Strategic Similarity and Emergent Conventions

Strategic Similarity And Emergent Conventions:
Evidence from Similar Stag Hunt Games

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

December 1998

Abstract: This paper reports evidence on the origin of convention in laboratory cohorts confronting similar but not identical strategic situations repeatedly. The experiment preserves the action space of the game, while randomly perturbing the payoffs and scrambling the action labels in an effort to blunt the salience of retrospective selection principles. Hence, the similarity between stage games is reduced to certain strategic details, like efficiency, security, and risk dominance. Nevertheless, we do observe conventions emerging in half of the laboratory cohorts. When a convention emerges subjects’s behavior conforms to the selection principles of efficiency rather than security or risk dominance.

Key words: evolutionary games, coordination, similarity, convention, payoff dominance, risk dominance, learning, human behavior.

JEL classification: c72, c78, c92, d83.

Acknowledgments: The National Science Foundation and the Texas Advanced Research Program provided financial support. Eric Battalio implemented the experimental design on the TAMU economics laboratory network. This paper was revised while Van Huyck was on a faculty development leave at the University of Pittsburgh.

I. Introduction

There is now a lot of evidence against the claim that people use efficiency to solve strategy coordination problems. For example, in a series of papers on two player stag hunt games investigators find that the observed emergent mutually consistent behavior need not be efficient. Battalio et al. (1997) review the evidence and conclude that while risk dominance is not used by a majority of the subjects initially it accurately predicts the emergent convention when the earnings difference between the two strategies is sufficiently large.

This evidence is from experiments using evolutionary matching protocols. In an evolutionary game, a stage game is played repeatedly by random subsets of the community, usually referred to as cohorts or populations in the experimental literature. A behavioral regularity in a recurrent situation amongst community members is a convention if it is customary, expected, and mutually consistent, see Lewis (1969).

In both the theoretical and experimental literature, subjects confront the same stage game repeatedly, either with the same opponent or with opponents drawn from a well defined community. These sequences of stage games have an extraordinary degree of similarity not observed in most field situations. Kreps’ (1990) argues that, "If we rely solely on the story of directly relevant experience to justify attention to Nash equilibria, and if by directly relevant experience we mean only experience with precisely the same game in precisely the same situation, then this story will take us very little distance outside the laboratory."

The inefficient behavior reported in the literature may reflect subjects learning to use a deductive selection principle, like risk-dominance or security. Alternatively, the behavior may reflect the coincidence of situation specific adaptive behavior converging to a mutually consistent outcome. In strategically similar, but contextually different situations, conventions based on non-strategic details, like action labels, player labels, or population membership, may be difficult or impossible to establish. In such environments, mutually consistent behavior, if it is to emerge at all, must be based on the strategic selection principles emphasized in a general theory of games.

This paper reports evidence on the origin of convention in laboratory cohorts confronting similar but not identical strategic situations repeatedly, all of which are two player stag hunts. The experiment preserves the action space of the game, while randomly perturbing the payoffs and scrambling the action labels in an effort to blunt the salience of retrospective selection principles. Hence, the similarity between stage games is reduced to certain strategic details, like efficiency, security, and risk dominance. Conventions based on strategic details require members of a community to focus on the same deductive concept derived from shared past instances of similar games and, further, to use that concept to solve the strategy coordination problem in the present game.

We do observe conventions emerging in laboratory cohorts playing a 75 period sequence of scrambled payoff perturbed 2×2 stag hunt game forms using an evolutionary matching protocol. The observed conventions require cohort members to recognize strategic similarities between stage games. When a convention emerges subjects’ behavior is consistent with efficiency rather than security or risk dominance.

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Conclusion

Three of the four cohorts that ran a full 75 periods coordinate on a convention of selecting the payoff dominant equilibrium. The other 75 period cohort and the two 56 period cohorts appear to be converging towards the same convention. In short, the observed emergent conventions were always based on payoff dominance rather than risk dominance or security.

Our results provide evidence on the ability of subjects to achieve mutually consistent outcomes in recurring strategic situations that are similar but not identical. Studying behavior in this framework is important since many recurring strategic situations in the field are not identical. Our results provide evidence that human subjects do recognize strategic principles when confronted with a sequence of similar but not identical strategic situations and, moreover, some cohorts are able to use these strategic similarities to solve their coordination problem.

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Footnotes

1. See Ochs (1995) for a general survey or Van Huyck, Battalio, and Rankin (1997) for the recent references.

2. However, in Sugden (1995) efficiency remains an essential principle in constructing a normative selection theory.

3. See Van Huyck, Battalio, and Rankin (1997) for examples of emergent conventions based on non-strategic details of a game.

4. See Rapoport, Guyer, and Gordon (1976) for a discussion of experimental designs using scrambling, and Crawford and Haller (1990) and Sugden (1995) for formal theories of scrambling.