A Bayesian Theory of Games： An Analysis of Strategic Interactions with Statistical Decision Theoretic Foundation  

作　　者：Jimmy Teng 

机构地区：[1]School of Economics, University of Nottingham Malaysia Campus, Selangor 43500, Malaysia

出　　处：《Journal of Mathematics and System Science》2012年第3期145-155,共11页数学和系统科学（英文版）

摘　　要：This paper introduces a new game theoretic equilibrium which is based upon the Bayesian subjective view of probability, BEIC （Bayesian equilibrium iterative conjectures）. It requires players to make predictions, starting from first order uninformative predictive distribution functions （or conjectures） and keep updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. Information known by the players such as the reaction functions are thereby incorporated into their higher order conjectures and help to determine the convergent conjectures and the equilibrium. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and conjectures. The BEIC approach is capable of analyzing a larger set of games than current Nash Equilibrium based games theory, including games with inaccurate observations, games with unstable equilibrium and games with double or multiple sided incomplete information games. On the other hand, for the set of games analyzed by the current games theory, it generates far lesser equilibriums and normally generates only a unique equilibrium. 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. Finally, it also resolves inconsistencies in equilibrium results by different solution concepts in current games theory such as that between Nash Equilibrium and iterative elimination of dominated strategies and that between Perfect Bayesian Equilibrium and backward inducti

关 键 词：New equilibrium concept iterative conjectures CONVERGENCE Bayesian decision theory Schelling point. 

分 类 号：O213[理学—概率论与数理统计] TP391.41[理学—数学]