http://www.mdpi.com/journal/games/special_issues/epistemic-gt/ Dear Colleagues, The contemporary culture of game theorists and experimentalists was formed in the period 1980-1995, and is virtually free of understanding of the role of the modal logic of knowledge and belief in evaluating models of rational behavior and their equilibrium properties. There is, of course, a specialized literature, including Nobel prize recipient Robert Aumann and his students, but this is ill-understood and indeed widely ignored outside this circle of experts. As a result, most economists simply do no know what the implications of rationality really are. I want papers in this special issue to show the relevance of epistemic game theory for the working economist and experimentalist. I tried to go some distance towards this goal in my recent book, The Bounds of Reason (Princeton, 2009), but there is much work to be done and much misinformation to be corrected. Prof. Dr. Herbert Gintis Guest Editor {snippet name="submission_info"} http://www.mdpi.com/2073-4336/2/1/52/ Logic and game theory have had a few decades of contacts by now, with the classical results of epistemic game theory as major high-lights. In this paper, we emphasize a recent new perspective toward “logical dynamics”, designing logical systems that focus on the actions that change information, preference, and other driving forces of agency. We show how this dynamic turn works out for games, drawing on some recent advances in the literature. Our key examples are the long-term dynamics of information exchange, as well as the much-discussed issue of extensive game rationality. Our paper also proposes a new broader interpretation of what is happening here. The combination of logic and game theory provides a fine-grained perspective on information and interaction dynamics, and we are witnessing the birth of something new which is not just logic, nor just game theory, but rather a Theory of Play. http://www.mdpi.com/2073-4336/2/1/52/ Wed, 16 Feb 2011 00:00:00 CET Games 2011-02-16 2 1 Article 52 86 2073-4336 Toward a Theory of Play: A Logical Perspective on Games and Interaction 2011-02-16 doi: 10.3390/g2010052 Johan Van Benthem Eric Pacuit Olivier Roy http://www.mdpi.com/2073-4336/1/4/478/ We propose some variants of a multi-modal of joint action, preference and knowledge that support reasoning about epistemic games in strategic form. The first part of the paper deals with games with complete information. We first provide syntactic proofs of some well-known theorems in the area of interactive epistemology that specify some sufficient epistemic conditions of equilibrium notions such as Nash equilibrium and Iterated Deletion of Strictly Dominated Strategies (IDSDS). Then, we present a variant of the logic extended with dynamic operators of Dynamic Epistemic Logic (DEL). We show that it allows to express the notion IDSDS in a more compact way. The second part of the paper deals with games with weaker forms of complete information. We first discuss several assumptions on different aspects of perfect information about the game structure (e.g., the assumption that a player has perfect knowledge about the players’ strategy sets or about the preference orderings over strategy profiles), and show that every assumption is expressed by a corresponding logical axiom of our logic. Then we provide a proof of Harsanyi’s claim that all uncertainty about the structure of a game can be reduced to uncertainty about payoffs. Sound and complete axiomatizations of the logics are given, as well as some complexity results for the satisfiability problem. http://www.mdpi.com/2073-4336/1/4/478/ Tue, 02 Nov 2010 00:00:00 CET Games 2010-11-02 1 4 Article 478 526 2073-4336 A Modal Logic of Epistemic Games 2010-11-02 doi: 10.3390/g1040478 Emiliano Lorini François Schwarzentruber http://www.mdpi.com/2073-4336/1/4/415/ We introduce consistency of beliefs in the space of hierarchies of conditional beliefs (Battigalli and Siniscalchi) and use it to provide epistemic conditions for equilibria in finite multi-stage games with observed actions. http://www.mdpi.com/2073-4336/1/4/415/ Wed, 20 Oct 2010 00:00:00 CEST Games 2010-10-20 1 4 Article 415 421 2073-4336 Consistent Beliefs in Extensive Form Games 2010-10-20 doi: 10.3390/g1040415 Paulo Barelli http://www.mdpi.com/2073-4336/1/4/381/ It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski’s Fixpoint Theorem. http://www.mdpi.com/2073-4336/1/4/381/ Fri, 08 Oct 2010 00:00:00 CEST Games 2010-10-08 1 4 Article 381 394 2073-4336 The Role of Monotonicity in the Epistemic Analysis of Strategic Games 2010-10-08 doi: 10.3390/g1040381 Krzysztof R. Apt Jonathan A. Zvesper http://www.mdpi.com/2073-4336/1/3/168/ In this paper we want to shed some light on what we mean by backward induction and forward induction reasoning in dynamic games. To that purpose, we take the concepts of common belief in future rationality (Perea [1]) and extensive form rationalizability (Pearce [2], Battigalli [3], Battigalli and Siniscalchi [4]) as possible representatives for backward induction and forward induction reasoning. We compare both concepts on a conceptual, epistemic and an algorithm level, thereby highlighting some of the crucial differences between backward and forward induction reasoning in dynamic games. http://www.mdpi.com/2073-4336/1/3/168/ Fri, 02 Jul 2010 00:00:00 CEST Games 2010-07-02 1 3 Article 168 188 2073-4336 Backward Induction versus Forward Induction Reasoning 2010-07-02 doi: 10.3390/g1030168 Perea