A nonstandard characterization of sequential equilibrium,perfect equilibrium,and proper equilibrium

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.  

不完备偏好扩展式博弈的序贯均衡

将Kreps和Wilson提出的序贯均衡解概念推广到了存在不完备偏好的情形.首先给出了一个修正的颤抖手完美均衡的概念,然后应用它去证明不完备偏好扩展式博弈序贯均衡的存在性.  

A note on efficient signaling of bargaining power

Strategic delay and restricted offers are two modes of signaling bargaining power in alternating offers bargaining games. This paper shows that when both modes are available, the best signaling strategy of the “strong” type of the informed player consists of a pure strategic delay followed by an offer on the whole pie. There is no signaling motivation for issue-by-issue bargaining when the issues are perfectly substitutable. Received: July 1996/Final version: August 1999