments, security undermines the salience of either efficiency or symmetry. [4] These facts make us pessimistic about the usefulness of constructing purely deductive selection theories.

Repeated interaction may allow players to learn to coordinate on a mutual best response outcome. Following Lewis (1969), we distinguish between historical precedents in repeated games and conventions in evolutionary games. Selecting a mutual best response outcome based on precedent requires actors to focus on some salient analogy to a shared past instance of the present observable game and to expect others to focus on the same analogy. Crawford and Haller (1990) explain how players should use precedent to establish a common language that will allow players to resolve strategic uncertainty in repeated coordination games. Meyers et al. (1992) found that if subjects do not use precedent optimally in early periods of the repeated game it was very difficult for them to learn to do so.

Convention generalizes precedent to situations where one lacks shared experience, but knows that everyone involved is a member of the same community. An observable regularity in the behavior of members of a community in a recurrent situation is a convention if it is customary, expected, and mutually consistent, compare Lewis (1969) and Young (1993).

As mentioned above, Van Huyck, et al. (1995) found that security can undermine the salience of symmetry. Initially, this resulted in outcomes that were not mutually consistent. However, in one treatment the matching protocol divided subjects into two labeled populations: a row population and a column population. In five of eight sessions under this treatment they observed unequal-division conventions emerging in communities of symmetrically endowed subjects. In that paper, no distinction was made between conventions based on labels, the row and column position in the game, and conventions based on populations, own population players only meet other population players

This distinction reflects two different sources of mutually consistent behavior. Labels may serve as a focal point that solves the strategy coordination problem if their significance is recognized by members of the community, see Sugden (1995) for references. Alternatively, changing the matching protocol from one to two populations changes the state space of models of population dynamics and for many population dynamics this change has the implication that only strict equilibria are asymptotically stable, see Weibull (1995) for references. Consequently, inefficient but symmetric mixed strategy equilibria are no longer asymptotically stable.

This paper attempts to seperate the influence of labels and populations on the ability of subjects in an evolutionary coordination game to adopt a conventional way to play. Our labels treatments investigates the abstraction assumptions that underlie the concept of a strategy, while our population treatments investigate the attraction of alternative mutually consistent ways to play under adaptive behavior. We observe conventions emerging in communities with one population and labels and with two populations and no labels, but the most effective treatment is two labeled populations.

A final section, added in response to helpful comments by several referees, investigates individual subject behavior. Specifically, we estimate logistic response learning models, like Mookerjee and Sopher (1994) and Cheung and Friedman (1995). Of the models considered, a version of exponential fictitious play fits our data best. When estimated by treatment, the exponential fictitious play models converge toward best response fictitious play as one moves from the one population no labels treatment to the two labeled populations treatment.

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Conclusion

The experiment demonstrates that it is possible for conventions based on labels or on populations to emerge. Table 6 summarizes the results. Without non-strategic details, the outcome was inefficient as predicted by symmetry. Labeling subjects row or column but holding the number of populations constant at one allowed two of three sessions to coordinate on a convention, which improved efficiency. Two of three sessions under the two population no labels treatment coordinated on a convention, which also improved efficiency. A convention emerged in all three sessions of the two labeled populations treatment. It is in this sense that it was the most effective treatment.

We were pleasantly surprised by the ability of the exponential fictitious play model to fit our individual subject data. The experiment was designed and conducted before Fudenberg and Krep's (1993) published their seminal work on smooth fictitious play. Yet, of the numerous empirical models we have tried, this is the first which seems close to being right to us. We will certainly want to use it in designing future experiments.

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Footnotes

[1] See Kreps (1990, ch.6) for a non-technical discussion of the basic issues. See Bernheim (1984) and Brandenburger (1992) on the mutual consistency requirement. See Harsanyi/Selten (1988) on equilibrium selection.

[2] See also Cooper, DeJong, Forsythe, and Ross (1990; 1994) and Friedman (1996).

[3] Roth/Schoumaker (1983) and Binmore, et al. (1993) present evidence against equal-division in asymmetric Nash demand games.

[4] Of course, they don't claim that security always undermines efficiency and symmetry. Straub (1995) found that risk-dominance makes more accurate predictions than security in the class of coordination games he considers.