Game Solution, Epistemic Dynamics and Fixed-Point Logics

13 years 3 months ago

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Abstract. Current methods for solving games embody a form of “procedural rationality” that invites logical analysis in its own right. This paper is a brief case study of Backward Induction for extensive games, replacing earlier static logical deﬁnitions by stepwise dynamic ones. We consider a number of analysis from recent years that look different conceptually, and ﬁnd that they are all mathematically equivalent. This shows how an abstract logical perspective can bring out basic invariant structure in games. We then generalize this to an exploration of ﬁxed-point logics on ﬁnite trees that best ﬁt game-theoretic equilibria. We end with some open questions that suggest a broader program for merging current computational logics with notions and results from game theory. This paper is largely a program for opening up an area: an extended version of the technical results will be found in the forthcoming dissertation [26].

Johan van Benthem, Amélie Gheerbrant

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