Speaker: Sergei Artemov, CUNY Graduate Center
Title: Towards Syntactic Epistemic Game Theory.
Abstract:
The traditional semantic approach to consider a game as an Aumann structure, though flexible and convenient, is not foundationally satisfactory due to assumptions that a given Aumann structure adequately represents the game, normally described syntactically, and that this structure itself is common knowledge for the players.
These assumptions leave a gap between the officially syntactic character of the game description that often admits multiple models and studying a game as a specific model that is somehow assumed to be commonly known. This gap has been largely ignored or covered up by using as examples simple epistemic scenarios with natural models that were tacitly used as definitions of the game instead of declared syntactic game descriptions. Among others, Aumman found this unsatisfactory and argued for using what he called ‘Syntactic epistemic logic’ in reasoning about games.
In this talk, we outline a systematic approach to epistemic game theory which we suggest calling ‘Syntactic Epistemic Game Theory’, SEGT, consistent with Aumann’s suggestions, that studies games as they are normally described, in their syntactic form. In SEGT, semantic methods should be properly justified from the original game description. As a case study, we offer a SEGT theory of definitive solutions of strategic games with ordinal payoffs.
Read the paper here