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Bayesian equilibrium by iterative conjectures: a theory of games with players forming conjectures iteratively starting with first order uninformative conjectures

Teng, Jimmy (2011): Bayesian equilibrium by iterative conjectures: a theory of games with players forming conjectures iteratively starting with first order uninformative conjectures.

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Abstract

This paper introduces a new game theoretic equilibrium, Bayesian equilibrium by iterative conjectures (BEIC). It requires agents 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. In a BEIC, rationality is achieved for 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 also resolves inconsistencies in equilibrium results by different solution concepts in current games theory.

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