Game Solution, Epistemic Dynamics and Fixed-Point Logics

Issue title: Understanding Computers' Intelligence Celebrating the 100th Volume of Fundamenta Informaticae in Honour of Helena Rasiowa

Article type: Research Article

Authors: van Benthem, Johan | Gheerbrant, Amélie

Affiliations: ILLC, University of Amsterdam, The Netherlands. E-mail: johan@science.uva.nl, A.Gheerbrant@uva.nl

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].

Keywords: Backward Induction, ExtensiveGames, Dynamic-Epistemic Logic, Fixed-Point Logic

DOI: 10.3233/FI-2010-261

Journal: Fundamenta Informaticae, vol. 100, no. 1-4, pp. 19-41, 2010