Teng, Jimmy (2010): Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions.

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Abstract
Bayesian rational prior equilibrium requires agent to make rational statistical predictions and decisions, starting with first order non informative prior and keeps updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved.
The main difference between the Bayesian theory of games and the current games theory are:
I. It analyzes a larger set of games, including noisy games, games with unstable equilibrium and games with double or multiple sided incomplete information games which are not analyzed or hardly analyzed under the current games theory.
II. For the set of games analyzed by the current games theory, it generates far fewer equilibria and normally generates only a unique equilibrium and therefore functions as an equilibrium selection and deletion criterion and, selects the most common sensible and statistically sound equilibrium among equilibria and eliminates insensible and statistically unsound equilibria.
III. It differentiates between simultaneous move and imperfect information. The Bayesian theory of games treats sequential move with imperfect information as a special case of sequential move with observational noise term. When the variance of the noise term approaches its maximum such that the observation contains no informational value, there is imperfect information (with sequential move).
IV. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games.
Item Type:  MPRA Paper 

Original Title:  Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions 
English Title:  Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions 
Language:  English 
Keywords:  Games Theory, Bayesian Statistical Decision Theory, Prior Distribution Function, Conjectures, Subjective Probabilities 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  24189 
Depositing User:  jimmy teng 
Date Deposited:  02. Aug 2010 02:04 
Last Modified:  13. Feb 2013 01:03 
References:  Aumann, R. J. 1964. ``Mixed vs. behavior strategies in infinite extensive games,'' Annals of Mathematics Studies, 52, 627630. Aumann, R. J. 1985. ``What is game theory trying to accomplish?'' in K. Arrow and S. Honkapohja (eds.), Frontiers of Economics, Basil Blackwell, Oxford. Berger, J. O. 1980. Statistical Decison Theory and Bayesian Analysis, Second Edition, SpringerVerlag, New York. Berger, J. O. 1990. ``On the inadmissibility of unbiased estimators,'' Statistics & Probability Letters, 9, 381384. Bickel, P. J. and Doksum, K. A. 2001. Mathematical Statistics: Basic Ideas and Selected Topics, Vol. 1, second edition, PrenticeHall Inc., New Jersey. Dixit, A. and Skeath, S. 1999. Game of Strategy. W. W. Norton & Company. Fudenberg, D. and Levine, D. 1989. Reputation and equilibrium selection in games with a patient player, Econometrica, 57, 759778. . 1991. ``Maintaining a reputation when strategies are inaccurately observed,'' Review of Economic Studies, 59, 3, 561579. Harsanyi, J. C. 1967. ``Games with Incomplete Information by ``Bayesian'' Players, IIII. Part I. The Basic Model,'' Management Science, 14, 3, 159182. . 1968a. ``Games with Incomplete Information by ``Bayesian'' Players, IIII. Part II. Bayesian Equilibrium Points,'' Management Science, 14, 5, 320334. . 1968b. Games with Incomplete Information by Bayesian Players, IIII. Part III. The Basic Probability Distribution of the Game,Management Science, 14, 7, 486502. Harsanyi, J. C. and Selten, R. 1988. A General Theory of Equilibrium Selection in Games, the MIT Press, Cambridge, Massachusetts. Mariotti, M. 1995. ``Is Bayesian rationality compatible with strategic rationality,'' The Economic Journal, 105, 10991109. Morris, S. and Takashi, U. 2004. ``Best response equivalence,'' Games and Economic Behavior 49, 2, 260287. Schelling, T. 1960. The Strategy of Conflict, Harvard University Press. Teng, J. 2004. Rational Prior Perfect Bayesian Nash Equilibrium. MSc (Statistics) Thesis, Duke University. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/24189 