Abstract
We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.
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Battalio, R., Samuelson, L., & Van Huyck, J. (2001). Optimization incentives and coordination failure in laboratory stag-hunt games. Econometrica, 69, 749–764.
Binmore, K. (1992). Fun and games: a text on game theory. Lexington: Heath.
Brunnermeier, M. K., & Morgan, J. (2004). Clock games: theory and experiments (Mimeo).
Bryant, J. (1983). A simple rational-expectations Keynes-type model. Quarterly Journal of Economics, 98, 525–529.
Burdzy, K., Frankel, D. M., & Pauzner, A. (2001). Fast equilibrium selection by rational players living in a changing world. Econometrica, 69, 163–189.
Camerer, C. F., & Chong, J. C. (2002). Functional EWA: a one-parameter theory of learning in games (Mimeo).
Camerer, C. F., & Ho, T. H. (1999). Experience-weighted attraction learning in games: a unifying approach. Econometrica, 67, 827–874.
Carlsson, H., & van Damme, E. E. (1993). Global games and equilibrium selection. Econometrica, 61, 989–1018.
Charness, G., & Levin, D. (2005). When optimal choices feel wrong: a laboratory study of Bayesian updating, complexity, and affect. American Economic Review, 95, 1300–1309.
Cheung, Y. G., & Friedman, D. (2005). Speculative attacks: a laboratory study in continuous time (Working paper 606). Dept. of Economics, University of California, Santa Cruz.
Cooper, R., & John, A. (1988). Coordinating coordination failures in Keynesian models. Quarterly Journal of Economics, 103, 441–463.
Cornand, C. (2006). Speculative attacks and informational structure: a experimental study. Review of International Economics, 14, 797–817.
Costa-Gomes, M., & Crawford, V. P. (2002). Cognition and behavior in two-person guessing games: an experimental study. Manuscript in preparation, University of California, San Diego, and University of York.
Costa-Gomes, M., Crawford, V. P., & Broseta, B. (2001). Cognition and behavior in normal-form games: an experimental study. Econometrica, 69, 1193–1235.
Costain, J. (2004). A herding perspective on global games and multiplicity (Working Paper 03-29 (08), May 2003). Department of Economics, Universidad Carlos III Madrid. Revised May 2004.
Costain, J., Heinemann, F., & Ockenfels, P. (2005). Multiple outcomes of speculative behavior in theory and in the laboratory. Manuscript, Department of Economics, Universidad Carlos III Madrid.
Diamond, P. (1982). Aggregate demand management in search equilibrium. Journal of Political Economy, 90, 881–894.
Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance and liquidity. Journal of Political Economy, 91, 401–419.
Frankel, D. M., & Pauzner, A. (2000). Resolving indeterminacy in dynamic settings: the role of shocks. Quarterly Journal of Economics, 115, 285–304.
Goldstein, I. (1999). Interdependent banking and currency crises in a model of self-fulfilling beliefs (Mimeo). Tel-Aviv University.
Goldstein, I., & Pauzner, A. (1999). Endogenous probability of bank runs in a rational expectations model (Mimeo). Tel-Aviv University.
Harsanyi, J. C., et al. (1988). A general theory of equilibrium selection in games. Cambridge: MIT Press.
Hart, O. (1982). A model of imperfect competition with Keynesian features. Quarterly Journal of Economics, 97, 109–138.
Heinemann, F. (2000). Unique equilibrium in a model of self-fulfilling speculative attacks: comment. American Economic Review, 90, 316–318.
Heinemann, F., & Illing, G. (2002). Speculative attacks: unique sunspot equilibrium and transparency. Journal of International Economics, 58, 429–450.
Heinemann, F., Nagel, R., & Ockenfels, P. (2004). The theory of global games on test: experimental analysis of coordination games with public and private information. Econometrica, 72(5), 1583–1599.
Heinemann, F., Nagel, R., & Ockenfels, P. (2007). Measuring strategic uncertainty in coordination games (Working paper). Universitat Pompeu Fabra.
Kajii, A., & Morris, S. (1997). The robustness of equilibria to incomplete information. Econometrica, 65, 1283–1310.
Morris, S., & Shin, H. S. (1998). Unique equilibrium in a model of self-fulfilling currency attacks. American Economic Review, 88, 587–597.
Morris, S., Postlewaite, A., & Shin, H. S. (1995a). Depth of knowledge and the effect of higher order uncertainty. Economic Theory, 6, 453–467.
Morris, S., Rob, R., & Shin, H. S. (1995b). p-dominance and belief potential. Econometrica, 63, 145–157.
Myerson, R. B. (1991). Game theory: analysis of conflict. Cambridge: Harvard University Press.
Nagel, R. (1995). Unraveling in guessing games: an experimental study. American Economic Review, 85, 1313–1326.
Obstfeld, M. (1996). Models of currency crisis with self-fulfilling features. European Economic Review, 40, 1037–1047.
Rubinstein, A. (1989). The electronic mail game: strategic behavior under ‘almost common knowledge’. American Economic Review, 79, 385–391.
Sefton, M., & Yavaş, A. (1996). Abreu–Matsushima mechanisms: experimental evidence. Games and Economic Behavior, 16, 280–302.
Selten, R., Sadrieh, A., & Abbink, K. (1999). Money does not induce risk neutral behavior, but binary lotteries do even worse. Theory and Decision, 46, 211–249.
Shin, H. S. (1996). Comparing the robustness of trading systems to higher-order uncertainty. Review of Economic Studies, 63, 39–59.
Sonsino, D., Erev, I., & Gilat, S. (1999). On rationality, learning and zero-sum betting—an experimental study of the no-betting conjecture (Mimeo). Technion University.
Søvik, Y. (2000). Strength of dominance and depths of reasoning (Mimeo). University of Oslo.
Stahl, D. O., & Wilson, P. W. (1995). On players’ models of other players: theory and experimental evidence. Games and Economic Behavior, 10, 218–254.
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Cabrales, A., Nagel, R. & Armenter, R. Equilibrium selection through incomplete information in coordination games: an experimental study. Exp Econ 10, 221–234 (2007). https://doi.org/10.1007/s10683-007-9183-z
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DOI: https://doi.org/10.1007/s10683-007-9183-z