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79Varieties of interpersonal compatibility of beliefsIn Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema (eds.), Essays dedicated to Johan van Benthem on the occasion of his 50th birthday, Amsterdam University Press. 1999.Since Lewis’s (1969) and Aumann’s (1976) pioneering contributions, the concepts of common knowledge and common belief have been discussed extensively in the literature, both syntactically and semantically1. At the individual level the difference between knowledge and belief is usually identified with the presence or absence of the Truth Axiom ( iA → A), which is interpreted as ”if individual i believes that A, then A is true”. In such a case the individual is often said to know that A (thus it i…Read more
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256A characterization of Von Neumann games in terms of memorySynthese 139 (2). 2004.An information completion of an extensive game is obtained by extending the information partition of every player from the set of her decision nodes to the set of all nodes. The extended partition satisfies Memory of Past Knowledge (MPK) if at any node a player remembers what she knew at earlier nodes. It is shown that MPK can be satisfied in a game if and only if the game is von Neumann (vN) and satisfies memory at decision nodes (the restriction of MPK to a player's own decision nodes). A game…Read more
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42Revising predictionsIn Johan van Benthem (ed.), Theoretical aspects of rationality and knowledge, . 2001.Making a prediction is essentially expressing a belief about the future. It is therefore natural to interpret later predictions as revisions of earlier ones and to investigate the notion of belief revision in this context. We study, both semantically and syntactically, the following principle of minimum revision of prediction: “as long as there are no surprises, that is, as long as what actually occurs had been predicted to occur, then everything which was predicted in the past, if still possibl…Read more
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42On the Logic of Common BeliefMathematical Logic Quarterly 42 (1): 305-311. 1996.We investigate an axiomatization of the notion of common belief that makes use of no rules of inference and highlight the property of the set of accessibility relations that characterizes each axiom
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76Memory and perfect recall in extensive gamesGames and Economic Behavior 47 (2): 237-256. 2004.The notion of perfect recall in extensive games was introduced by Kuhn (1953), who interpreted it as "equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves''. We provide a characterization and axiomatization of perfect recall based on two notions of memory: (1) memory of past knowledge and (2) memory of past actions.
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39Oligopoly equilibria when firms have local knowledge of demandInternational Economic Review 29 (1): 45-55. 1988.The notion of Nash equilibrium in static oligopoly games is based on the assumption that each firm knows its entire demand curve (and, therefore, its entire profit function). It is much more likely, however, that firms only have some idea of the outcome of small price variations within some relatively small interval of prices. This is because firms can only learn their demand functions through price experiments and if they are risk-averse and/or have a low discount factor, they will be unwilling…Read more
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106Belief Change in Branching Time: AGM-consistency and Iterated Revision (review)Journal of Philosophical Logic 41 (1): 201-236. 2012.We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AG…Read more
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44Temporal Interaction of Information and BeliefStudia Logica 86 (3): 375-401. 2007.The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t, contains a normal belief operator B t and a non-normal information operator I t which is analogous to the ‘only knowing’ operator discussed in the computer science literature. Soundness and completeness of the logic are proved and the relationship between the proposed logic, the AGM theory of belief revision and the notion of plausibility is discussed.
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15Logic and the Foundations of Game and Decision Theory (edited book)Amsterdam University Press. 2008.This volume is a collects papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT), held at the University of Liverpool in July 2006. LOFT is a key venue for presenting research at the intersection of logic, economics, and computer science, and this collection gives a lively and wide-ranging view of an exciting and rapidly growing area.
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103Common belief with the logic of individual beliefMathematical Logic Quarterly 46 (1): 49-52. 2000.The logic of common belief does not always reflect that of individual beliefs. In particular, even when the individual belief operators satisfy the KD45 logic, the common belief operator may fail to satisfy axiom 5. That is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. We identify the intersubjective restrictions on individual beliefs that are incorporated in axiom 5 for common belief
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46Rationality and Coordination, Bicchieri Cristina. Cambridge University Press, 1994, xiii + 270 pages (review)Economics and Philosophy 11 (2): 359. 1995.
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97Axiomatic characterization of the AGM theory of belief revision in a temporal logicArtificial Intelligence 171 (2-3): 144-160. 2007.Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiom…Read more
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30Reply to `social cost and Groves mechanisms'Economic Notes 31 173-176. 2002.In my 1992 paper in Economic Notes, I argued that the traditional heuristic interpretation of taxes in the pivotal mechanism (in terms of the utility loss imposed by the taxed individual on the rest of society) is not correct, since it takes into account only the effect that the individual has on the decision concerning the project and disregards the effect that the same individual has on the taxes paid by the other members of society. Campbell criticizes my observation on two grounds
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95Can good news lead to a more pessimistic choice of action?Theory and Decision 25 (2): 123-136. 1988.Adapting a definition introduced by Milgrom (1981) we say that a signal about the environment is good news relative to some initial beliefs if the posterior beliefs dominate the initial beliefs in the sense of first-order stochastic dominance (the assumption being that higher values of the parameter representing the environment mean better environments). We give an example where good news leads to the adoption of a more pessimistic course of action (we say that action a, reveals greater pessimis…Read more
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130Modal logic and game theory: Two alternative approachesRisk Decision and Policy 7 309-324. 2002.Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It is shown that the same mathematical tool, namely modal logic, can be used to explicitly model both views.
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50Intensity of competition and the choice between product and process innovationInternational Journal of Industrial Organization 16 (4): 495-510. 1998.Two questions are examined within a model of vertical differentiation. The first is whether cost-reducing innovations are more likely to be observed in regimes of more intense or less intense competition. Following Delbono and Denicolo (1990) and Bester and Petrakis (1993) we compare two identical industries that differ only in the regime of competition: Bertrand versus Cournot. Since Cournot competition leads to lower output and higher prices, it can be thought of as a regime of less intense co…Read more
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91The Logic of Belief PersistenceEconomics and Philosophy 13 (1): 39-59. 1997.The principle of belief persistence, or conservativity principle, states that ’\Nhen changing beliefs in response to new evidence, you should continue to believe as many of the old beliefs as possible' (Harman, 1986, p. 46). In particular, this means that if an individual gets new information, she has to accommodate it in her new belief set (the set of propositions she believes), and, if the new information is not inconsistent with the old belief set, then (1) the individual has to maintain all …Read more
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68Rational choice and agm belief revisionArtificial Intelligence 173 (12-13): 1194-1203. 2009.We establish a correspondence between the rationalizability of choice studied in the revealed preference literature and the notion of minimal belief revision captured by the AGM postulates. A choice frame consists of a set of alternatives , a collection E of subsets of (representing possible choice sets) and a function f : E ! 2 (representing choices made). A choice frame is rationalizable if there exists a total pre-order R on..
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Logic and the Foundations of Game and Decision Theory  Loft 8 (edited book)Springer Berlin Heidelberg. 2010.
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58Editorial Introduction to the Special Issue LOFT SevillaJournal of Philosophical Logic 42 (6): 795-798. 2013.
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44Reply to VilksEconomics and Philosophy 10 (1): 115. 1994.In his note Arnis Vilks raises two criticisms concerning my paper "The Logic of Rational Play in Extensive Games". The author gives two examples: one to show that my logic "is inconsistent.
London School of Economics
PhD, 1985
Davis, California, United States of America
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Epistemology |
Logic and Philosophy of Logic |
Other Academic Areas |