A nonstandard characterization of sequential equilibrium,perfect equilibrium,and proper equilibrium |
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Authors: | Joseph Y Halpern |
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Institution: | (1) Computer Science Department, Cornell University, Ithaca, NY, USA |
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Abstract: | New characterizations of sequential equilibrium, perfect equilibrium, and proper equilibrium are provided that use nonstandard
probability. It is shown that there exists a belief system μ such that is a sequential equilibrium in an extensive game with perfect recall iff there exist an infinitesimal and a completely mixed behavioral strategy profile σ′ (so that assigns positive, although possibly infinitesimal, probability to all actions at every information set) that differs only
infinitesimally from such that at each information set I for player i, σ
i
is an -best response to conditional on having reached I. Note that the characterization of sequential equilibrium does not involve belief systems. There is a similar characterization
of perfect equilibrium; the only difference is that σ
i
must be a best response to conditional on having reached I. Yet another variant is used to characterize proper equilibrium.
This work was supported in part by NSF under grants CTC-0208535, ITR-0325453, and IIS-0534064, and by AFOSR under grant FA9550-05-1-0055. |
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Keywords: | Sequential equilibrium Perfect equilibrium Proper equilibrium Nonstandard probability |
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