Shachat, Jason and Swarthout, J. Todd and Wei, Lijia (2012): A hidden Markov model for the detection of pure and mixed strategy play in games.
Download (700kB) | Preview
We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies, and allows switching between these states. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that always follows its part of the unique mixed strategy Nash equilibrium profile. Estimated results show significant mixed strategy play and non-stationary dynamics. We also explore the ability of the model to forecast action choice.
|Item Type:||MPRA Paper|
|Original Title:||A hidden Markov model for the detection of pure and mixed strategy play in games|
|Keywords:||Mixed Strategy; Experiment; Hidden Markov Model|
|Subjects:||C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C92 - Laboratory, Group Behavior
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General
|Depositing User:||Jason Shachat|
|Date Deposited:||07 Jul 2012 03:44|
|Last Modified:||31 Aug 2016 03:24|
Aumann, Robert J. (1985), “On the non-transferable utility value: A comment on the Roth-Shafer examples.” Econometrica, 53, 667–678.
Bareli, M, O Azar, I Ritov, Y Keidarlevin, and G Schein (2007), “Action bias among elite soccer goalkeepers: The case of penalty kicks.” Journal of Economic Psychology, 28, 606–621.
Binmore, Ken, Joe Swierzbinski, and Chris Proulx (2001), “Does minimax work? an experimental study.” Economic Journal, 111, 445–64.
Bloomfield, Robert (1994), “Learning a mixed strategy equilibrium in the laboratory.” Journal of Economic Behavior & Organization, 25, 411–436.
Chiappori, Pierre, Steven Levitt, and T. Groseclose (2002), “Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer.” American Economic Review, 92, 1138–1151.
Geweke, John (1991), “Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments.” Staff Report 148, Federal Reserve Bank of Minneapolis.
Greiner, Ben (2004), “An online recruitment system for economic experiments.” In Forschungund wissenschaftliches Rechnen (Kurt Kremer and Volker Macho, eds.), volume 63 of Ges.fur Wiss. Datenverarbeitung, 79–93, GWDG Bericht.
Morgan, John and Martin Sefton (2002), “An experimental investigation of unprofitable games.” Games and Economic Behavior, 40, 123–146.
Nash, John (1951), “Non-Cooperative Games.” The Annals of Mathematics, 54, 286–295.
Noussair, Charles and Marc Willinger (2011), “Mixed strategies in an unprofitable game: an experiment.” Working papers, LAMETA, Universtiy of Montpellier.
Nyarko, Yaw and Andrew Schotter (2002), “An experimental study of belief learning using elicited beliefs.” Econometrica, 70, 971–1005.
Ochs, Jack (1995), “Games with unique, mixed strategy equilibria: An experimental study.” Games and Economic Behavior, 10, 202–217.
O’Neill, Barry (1987), “Nonmetric test of the minimax theory of two-person zero-sum games.” Proceedings of the National Academy of Sciences, U.S.A., 84, 2106–2109.
Palacios-Huerta, Ignacio (2003), “Professionals play minimax.” Review of Economic Studies, 70, 395–415.
Rabiner, Lawrence R. (1989), “A tutorial on hidden markov models and selected applications in speech recognition.” Proceedings of the IEEE, 77, 257–286.
Rosenthal, Robert W., Jason Shachat, and Mark Walker (2003), “Hide and seek in arizona.” International Journal of Game Theory, 32, 273–293.
Selten, Reinhard and Thorsten Chmura (2008), “Stationary concepts for experimental 2x2 games.” American Economic Review, 98, 938–966.
Shachat, Jason (2002), “Mixed strategy play and the minimax hypothesis.” Journal of Economic Theory, 104, 189–226.
Shachat, Jason and J. Todd Swarthout (2004), “Do we detect and exploit mixed strategy play by opponents?” Mathematical Methods of Operations Research, 59, 359–373.
Von Neumann, John (1928), “Zur theorie der gesellschaftsspiele.” Mathematische Annalen, 100, 295–320.
Von Neumann, John and Oskar Morgenstern (1944), Theory of Games and Economic Behavior. Princeton University Press.
Walker, Mark and John Wooders (2001), “Minimax play at Wimbledon.” American Economic Review, 91, 1521–1538.