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Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach

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  • Teng, Jimmy

Abstract

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.

Suggested Citation

  • Teng, Jimmy, 2012. "Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach," MPRA Paper 40061, University Library of Munich, Germany, revised 12 Jul 2012.
    • Handle: RePEc:pra:mprapa:40061
    as

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    File URL: https://mpra.ub.uni-muenchen.de/40061/1/MPRA_paper_40061.pdf
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    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. Powell, Robert, 1988. "Nuclear Brinkmanship with Two-Sided Incomplete Information," American Political Science Review, Cambridge University Press, vol. 82(1), pages 155-178, March.
    3. Peter C. Cramton, 1984. "Bargaining with Incomplete Information: An Infinite-Horizon Model with Two-Sided Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 579-593.
    4. Mariotti, Marco, 1995. "Is Bayesian Rationality Compatible with Strategic Rationality?," Economic Journal, Royal Economic Society, vol. 105(432), pages 1099-1109, September.
    5. Urs Schweizer, 1989. "Litigation and Settlement under Two-Sided Incomplete Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(2), pages 163-177.
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    More about this item

    Keywords

    new equilibrium concept; two and multiple sided incomplete information; iterative conjectures; convergence; Bayesian decision theory; Schelling point;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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