•  564
    Decision Making
    CreateSpace Independent Publishing Platform. 2017.
    This text provides an introduction to the topic of rational decision making as well as a brief overview of the most common biases in judgment and decision making. "Decision Making" is relatively short (300 pages) and richly illustrated with approximately 100 figures. It is suitable for both self-study and as the basis for an upper-division undergraduate course in judgment and decision making. The book is written to be accessible to anybody with minimum knowledge of mathematics (high-school level…Read more
  •  378
    There is an ongoing debate in the philosophical literature whether the conditionals that are central to deliberation are subjunctive or indicative conditionals and, if the latter, what semantics of the indicative conditional is compatible with the role that conditionals play in deliberation. We propose a possible-world semantics where conditionals of the form “if I take action _a_ the outcome will be _x_” are interpreted as material conditionals. The proposed framework is illustrated with famili…Read more
  •  299
    Logics for Belief as Maximally Plausible Possibility
    Studia Logica 108 (5): 1019-1061. 2020.
    We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction properties between certainty and pl…Read more
  •  289
    Game Theory
    CreateSpace Independent Publishing Platform. 2018.
    This is a two-volume set that provides an introduction to non-cooperative Game Theory. Volume 1 covers the basic concepts, while Volume 2 is devoted to advanced topics. The book is richly illustrated with approximately 400 figures. It is suitable for both self-study and as the basis for an undergraduate course in game theory as well as a first-year graduate-level class. It is written to be accessible to anybody with high-school level knowledge of mathematics. At the end of each chapter there i…Read more
  •  247
    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
  •  134
    Belief revision in a temporal framework
    In Krzysztof Apt & Robert van Rooij (eds.), New Perspectives on Games and Interaction, Amsterdam University Press. 2008.
    The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update (see [6]). The former deals with situations where the objective facts describing the world do not change (so that only the beliefs of the agent change over time), while the letter allows for situations where both the facts and the doxastic state of the agent change over time. We focus on belief revision and…Read more
  •  128
    Modal logic and game theory: Two alternative approaches
    Risk 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.
  •  119
    A Simple Modal Logic for Belief Revision
    Synthese 147 (2): 193-228. 2005.
    We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes’ rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows and iterated revision are also discussed.
  •  112
    The Logic of Belief Persistence
    with Pierpaolo Battigalli
    Economics 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
  •  99
    Belief 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
  •  99
    Common belief with the logic of individual belief
    Mathematical 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
  •  95
    Introduction to the special issue of economics and philosophy on neuroeconomics
    with Christian List, Bertil Tungodden, and Peter Vallentyne
    Economics and Philosophy 24 (3): 301-302. 2008.
    ABSTRACT The past fifteen years or so have witnessed considerable progress in our understanding of how the human brain works. One of the objectives of the fast-growing field of neuroscience is to deepen our knowledge of how the brain perceives and interacts with the external world. Advances in this direction have been made possible by progress in brain imaging techniques and by clinical data obtained from patients with localized brain lesions. A relatively new field within neuroscience is neuroe…Read more
  •  93
    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
  •  92
    Can 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
  •  86
    Rational beliefs in extensive games
    Theory and Decision 33 (2): 153-176. 1992.
  •  84
    How to make sense of the com M on P ri or assumption under incomplete information
    with Klaus Nehring
    International Journal of Game Theory 28 (3): 409-434. 1999.
    The Common Prior Assumption (CPA) plays an important role in game theory and the economics of information. It is the basic assumption behind decision-theoretic justifications of equilibrium reasoning in games (Aumann, 1987, Aumann and Brandenburger, 1995) and no-trade results with asymmetric information (Milgrom and Stokey, 1982). Recently several authors (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned whether the CPA is meaningful in situations of incomplete information, where th…Read more
  •  81
    A syntactic approach to rationality in games with ordinal payoffs
    In Giacomo Bonanno, Wiebe van der Hoek & Michael Wooldridge (eds.), Logic and the Foundations of Game and Decision Theory, Amsterdam University Press. 2008.
    We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom s…Read more
  •  73
    Memory and perfect recall in extensive games
    Games 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.
  •  72
    The Logic of Rational Play in Games of Perfect Information
    Economics and Philosophy 7 (1): 37-65. 1991.
    For the past 20 years or so the literature on noncooperative games has been centered on the search for an equilibrium concept that expresses the notion of rational behavior in interactive situations. A basic tenet in this literature is that if a “rational solution” exists, it must be a Nash equilibrium. The consensus view, however, is that not all Nash equilibria can be accepted as rational solutions. Consider, for example, the game of Figure 1
  •  70
    Guest Editors' Introduction
    with James Delgrande and Hans Rott
    Journal of Philosophical Logic 41 (1): 1-5. 2012.
    The contributions to the Special Issue on Multiple Belief Change, Iterated Belief Change and Preference Aggregation are divided into three parts. Four contributions are grouped under the heading "multiple belief change" (Part I, with authors M. Falappa, E. Fermé, G. Kern-Isberner, P. Peppas, M. Reis, and G. Simari), five contributions under the heading "iterated belief change" (Part II, with authors G. Bonanno, S.O. Hansson, A. Nayak, M. Orgun, R. Ramachandran, H. Rott, and E. Weydert). These pa…Read more
  •  68
    Varieties of interpersonal compatibility of beliefs
    In 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
  •  68
    Temporal Interaction of Information and Belief
    Studia 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.
  •  64
    Rational choice and agm belief revision
    Artificial 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..
  •  62
    On Stalnaker's Notion of Strong Rationalizability and Nash Equilibrium in Perfect Information Games
    with Klaus Nehring
    Theory and Decision 45 (3): 291-295. 1998.
    Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition ‘strong rationalizability’), then the true (or actual) strategy profile is path equivalent to a Nash e…Read more
  •  60
    Branching time, perfect information games and backward induction
    Games and Economic Behavior 36 (1): 57-73. 2001.
    The logical foundations of game-theoretic solution concepts have so far been explored within the con¯nes of epistemic logic. In this paper we turn to a di®erent branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. The branching time framework is extended by adding agents and by de¯ning the notion of prediction. A syntactic characterization of backward induction in terms of the property of internal consistency of pred…Read more
  •  59
    Introduction to the special issue of economics and philosophy on ambiguity aversion
    with Martin van Hees, Christian List, and Bertil Tungodden
    Economics and Philosophy 25 (3): 247-248. 2009.
    The paradigm for modelling decision-making under uncertainty has undoubtedly been the theory of Expected Utility, which was first developed by von Neumann and Morgenstern (1944) and later extended by Savage (1954) to the case of subjective uncertainty. The inadequacy of the theory of Subjective Expected Utility (SEU) as a descriptive theory was soon pointed out in experiments, most famously by Allais (1953) and Ellsberg (1961). The observed departures from SEU noticed by Allais and Ellsberg beca…Read more
  •  52
    Vertical separation
    with John Vickers
    Journal of Industrial Economics 36 (3): 257-265. 1988.
    behaviour from the rival manufacturer. We consider the case where franchise fees can be used to extract retailers' surplus. We show that vertical separation is in the collective, as well as individual, interest of manufacturers, and hence facilitates some collusion in the simple setting..
  •  50
    Memory of Past Beliefs and Actions
    Studia Logica 75 (1): 7-30. 2003.
    Two notions of memory are studied both syntactically and semantically: memory of past beliefs and memory of past actions. The analysis is carried out in a basic temporal logic framework enriched with beliefs and actions.
  •  50
    Review of Cristina Bicchieri's rationality and coordination (review)
    Economics and Philosophy 11 (2): 359-366. 1995.
    In her book Rationality and coordination (Cambridge University Press, 1994) Cristina Bicchieri brings together (and adds to) her own contributions to game theory and the philosophy of economics published in various journals in the period 1987-1992. The book, however, is not a collection of separate articles but rather a homogeneous unit organized around some central themes in the foundations of non-cooperative game theory. Bicchieri’s exposition is admirably clear and well organized. Somebody wi…Read more