TITLE: GAME SOLUTION, EPISTEMIC DYNAMICS, AND FIXED-POINT LOGICS

SPEAKER: Johan van Benthem, Amsterdam & Stanford, http://staff.science.uva.nl/~johan
 
WHEN: 10:00-12:00, 27 April
 
WHERE: Room 2736, 理科2号楼7层， Peking University

ABSTRACT: Logic, game theory and computer science share many research themes. This
lecture is about one more interface, taking a model-theoretic look at games.
Current methods for solving games embody a form of ‘procedural rationality’
that invites logical analysis in its own right. This lecture is a brief case study
of Backward Induction for extensive games, replacing the usual static epistemic
foundations of game theory by dynamic ones. We will analyze some new logical
proposals for game solution from recent years, in particular, iterated announce-
ments of players' rationality, and iterated belief revision by plausibility upgrade
with 'rationality-in-beliefs'. We find that these views are mathematically equivalent,
pointing at an underlying invariant logical structure. We then explore how standard
fixed-point logics on finite trees may fit such game-theoretic equilibrium invariants.
We end with a broader program for interfacing computational logic and game theory.

References: (a) J. van Benthem, 2010, "Logical Dynamics of Information and Interaction",
Cambridge University Press, Cambridge. (b) A. Gheerbrant, 2010, "Logics of Finite Trees",
dissertation, Institute for Logic, Language and Computation ILLC, University of Amsterdam.