Strategic uncertainty, equilibrium selection principles, and coordination failure

Strategic Uncertainty, Equilibrium Selection Principles,
and Coordination Failure in Average Opinion Games

John B. Van Huyck, Raymond C. Battalio, and Richard O. Beil

Revised December 1989

[ Introduction | Conclusion | References | Footnotes | John's Web ]

Abstract: Deductive equilibrium methods are powerful tools for analyzing economies that exhibit strategic interdependence. The power of the equilibrium method derives from its ability to abstract from the complicated dynamic process that induces equilibrium and to abstract from the historical accident that initiated the process. Unfortunately, deductive equilibrium analysis often fails to determine a unique equilibrium solution in many economies and, hence, often fails to prescribe or predict rational behavior. Consequently, a theory of equilibrium selection would be a useful complement to the theory of equilibrium points. An interesting conjecture-- Schelling's conjecture--is that decision makers may focus on some selection principle to identify a specific equilibrium point in situations involving multiple equilibria. This salient principle would allow the decision makers to implement an equilibrium. The salience of an equilibrium selection principle is essentially an empirical question. This paper uses the experimental method to examine the salience of payoff-dominance, security, and historical precedents in related average opinion games.

Acknowledgment: Ann Gillette, Sophon Khanti-Akom, and Kirsten Madsen provided research assistance. The National Science Foundation (SES-8420240;SES-8911032), The Texas Engineering Extension Service, and the Texas A&M University Center for Mineral and Energy Research provided financial support.

Introduction

A central question in economics is how do markets coordinate the behavior of decision makers in a decentralized economy. A successful answer to this question requires understanding how decision makers behave in environments that exhibit strategic interdependence. In such environments, a decision maker's best strategy depends on the strategy adopted by related decision makers. In most economic situations, it is not possible to prescribe, describe, or predict a decision maker's behavior or the market outcome without a theory of inter-dependent decision making.

Deductive equilibrium methods are powerful tools for analyzing economies that exhibit strategic interdependence. A common assumption is that decision makers behave as if they form beliefs based on deductive equilibrium concepts. For example, the Rational Expectations Equilibrium concept requires that decision makers behave as if they believe that the economy will yield a Rational Expectations Equilibrium. Similarly, a Bayesian-Nash Equilibrium requires that decision makers behave as if they believe the economy will yield a Bayesian-Nash Equilibrium. Deductive Bayesian-Nash beliefs have the desirable property that they are individually rational and consistent, that is, when unanimously expected a Bayesian-Nash Equilibrium is self-fulfilling.

Typically, deductive equilibrium analysis does not explain the process by which decision makers acquire equilibrium beliefs. The presumption is that actual economies have achieved a steady state. In economies with stable and unique equilibrium points, the influence of inconsistent beliefs would disappear over time, see Lucas (1987). The power of the equilibrium method derives from its ability to abstract from the complicated dynamic process that induces equilibrium and to abstract from the historical accident that initiated the process.

Unfortunately, deductive equilibrium analysis often fails to determine a unique equilibrium solution in many economies and, hence, often fails to prescribe or predict rational behavior. In economies with multiple equilibria, the rational decision maker formulating beliefs using deductive equilibrium concepts is uncertain which equilibrium strategy other decision makers will use and, in general, this uncertainty will influence the rational decision maker's behavior. Strategic uncertainty arises even in situations where objectives, feasible strategies, and institutions are completely specified and are common knowledge. [1]

The deductive equilibrium method is incomplete. A satisfactory theory of interdependent decisions not only must identify the outcomes that are equilibria when expected, but also must explain the process by which decision makers acquire equilibrium beliefs. Consequently, a theory of equilibrium selection would be a useful complement to the theory of equilibrium points.

An interesting conjecture--Schelling's conjecture--is that decision makers may focus on some selection principle to identify a specific equilibrium point in situations involving multiple equilibria. This salient principle would allow the decision makers to implement an equilibrium. A salient principle selects an equilibrium point based on its conspicuous uniqueness in some respect. The salience of an equilibrium selection principle is essentially an empirical question.

This paper uses the experimental method to examine the salience of payoff-dominance, security, and historical precedents in related average opinion games. The average opinion games studied exhibit multiple equilibria, which in the baseline experiments were pareto ranked. The experimental results are summarized in the paper's conclusion.

Conclusions

In the baseline average opinion game, which has a unique payoff-dominant equilibrium and a unique secure equilibrium, neither payoff-dominance nor security were salient equilibrium selection principles. Instead, the modal response was between the payoff-dominant and the secure action. Repeated interaction produced simple dynamics that converged to the equilibrium selected by the historical accident of the initial median. Since all baseline experiments exhibit coordination failure, they provide a striking example of how strategic uncertainty can lead to coordination failure.

Treatment Omega reduced the strategic uncertainty confronting subjects by eliminating considerations of security. Payoff-dominance accurately predicts the modal response to period game . Treatment Phi reduced the strategic uncertainty confronting subjects by eliminating considerations of payoff-dominance. Security accurately predicts the modal response to period game .

As with the baseline treatment, the historical accident of the initial median selected the equilibrium outcome implemented in all three Omega treatments and all three Phi treatments.

Continuation treatments found little evidence for the salience of weak precedent. Instead, experience in related games increased the salience of payoff-dominance. However, like the initial treatment, the historical accident of the period eleven median determines which equilibrium point obtains in the continuation treatment. Hence, all treatments provide evidence that the initial median in a treatment provides a salient precedent in average opinion games.

References

T. Basar and G.J. Olsder, Dynamic Noncooperative Game Theory, (New York: Academic Press, 1982).

R.C. Battalio, C. Kogut, and D. Meyer, "The Effects of Varying Number of Bidders in First Price Private Value Auctions: An Application of a Dual Market Bidding Technique", Advances in Behavioral Economics Vol. 2, in press.

A. Brandenburger and E. Dekel, "The Role of Common Knowledge Assumptions in Game Theory," in The Economics of Missing Markets, Information, and Games, F. Hahn ed. (Oxford: Clarendon Press, 1989).

J. Bryant, "A Simple Rational Expectations Keynes-Type Model," Quarterly Journal of Economics, 98(3), August 1983, 525-528.

C. Camerer, "Behavioral Game Theory," unpublished, February 1989; forthcoming in Insights in Decision Making, ed. R. Hogarth (Chicago: University of Chicago Press).

R. Cooper, D.V. DeJong, R. Forsythe, and T.W. Ross, "Selection Criteria in Coordination Games: Some Experimental Results," forthcoming American Economic Review, March 1990.

R. Cooper and A. John, "Coordinating Coordination Failures in Keynesian Models," Quarterly Journal of Economics, 103(3), August 1988, 441-464.

V.P. Crawford, "An `Evolutionary' Interpretation of Van Huyck, Battalio, and Beil's Experimental Results on Coordination," unpublished, July 1989.

P. Diamond, "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, 90(5), October 1982, 881-885.

R. Frydman and E.S. Phelps eds., Individual Forecasting and Aggregate Outcomes, (Cambridge: Cambridge University Press, 1983).

J. Harsanyi and R. Selten, A General Theory of Equilibrium Selection in Games, (Cambridge: MIT Press, 1988).

J.M. Keynes, The General Theory of Employment, Interest, and Money, (New York: Harcourt, Brace, & World,Inc, 1964.)

R.E. Lucas, Jr. "Adaptive Behavior and Economic Theory," in Rational Choice, eds. R.M. Hogarth and M.W. Reder, (Chicago: University of Chicago Press, 1987)

R.D. Luce and H. Raiffa, Games and Decisions, (New York: Wiley, 1957)

T.C. Schelling, The Strategy of Conflict, (Cambridge: Harvard University Press, 1980).

R. Sugden, "Spontaneous Order," Journal of Economic Perspectives, 3(4), Fall 1989, 85-98.

J.B. Van Huyck, R.C. Battalio, and R.O. Beil, "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," forthcoming American Economic Review, March 1990.

J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, (Princeton: Princeton University Press, 1972)

Footnotes

[1] Sugden (1989;p.88) provides a lucid critique of the view that a rational decision maker can deduce a unique "rational" strategy from the information contained in a complete information description of a game. Strategic uncertainty should not be confused with uncertainty arising from incomplete information about other aspects of a decision maker's environment. Keynes's (1936;p.156) discussion of the average opinion problem in newspaper beauty contests and in stock markets is a venerable example of strategic uncertainty.