Teng, Jimmy (2012): Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach.
Download (210kB) | Preview
This paper proposes a way to solve two (and multiple) sided incomplete information games which generally generates a unique equilibrium. The approach uses iterative conjectures updated by game theoretic and Bayesian statistical decision theoretic reasoning. Players in the games form conjectures about what other players want to do, starting from first order uninformative conjectures and keep updating with games theoretic and Bayesian statistical decision theoretic reasoning until a convergence of conjectures is achieved. The resulting convergent conjectures and the equilibrium (which is named Bayesian equilibrium by iterative conjectures) they supported form the solution of the game. The paper gives two examples which show that the unique equilibrium generated by this approach is compellingly intuitive and insightful. The paper also solves an example of a three sided incomplete information simultaneous game.
|Item Type:||MPRA Paper|
|Original Title:||Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach|
|English Title:||Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach|
|Keywords:||new equilibrium concept, two and multiple sided incomplete information, iterative conjectures, convergence, Bayesian decision theory, Schelling point|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||jimmy teng|
|Date Deposited:||14 Jul 2012 13:56|
|Last Modified:||03 Aug 2016 20:00|
Berger, J. O. 1980. Statistical Decision Theory and Bayesian Analysis, Second Edition, Springer-Verlag, New York.
Chatterjee, K. and Samuelson, L. 1987. Bargaining under Two-Sided Incomplete Information: The Unrestricted Offers Case, Operations Research,36, 4, 605-618.
Cramton, P. C. 1984. Bargaining with Incomplete Information: An Infinite-Horizon Model with Two-Sided Uncertainty, Review of Economic Studies, 51, 579-593.
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, 1099-1109.
Powell, R. 1988. Nuclear Brinkmanship with Two-Sided Incomplete Information, American Political Science Review, 82, 1, 155-178.
Schweizer, U. 1989. Litigation and Settlement under Two-Sided Incomplete Information, Review of Economic Studies, 56, 2, 163-177.
Teng, J. 2012. A Bayesian Theory of Games: An Analysis of Strategic Interactions with Statistical Decision Theoretic Foundation, Journal of Mathemathetics and System Science 2.
Watson, J. 1995. Alternating-Offer Bargaining with Two-Sided Incomplete Information, Review of Economic Studies, 65, 573-594.