Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure.

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

American Economic Review, March 1990.

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Introduction

Deductive equilibrium methods--such as Rational Expectations or Bayesian Nash Equilibrium--are powerful tools for analyzing economies that exhibit strategic interdependence. 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 and, hence, actions would disappear over time, see Robert 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, when the equilibria are not interchangeable, this uncertainty will influence the rational decision maker's behavior. Strategic uncertainty arises even in situations where objectives, feasible strategies, institutions, and equilibrium conventions are completely specified and are common knowledge. While multiple equilibria are common in theoretical analysis, consideration of specific economies suggests that many equilibrium points are implausible and unlikely to be observed in actual economies.

One response to multiple equilibria is to argue that some Nash equilibrium points are not self-enforcing and, hence, are implausible, because they fail to satisfy one or more of the following refinements: elimination of individually unreasonable actions, sequential rationality, and stability against perturbations of the game--see Elon Kohlburg and Jean-Francois Mertens (1986) for examples and references. Equilibrium refinements determine when an outcome that is already expected would be implemented by rational decision makers.

In general, many outcomes will satisfy the conditions of a given equilibrium refinement. The equilibrium selection literature attempts to determine which, if any, self-enforcing equilibrium point will be expected. A satisfactory theory of interdependent decisions must not only identify the outcomes that are self-enforcing when expected but also must identify the expected outcomes. Consequently, a theory of equilibrium selection would be a useful complement to the theory of equilibrium points.

The experimental method provides a tractable and constructive approach to the equilibrium selection problem. This paper studies a class of tacit pure coordination games with multiple equilibria, which are strictly Pareto ranked, and it reports experiments that provide evidence on how human subjects make decisions under conditions of strategic uncertainty.

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Primary Data Set

1987 Working Paper including instructions and prediction analysis deleted from published paper but not sessions 8 and 9.

Primary Data Set available here. (File size is 180k.)

Description of Primary Data Set available here.

Surface mail request (comments, suggestions, references, etc.): john.vanhuyck@tamu.edu

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Conclusion

These experiments provide an interesting example of coordination failure. The minimum was never above four in period one and all seven experiments converged to a minimum of one within four periods. Since the payoff-dominant equilibrium would have paid all subjects $19.50 in the A and A' treatments--excluding predictions--and the average earnings were only $8.80, the observed behavior cost the average subject $10.70 in lost earnings.

This inefficient outcome is not due to conflicting objectives as in "prisoner's dilemma" games or to asymmetric information as in "moral hazard" games. Rather coordination failure results from strategic uncertainty: some subjects conclude that it is too "risky" to choose the payoff-dominant action and most subjects focus on outcomes in earlier period games. The minimum rule interacting with this dynamic behavior causes the A and A' treatments to converge to the most inefficient outcome.

Deductive methods imply that all feasible actions are consistent with some equilibrium point in this experimental coordination game. However, the experimental results suggest that the first best outcome, which is the payoff-dominant equilibrium, is an extremely unlikely outcome either initially or in repeated play. Instead, the results suggest that the initial outcome will not be an equilibrium point and only the secure--but very inefficient--equilibrium describes behavior that actual subjects are likely to coordinate on in repeated play of period game A when the number of players is not small.

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References

Basar, Tamer and Olsder, Geert J., Dynamic Noncooperative Game Theory, New York: Academic Press, 1982.

Bryant, John, "A Simple Rational Expectations Keynes-Type Model", The Quarterly Journal of Economics, vol. 98, no.3, August 1983, 525-528.

Cooper, Russell, DeJong, Douglas V., Forsythe, Robert, and Ross, Thomas W., "Selection Criteria in Coordination Games: Some Experimental Results," unpublished manuscript, October 1987.

Cooper, Russell, and John, Andrew, "Coordinating Coordination Failures in Keynesian Models", The Quarterly Journal of Economics, vol. 103, no. 3, August 1988.

Crawford, Vincent P., "An 'Evolutionary' Interpretation of Van Huyck, Battalio, and Beil's Experimental Results on Coordination," unpublished manuscript, January 1989.

Harsanyi, John C., and Selten, Reinhard, A General Theory of Equilibrium Selection in Games, Cambridge: The MIT press, 1988.

Kohlberg, Elon and Mertens, Jean-Francois, "On the Strategic Stability of Equilibria," Econometrica, vol.54, no.5, September 1986.

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

Luce, R. Duncan and Raiffa, Howard, Games and Decisions, New York: John Wiley & Sons, Inc., 1957.

Mood, A.M., Graybill, F.A., and Boes, D.C., Introduction to the Theory of Statistics, 3rd Edition, New York: McGraw-Hill, 1974.

Osborne, Martin J., "Signaling, Forward Induction, and Stability in Finitely Repeated Games," unpublished manuscript, November 1987.

Schelling, Thomas C., The Strategy of Conflict, Cambridge: Harvard University Press, 1980.

van Damme, Eric, "Stable Equilibria and Forward Induction," Universitat Bonn Discussion paper no. 128, August 1987.

Van Huyck, John B., Battalio, Raymond C., and Beil, Richard O., "Keynesian Coordination Games, Strategic Uncertainty, and Coordination Failure," unpublished manuscript, October 1987.

Von Neumann, John and Morgenstern, Oskar, Theory of Games and Economic Behavior, Princeton: Princeton University Press, 1972.

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Footnotes

* Department of Economics, Texas A&M University, College Station, TX 77843; Department of Economics, Texas A&M University, College Station, TX 77843; and Department of Economics, Auburn University, Auburn, AL 36849, respectively. Orley Ashenfelter, Mike Baye, John Bryant, Colin Camerer, Russell Cooper, Vincent Crawford, John Haltiwanger, Pat Kehoe, Tom Saving, Steve Wiggins, Casper de Vries, a referee, and seminar participants at the NBER/FMME 1987 Summer Institute, the 1988 meetings of the Economic Science Association, the University of New Mexico, and Texas A&M University made constructive comments on earlier versions of this paper. Sophon Khanti-Akom, Kirsten Madsen, and Andreas Ortmann provided research assistance. The National Science Foundation (SES-8420240), the Texas A&M University Center for Mineral and Energy Research, and the Lynde and Harry Bradley Foundation provided financial support. A Texas A&M University TEES Fellowship has supported Battalio.

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