Recent results on belief, knowledge and the epistemic foundations of game theory

Abstract

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Epistemic Games in Modal Logic: Joint Actions, Knowledge and Preferences All Together

“…The following EDLA formula characterizes a notion of rationality which is commonly supposed in epistemic analysis of games (see, e.g., [3,5]):…”

“…Our logic supports reasoning about epistemic games in strategic form in which agents decide what to do according to some general principles of rationality while being uncertain about several aspects of the interaction such as other agents' choices, other agents' preferences, etc. Although epistemic games have been extensively studied in economics in the so-called area of interactive epistemology (see, e.g., [1,10,9,3,11]) and there have been some analysis of epistemic games in modal logic (see, e.g., [5,12,9,21]), no modal approach to epistemic games in strategic form has been proposed up to now which addresses all the following issues at the same time: to provide a formal language, and a corresponding formal semantics, which is sufficiently general to express solution concepts like Nash Equilibrium or Iterated Deletion of Strictly Dominated Strategies (IDSDS) and to deduce formally the epistemic and rationality conditions on which such solution concepts are based; to prove its soundness and completeness; to study its computational properties like decidability and complexity. In this paper, we try to fill this gap by proposing a sound and complete modal logic for epistemic games interpreted on a Kripke-style semantics.…”

Reasoning About Strategies and Rational Play in Dynamic Games

“…16 Thus, if at a state ω there is common belief of rationality then, for every player i, σ i (ω) survives the iterated deletion of strictly dominated strategies. For more details on this result, which originates in Bernheim (1984) and Pearce (1984), and relevant references, see Battigalli and Bonanno (1999), Bonanno (forthcomingb), Dekel and Gul (1997), Perea (2012). 17 For an extensive discussion see Halpern (1999b).…”

“…Such functions are called possibility correspondences (or information functions) in the game-theoretic literature. 7 For more details see the survey in Battigalli and Bonanno (1999). 8 In modal logic belief operators are defined as syntactic operators on formulas.…”

Strategy Elimination in Games with Interaction Structures

“…There is a substantial amount of research within game theory on the implications of assumptions concerning players' knowledge and beliefs [5]. In particular, Tan and Werlang [16] have shown that if payoffs are commonly known and all players are rational and commonly believe in each other's rationality, they will only play strategies that survive iterated elimination of strictly dominated strategies (IESDS).…”