随机博弈中监测结构的渐近价值
Asymptotic Value of Monitoring Structures in Stochastic Games
AI总结：
本文提出加权混淆序来比较随机博弈中的监测结构，证明极限完美公共均衡支付集随监测信息量增加而单调扩大，并推广到对称博弈及不同状态转移律的比较。
摘要：
本文研究改进的监测如何影响具有不完全公共监测的随机博弈的极限均衡支付集。我们引入一种对Blackwell混淆的简单推广，称为加权混淆，以比较此类博弈的不同监测结构。我们的主要结果是极限完美公共均衡（PPE）支付集关于该信息序的单调性。我们证明，当监测结构在加权混淆序下更具信息量时，极限PPE支付集会扩大。我们还证明，对于对称随机博弈的强对称均衡，类似的单调性也成立。最后，我们证明，当极限可行支付集相同时，我们的加权混淆序有助于比较不同状态转移律和监测结构下的极限PPE支付集。
英文摘要：
This paper studies how improved monitoring affects the limit equilibrium payoff set for stochastic games with imperfect public monitoring. We introduce a simple generalization of Blackwell garbling called weighted garbling in order to compare different monitoring structures for this class of games. Our main result is the monotonicity of the limit perfect public equilibrium (PPE) payoff set with respect to this information order. We show that the limit PPE payoff set expands when the monitoring structure gets more informative with respect to the weighted garbling order. We also show that a similar monotonicity holds for strongly symmetric equilibrium for symmetric stochastic games. Finally, we show that our weighted garbling order is useful to compare the limit PPE payoff set for different state transition laws and monitoring structures when the limit feasible payoff set is the same.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
