Convergence and approximation results for non-cooperative Bayesian games: Learning theorems |
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Authors: | Leonidas C Koutsougeras Nicholas C Yannelis |
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Institution: | (1) Department of Economics, University of Illinois at Urbana-Champaign, 61820 Champaign, Illinois, USA |
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Abstract: | Summary LetT denote a continuous time horizon and {G
t
:tT} be a net (generalized sequence) of Bayesian games. We show that: (i) if {x
t
: tT} is a net of Bayesian Nash Equilibrium (BNE) strategies for Gt we can extract a subsequence which converges to a limit full information BNE strategy for a one shot limit full information Bayesian game, (ii) If {x
t
: tT} is a net of approximate or t-BNE strategies for the game Gt we can still extract a subsequence which converges to the one shot limit full information equilibrium BNE strategy, (iii) Given a limit full information BNE strategy of a one shot limit full information Bayesian game, we can find a net of t-BNE strategies {x
t
: tT} in {G
t
:tT} which converges to the limit full information BNE strategy of the one shot game.We wish to thank Larry Blume, Mark Feldman, Jim Jordan, Charlie Kahn, Stefan Krasa, Gregory Michalopoulos, Wayne Shafer, Bart Taub, and Anne Villamil for several useful discussions. The financial support of the University of Illinois at Urbana-Champaign Campus Research Board is gratefully acknowledged. |
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