[1985,  1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024,]

            To download the paper in pdf format click here:  predict.pdf  
48. Giacomo Bonanno, “Revising predictions ”,  in: Johan van Benthem (ed.), Theoretical aspects of rationality and knowledge
      (TARK 2001), Morgan Kaufman, San Francisco, 2001, pp. 273-286.

Abstract.

    Making a prediction is essentially expressing a belief about the future. It is therefore natural to interpret later predictions as revisions of earlier predictions 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 possible, should continue to be predicted, and no new predictions should be added". We also study and characterize a notion of consistency of prediction as well as further properties that one might want to impose on the notion of prediction.
 

            To download the paper in pdf format click here: revpred.pdf   also here: ACM_digital_lib           
49. Giacomo Bonanno, “Branching Time Logic, Perfect Information Games and Backward Induction”,
       Games and Economic Behavior, 36 (1), July 2001, pp. 57-73.
Abstract.
    The logical foundations of game-theoretic solution concepts have so far been developed within the confines of epistemic logic. In this paper we turn to a different branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. We extend the branching time framework by adding agents and by defining the notion of prediction. We show that perfect information games are a special case of extended branching time frames and that the backward-induction solution is a prediction. We also provide a characterization of backward induction in terms of the property of internal consistency of prediction.


           To download the paper in pdf format click here: bi_logic.pdf
           Link to the journal article:  published article
 

2002
50. Giacomo Bonanno, Reply to “Social cost and Groves mechanisms”, Economic Notes, 31, 2002, pp. 173-176.

Abstract.

    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 criticized my observation on the grounds that (1) “[Bonanno’s] analysis cannot be generalized to the case of positive cost because the allocation that [Bonanno] employs to compute social cost is not feasible in that case”, and (2) “[Bonanno’s] definition is not institution free”.  In this paper  I reply to both charges and defend my original observation.

            To download the paper in pdf format click here: Reply.pdf

51. Giacomo Bonanno, “Information, knowledge and belief”, Bulletin of Economic Research, 54, January 2002, pp. 47-67.

Abstract.

    We model information as possibilities consistent with signals received from the environment. Knowledge is obtained by reasoning about the signals received as well as those that might have been received but were not. We use the term `knowledge' to refer to those beliefs that are obtained by reasoning about the available information and nothing else. That is, one ought to be able to fully justify what one knows by means of the information that is available to her. We use the term `belief' to refer to those beliefs that are based on information but not necessarily only on information. We investigate the relationship between information, knowledge and belief, as well as the issue of updating knowledge and belief in response to changes in information.

            To download the paper in pdf format click here: information.pdf           

52. Giacomo Bonanno, “Modal logic and game theory: two alternative approaches”, Risk Decision and Policy, 7,
                                         December 2002, pp. 309-324.

Abstract.

    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.

            To download the paper in pdf format click here: Rimini.pdf           

2003

53. Giacomo Bonanno, “A syntactic characterization of perfect recall in extensive games”, Research in Economics,
                                         57 (3), September 2003, pp. 201-217.

Abstract.

    We provide a syntactic characterization of the property of perfect recall in extensive games. The language we use is basic temporal logic with the addition of a knowledge operator for every player.
.

            To download the paper in pdf format click here: Loft5.pdf           
           Link to the journal article:  http://authors.elsevier.com/sd/article/S1090944303000358

54. Giacomo Bonanno, “Memory of past beliefs and actions”, Studia Logica, 75 (1), October 2003, pp. 7-30.

Abstract.

    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. .

            To download the paper in pdf format click here:  from JSTOR  or  Memory.pdf            

2004

55. Giacomo Bonanno, “Memory and perfect recall in extensive games”, Games and Economic Behavior, 47 (2), May 2004, pp. 237-256.

Abstract.

    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..
.

            To download the paper in pdf format click here: PerfRec.pdf
           Also available at:  http://repositories.cdlib.org/postprints/26
            Link to the journal article:  http://authors.elsevier.com/sd/article/S0899825603001933

56. Giacomo Bonanno, “A characterization of von Neumann games in terms of memory", Synthese, 139 (2), March 2004, pp. 237-256 (and Knowledge, Rationality and Action, 2004, pp. 117-131).

Abstract.

    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 is vN if any two
decision nodes that belong to the same information set of a player have the same number of predecessors. By providing an axiom for MPK we also obtain a syntactic characterization
of the said class of vN games..
.

            To download the paper in pdf format click here:  from JSTOR   or   pre-print: vNM.pdf
           Link to the journal article: http://dx.doi.org/10.1023/B:SYNT.0000024905.25386.3d

2005

57. Giacomo Bonanno, “A simple modal logic for belief revision”, Synthese, 147 (2), 2005, pp. 193-228 (and Knowledge, Rationality and Action, 2005, pp. 5-40).
      Reprinted in van der Hoek, Wiebe, (Ed.), Uncertainty, rationality and agency, Springer, Dordrect, 2006, pp. 139-174.

Abstract.

    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.
.

            To download the paper in pdf format click here:  from JSTOR  or   pre-print: BelRev.pdf
            Link to the journal article: http://dx.doi.org/10.1007/s11229-005-1348-8

2006

58. Giacomo Bonanno, “Belief revision in a temporal framework: extended abstract”, Proceedings of the 7th conference on Logic and the Foundations of Game and Decision Theory, University of Liverpool, 2006, pp. 43-50.
Abstract.

    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. 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 propose a temporal framework that allows for iterated revision. We model the notion of "minimal" or "conservative" belief revision by considering logics of increasing strength. We move from one logic to the next by adding one or more axioms and show that the corresponding logic captures more stringent notions of minimal belief revision.

            To download the paper in pdf format click here: LOFT7.pdf


2007

59. Giacomo Bonanno, “Axiomatic characterization of the AGM theory of belief revision in a temporal logic”, Artificial Intelligence,  171 (2-3), February 2007, pp. 144–160.

Abstract.

    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 axiomatic characterization of the full set of AGM postulates.

            To download the pre-print version in pdf format click here: AGM.pdf

            Link to the journal article: http://dx.doi.org/10.1016/j.artint.2006.12.001


60. Giacomo Bonanno, "Temporal interaction of information and belief", Studia Logica,  86, 2007, pp. 381-407.

Abstract.

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 Bt and a non-normal information operator It 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 plausbility is discussed.

           To download the paper in pdf format click here:  from JSTOR  or   InfBel.pdf


2008

61. Giacomo Bonanno, "A syntactic approach to rationality in games with ordinal payoffs", in: G. Bonanno, W. van der Hoek and M. Wooldridge (eds.), Logic and the Foundations of Game and Decision Theory, Texts in Logic and Games Series, Amsterdam University Press, 2008, pp. 59-86.  (ISBN: 978 908 964 0260)

Abstract.

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 says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994). Frame characterization results are also provided.

           To download the paper in pdf format click here: CBR.pdf   or  from JSTOR


62. Giacomo Bonanno, “Belief revision in a temporal framework”, in Krzysztof R. Apt and Robert van Rooij (eds.), New Perspectives on Games and Interaction, Texts in Logic and Games Series, Amsterdam University Press, 2008, pp. 45-79.

Abstract.

We study a branching-time temporal logic of belief revision where the interaction of belief and information is modeled explicitly. The logic is based on three modal operators: a belief operator, an information operator and a next-time operator. We consider three logics of increasing strength. The first captures the most basic notion of minimal belief revision. The second characterizes the qualitative content of Bayes' rule. The third is the logic proposed in Bonanno, Artificial Intelligence, 2007, where some aspects of its relationship with the AGM theory of belief revision were investigated. We further explore the relationship to AGM with the help of semantic structures that have been used in the rational choice literature. Further strengthening of the logic are also investigated.

           To download the paper in pdf format click here:  from JSTOR   or   pre-print: KNAW.pdf


63. Giacomo Bonanno, "A sound and complete temporal logic for belief revision", in Cédric Dégremont, Laurent Keiff and Helge Rückert (eds), Dialogues, Logics and Other Strange Things: Essays in Honour of Shahid Rahman, College Publications, 2008 (http://www.collegepublications.co.uk/tributes/?00007), pp. 67-80.

Abstract.

Branching-time temporal logic offers a natural setting for a theory of belief change. We propose a temporal logic that, besides the next-time operator, contains a belief operator and an information operator. It is shown that this logic is sound and complete with respect to the class of branching-time frames augmented, for each instant t, with a set of states and two binary relations on it, representing beliefs and information, respectively.

           To download the paper in pdf format click here: Complete.pdf


2009

64. Giacomo Bonanno, "Rational choice and AGM belief revision", Artificial Intelligence, 173, 2009, pp. 1194-1203.

Abstract.

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 W, a collection C of subsets of W (representing possible choice sets) and a function f  from C  into the set of subsets of W  (representing choices made). A choice frame is rationalizable if there exists a total pre-order R on W such that, for every E in C, f(E) coincides with the best elements of E relative to R. We re-interpret choice structures in terms of belief revision. An interpretation is obtained by adding a valuation that assigns to every atom p the subset of W at which p is true. Associated with an interpretation is an initial belief set and a partial belief revision function. A choice frame is AGM-consistent if, for every interpretation of it, the associated partial belief revision function can be extended to a full-domain belief revision function that satisfies the AGM postulates. It is shown that a finite choice structure is AGM-consistent if and only if  it is rationalizable..

           To download the pre-print version  in pdf format click here: Choice_AI.pdf

           Link to the journal article: http://dx.doi.org/10.1016/j.artint.2009.05.001


2010

65. Giacomo Bonanno, "Answers to five questions on epistemic logic", in Vincent F. Hendricks and Olivier Roy (Eds.), Epistemic logic: 5 questions, Automatic Press / VIP, pp. 37-47.

Editors' abstract.

Epistemic Logic: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in the field. We hear their views on the field, the aim, the scope, the future direction of research and how their work fits in these respects. Interviews with Horacio Arló-Costa, Sergei Artemov, Robert Aumann, Johan van Benthem, Giacomo Bonanno, Adam Brandenburger, Hans van Ditmarsch, Melvin Fitting, Paul Gochet, Joseph Y. Halpern, Sven Ove Hansson, Aviad Heifetz, Jaakko Hintikka, Wiebe van der Hoek, Wolfgang Lenzen, John-Jules Ch. Meyer, Lawrence S. Moss, Rohit Parikh, Wlodek Rabinowicz, R. Ramanujam, Krister Segerberg, Yoav Shoham, John Sowa, Robert Stalnaker, Timothy Williamson
.

           To download the pre-print version  in pdf format click here: 5Questions.pdf

           Link to Amazon's site for the book: http://www.amazon.com/exec/obidos/ASIN/8792130240/ref=nosim/porfessionalp4-20


2011

66. Giacomo Bonanno, "Game Theory", Chapter 15 of the Sage Handbook of Philosophy of the Social Science edited by Ian C Jarvie and Jesus Zamora-Bonilla, Sage Publications,  2011, 322-338.

Abstract.

Game theory, which deals with interactive decision making, plays a central role in the social sciences. This chapter provides an introduction to non-cooperative game theory with a focus on philosophical and epistemological issues. The analysis covers both strategic-form (or normal-form) games and extensive-form (or dynamic) games. The focus of the chapter is on the epistemic foundation program in game theory which aims to identify, for every game, the strategies that might be chosen by rational and intelligent players who know the structure of the game and the preferences of their opponents and who recognize each other’s rationality.  Important notions, such as (common) belief and (common) knowledge, are defined precisely, by means of multi-agent Kripke models. The relationship between common belief of rationality and various solution concepts (such as the elimination of dominated strategies, Nash equilibrium and backward induction) is explored. The role of counterfactual reasoning in games is also addressed. Games of incomplete information are also discussed and analyzed in terms of Kripke structures.
.

           Link to publisher's site for the handbook: http://www.uk.sagepub.com/booksProdDesc.nav?contribId=512629&prodId=Book232751#tabview=toc 

67. Giacomo Bonanno, "AGM belief revision in dynamic games", in: Krzysztof R. Apt (Editor),  Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XIII), ACM, New York, 2011, 37-45.

Abstract.

Within the context of extensive-form (or dynamic) games, we use choice frames to represent the initial beliefs of a player as well as her disposition to change those beliefs when she learns that an information set of hers has been reached. As shown in Bonanno (Artificial Intelligence 173: 1194-1203), in order for the revision operation to be consistent with the AGM postulates, the player's choice frame must be rationalizable in terms of a total pre-order on the set of histories. We consider four properties of choice frames and show that, together with the hypothesis of a common prior, are necessary and sufficient for the existence of a plausibility order that rationalizes the epistemic state (that is, initial beliefs and disposition to revise those beliefs) of all the players. The plausibility order satisfies the properties introduced in a companion paper (see item 69 below) as part of a new definition of perfect Bayesian equilibrium for dynamic games. Thus the present paper provides epistemic foundations for that solution concept.

      Download the pdf file form the TARK website: TARK_2011.pdf      (http://www.tark.org/proceedings/tark_jul11_11/proceedings.html)

      Link to the published article:  http://dl.acm.org/authorize?445343   (also http://dl.acm.org/toc.cfm?id=2000378 )


68. Giacomo Bonanno, "Economics of uncertainty and information",  in Fundamental Economics [Ed. Mukul Majmdar], in Encyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, EOLSS Publishers, Oxford, UK, 2011.

Abstract.

This chapter gives a non-technical overview of the main topics in the economics of uncertainty and information. We begin by distinguishing between uncertainty and risk and defining possible attitudes to risk. We then focus on  risk-aversion and examine its role in insurance markets. The next topic is asymmetric information, that is, situations where two parties to a potential transaction do not have the same information; in particular, one of the two parties has valuable information that is not available to the other party. Three important phenomena that arise in situations of asymmetric information are adverse selection, signaling and screening. Each of these topics is analyzed in detail with the help of simple examples. We then turn to the issue of optimal risk-sharing in contracts between two parties, called Principal and Agent, when the outcome of the contractual relationship depends on external states that are not under the control of either party. Finally we touch on the issues that arise when the Agent does have partial control over the outcome, through the level of effort that he chooses to exert. Such situations are referred to as moral hazard situations. Throughout the chapter we make use of simple illustrative examples and diagrams. A selected bibliography at the end provides suggestions to readers who wish to pursue some of the topics to a greater depth.

      Link to the published article: http://www.eolss.net

 
2012

69. Giacomo Bonanno, "Belief Change in Branching Time: AGM-consistency and Iterated Revision", Journal of Philosophical Logic, Volume 41, Issue 1, 2012, 201-236. 
    (DOI: 10.1007/s10992-011-9202-6)

Abstract.

We study belief change in the branching-time structures introduced in Bonanno (Artificial Intelligence 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 AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artificial Intelligence 171:144–160, 2007). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically.

      To download the pdf  click here:  from JSTOR   or   preprint: plausibility.pdf

      Link to the journal article: http://www.springerlink.com/content/77748356775w6477/

2013
70. Giacomo Bonanno, "AGM-consistency and  perfect Bayesian equilibrium.  Part I: definition and properties", International Journal of Game Theory, Volume 42, Issue 3, 2013, 567-592.
(DOI: 10.1007/s00182-011-0296-4)

Abstract.

We provide a general notion of perfect Bayesian equilibrium which can be applied to arbitrary extensive-form games and is intermediate between subgame-perfect equilibrium and sequential equilibrium. The essential ingredient of the proposed definition is the qualitative notion of AGM-consistency, which has an epistemic justification based on the theory of belief revision introduced by Alchourrón, Gärdenfors and Makinson. AGM-consistency is a generalization of the notion of consistency introduced by Kreps and Wilson as part of the definition of sequential equilibrium.

      To download the pre-print version  in pdf format click here: PBE-1.pdf

      Link to the journal article: http://www.springer.com/alert/urltracking.do?id=L27d4ea9Mcb207aS29afd7a

 
71. Giacomo Bonanno, "A dynamic epistemic characterization of backward induction without counterfactuals", Games and Economic Behavior, Volume 78, 2013, 31-43.

Abstract.

    The analysis of rational play in dynamic games is usually done within a static framework that specifies a player's initial beliefs as well as his disposition to revise those beliefs conditional on hypothetical states of information. We suggest a simpler approach, where the rationality of a player's choice is judged on the basis of the actual beliefs that the player has at the time he has to make that choice. We propose a dynamic framework where the set of  "possible worlds" is given by state-instant pairs (w,t). Each state w specifies the entire play of the game and, for every instant t, (w,t) specifies the history that is reached at that instant (in state w). A player is said to be active at (w,t) if the history reached in state w at date t is a decision history of his. At every state-instant pair (w,t) the beliefs of the active player provide an answer to the question "what will happen if I take action a", for every available action a. A player is said to be rational at (w,t) if either he is not active there or the action he ends up taking at state w is "optimal" given his beliefs at (w,t). We provide a characterization of backward induction in terms of the following event: the first mover (i) is rational and has correct beliefs, (ii) believes that the active player at date 1 is rational and has correct beliefs, (iii) believes that the active player at date 1 believes that the active player at date 2 is rational and has correct beliefs, etc. Thus our epistemic characterization does not rely on dispositional belief revision or on (objective or subjective) counterfactuals.

             To download the files in pdf format click here: bi_dynamic.pdf

             Link to the journal article:  http://www.sciencedirect.com/science/article/pii/S0899825612001856
 

2014
72. Giacomo Bonanno, "A doxastic behavioral characterization of generalized backward induction", Games and Economic Behavior, Volume 88, 2014, 221-241.
      (http://dx.doi.org/10.1016/j.geb.2014.10.004)

Abstract.

   We investigate an extension of the notion of backward induction to dynamic games with imperfect information and provide a doxastic characterization of it. Extensions of the idea of backward induction were proposed by Penta (2009) and later by Perea (2014), who also provided a doxastic characterization in terms of the notion of common belief of future rationality. The characterization we propose, although differently formulated, is conceptually the same as Perea's and so is the generalization of backward induction. The novelty of this contribution lies in the models that we use, which are dynamic, behavioral models where strategies play no role and the only beliefs that are specified are the actual beliefs of the players at the time of choice. Thus players' beliefs are modeled as temporal, rather than conditional, beliefs and rationality is defined in terms of actual choices, rather than hypothetical plans.

      To download the pre-print version  in pdf format click here: GBI.pdf

      Link to the journal article:  http://dx.doi.org/10.1016/j.geb.2014.10.004  or  http://www.sciencedirect.com/science/article/pii/S089982561400147X

 
73. Giacomo Bonanno and Cédric Dégremont, "Logic and game theory", ” in: Alexandru Baltag and Sonja Smets (Eds), Johan van Benthem on Logic and
       Information Dynamics, Outstanding Contributions to Logic Volume 5, Springer, 2014, pp 421-449.      

Abstract.

   Johan van Benthem has highlighted in his work that many questions arising in the analysis of strategic interaction call for logical and computational analysis. These questions lead to both formal and conceptually illuminating answers, in that they contribute to clarifying some of the underlying assumptions behind certain aspects of game-theoretical reasoning. We focus on the insights of  a part of the literature at the interface of game theory and mathematical logic that gravitates around van Benthem's work. We discuss the formal questions raised by the perspective consisting in taking games as models for formal languages -- in particular modal languages -- and how eliminative reasoning processes and solution algorithms can be analyzed logically as epistemic dynamics and discuss the role played by beliefs in game-theoretical analysis and how they should be modeled from a logical point of view. We give many pointers to the literature throughout the paper.

      To download the pre-print version  in pdf format click here: BD_LG.pdf

      Link to the publisher:  http://link.springer.com/chapter/10.1007/978-3-319-06025-5_15 (for the chapter)
                                            http://link.springer.com/book/10.1007/978-3-319-06025-5 (for the entire book)

 
2015

74. Giacomo Bonanno, "Epistemic foundations of game theory", in: H. van Ditmarsch, J.Y. Halpern, W. van der Hoek and B. Kooi (eds),
      Handbook of Logics for Knowledge and Belief, College Publications, 2015, pp. 411–450.
Contents
1. Introduction
2. Epistemic Models of Strategic-Form Games
3. Semantic Analysis of Common Belief of Rationality
4. Syntactic Characterization of Common Belief of Rationality
5. Common Belief versus Common Knowledge
6. Probabilistic Beliefs and von Neumann-Morgenstern Payoffs
7. Dynamic Games with Perfect Information
8. The Semantics of Belief Revision
9. Common Belief of Rationality in Perfect-Information Games
10. Literature Review

   To download the pre-print version  in pdf format click here: handbook.pdf
   
   Link to the publisher:  http://collegepublications.co.uk/handbooks/?00002


75. Giacomo Bonanno, "Counterfactuals and the Prisoner's Dilemma", in: M. Peterson (ed), The Prisoner's Dilemma,
      Cambridge University Press, 2015, pp. 133–155.

Abstract.

This is a chapter in a  book on the Prisoner’s Dilemma, edited by Martin Peterson, published by Cambridge University Press. It discusses the nature of the conditionals involved in deliberation, taking the Prisoner's Dilemma game as point of departure.                         

  To download the pre-print version  in pdf format click here: PD.pdf

  Link to the publisher:  http://www.cambridge.org/us/academic/subjects/philosophy/philosophy-science/prisoners-dilemma?format=PB



76. Giacomo Bonanno, "Reasoning about strategies and rational play in dynamic games", in: J. van Benthem, S. Ghosh
      and R. Verbrugge (eds), Models of Strategic Reasoning,  LNCS 8972, Springer, 2015, pp. 34–62.

Abstract.

We discuss the issues that arise in modeling the notion of common belief of rationality in epistemic models of dynamic games, in particular at the level of interpretation of strategies. A strategy in a dynamic game is defined as a function that associates with every information set a choice at that information set. Implicit in this definition is a set of counterfactual statements concerning what a player would do at information sets that are not reached, or a belief revision policy concerning behavior at information sets that are ruled out by the initial beliefs. We discuss the role of both objective and subjective counterfactuals in attempting to flesh out the interpretation of strategies in epistemic models of dynamic games.                         

  To download the pre-print version  in pdf format click here: SR.pdf

  Link to the publisher:  http://link.springer.com/chapter/10.1007/978-3-662-48540-8_2



2016

77. Giacomo Bonanno,  "AGM-consistency and perfect Bayesian equilibrium.   Part II: from PBE to sequential equilibrium",
       International Journal of Game Theory, November 2016, Volume 45, Issue 4, pp. 1071-1094.

Abstract.

In Bonanno (Int. J. Game Theory, 42:567-592, 2013) a general notion of perfect Bayesian equilibrium (PBE) was introduced for extensive-form games and shown to be intermediate between subgame-perfect equilibrium and sequential equilibrium. The essential ingredient of the proposed notion is the existence of a plausibility order on the set of histories that rationalizes a given assessment. In this paper we study restrictions on the belief revision policy encoded in a plausibility order and provide necessary and sufficient conditions for a PBE to be a sequential equilibrium.                        

Read the published article at:   https://rdcu.be/7n6q  or  http://link.springer.com/article/10.1007/s00182-015-0506-6

To download the pre-print version  in pdf format click here:  PBEII.pdf


78. Giacomo Bonanno,  "Exploring the gap between perfect Bayesian equilibrium and sequential equilibrium",
      Games, November 2016, 7(4), 35, pp. 1-23. [Reprinted in: Paul Weirich (Editor), Epistemic game theory and logic,
      MDPI, Basel, Switzerland, pp. 20-42 (ISBN 978-3-03842-422-2,  http://www.mdpi.com/books/pdfview/book/312 )]

Abstract.

In [Bonanno, Int. J. Game Theory, 42:567-592, 2013] a solution concept for extensive-form games was introduced, called perfect Bayesian equilibrium (PBE), and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In [Bonanno, Int. J. Game Theory, 2016, forthcoming] the notion of PBE was used to provide a characterization of SE in terms of a strengthening the two defining components of PBE (besides sequential rationality), namely AGM consistency and Bayes consistency. In this paper we explore the gap between PBE and SE by identifying solution concepts that lie strictly between PBE and SE; these solution concepts embody a notion of "conservative" belief revision. Furthermore, we provide a method for determining if a plausibility order on the set of histories is choice measurable, which is a necessary condition for a PBE to be a SE.                          

  To download the paper in pdf format click here:  PBE_III.pdf

  Link to the publisher: http://www.mdpi.com/2073-4336/7/4/35/


2018

79. Giacomo Bonanno,  "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction",
       International Journal of Game Theory, September 2018, Volume 47, Number 3,  pp. 1001-1032.

Abstract.

Doxastic characterizations of the set of Nash equilibrium outcomes and of the set of backward-induction outcomes are provided for general perfect-information games (where there may be multiple backward-induction solutions). We use models that are behavioral, rather than strategy-based, where a state only specifies the actual play of the game and not the hypothetical choices of the players at nodes that are not reached by the actual play. The analysis is completely free of counterfactuals and no belief revision theory is required, since only the beliefs at reached histories are specified.
       
To download the pre-print version in pdf format click here:  BhvDlb.pdf 

Link to the published paper: https://link.springer.com/article/10.1007%2Fs00182-017-0595-5

Link to Springer Nature SharedIt: http://rdcu.be/wlnw   


80. Giacomo Bonanno and Elias Tsakas,  "Common belief of weak-dominance rationality in strategic-form games: A qualitative analysis",
       Games and Economic Behavior, Vol. 112, November 2018, pp. 231-241.

Abstract.

We study common belief of weak-dominance rationality in strategic-form games with ordinal utilities, employing a qualitative model of beliefs. We characterize two standard solution concepts for such games: the Iterated Deletion of Börgers-dominated Strategies (IDBS) and the Iterated Deletion of Inferior Strategy Profiles (IDIP). We do so by imposing nested restrictions on the doxastic models: namely, the respective epistemic conditions differ in the fact that IDIP requires the truth axiom whereas IDBS does not. Hence, IDIP refines IDBS.
       
To download the pre-print version in pdf format click here:  CBWD.pdf 

Link to the published paper: https://doi.org/10.1016/j.geb.2018.09.003

2019

81. Giacomo Bonanno,  "Credible Information, Allowable Information and Belief Revision - Extended Abstract", in:
      Lawrence S. Moss (editor): Proceedings Seventeenth Conference on Theoretical Aspects of Rationality and
      Knowledge (TARK 2019), Electronic Proceedings in Theoretical Computer Science 297, pp. 82–90, July 2019.

Abstract.

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the choice structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of (a generalized notion of) choice structure in terms of belief revision by adding: (1) the possibility that an item of "information" might be discarded as not credible (thus dropping the AGM success axiom) and (2) the possibility that an item of information, while not accepted as fully credible, may still be "taken seriously" (we call such items of information "allowable"). We establish a correspondence between generalized choice structures (GCS) and AGM belief revision; furthermore, we provide a syntactic analysis of the proposed notion of belief revision, which we call filtered belief revision.

Link to the published paper: http://dx.doi.org/10.4204/EPTCS.297.6   

2020

82. Giacomo Bonanno,  "Logics for belief as maximally plausible possibility",  Studia Logica, Vol. 108, 2020, pp. 1019-1061.

Abstract.

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 (corresponding - semantically - to a binary Kripke relation), while the latter is merely a classical operator (corresponding - semantically - to a neighborhood structure). We then define belief, interpreted as ``maximally plausible possibility'', in terms of these two notions: the agent believes A if (1) she cannot rule out A (that is, it is not the case that she is certain that not-A), (2) she judges A to be plausible and (3) she does not judge not-A to be plausible. We consider several interaction properties between certainty and plausibility and study how these properties translate into properties of belief (positive and negative introspection, their converses, conjunction, etc.). We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility and identify the corresponding logics.

To download the pre-print version in pdf format click here:  CPB_logic.pdf

Link to the published paper: https://link.springer.com/article/10.1007%2Fs11225-019-09887-w  or   https://rdcu.be/b7nym

2021

83. Giacomo Bonanno,  "Prefazione introduttiva alla Teoria dei giochi  di Pierpaolo Battigalli", Treccani Libri, 2021, pp.7-25.  

Link to the publisher : https://www.treccanilibri.it/catalogo/teoria-dei-giochi/

2022

84. Giacomo Bonanno, "Filtered belief revision: syntax and semantics", Journal of Logic, Language and Information, Vol. 31 (4), December 2022, pp. 645-675.
Abstract.
In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the set-theoretic structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of those structures in terms of one-shot belief revision by relating them to the trichotomous attitude towards information studied in Garapa (Rev Symb Logic, 1–21, 2020) where information may be either (1) fully accepted or (2) rejected or (3) taken seriously but not fully accepted. We begin by introducing the syntactic notion of filtered belief revision and providing a characterization of it in terms of a mixture of both AGM revision and contraction. We then establish a correspondence between the proposed notion of filtered belief revision and the above-mentioned set-theoretic structures, interpreted as semantic partial belief revision structures. We also provide an interpretation of the trichotomous attitude towards information in terms of the degree of implausibility of the information.

Link to the Open Access published paper: https://link.springer.com/article/10.1007/s10849-022-09374-x


85. Giacomo Bonanno, "Minimax regret with imperfect ex-post knowledge of the state",  Research in Economics, Vol. 76 (4), December 2022, pp. 403-412.
Abstract.
We consider decision problems under complete ignorance and extend the minimax regret principle to situations where, after taking an action, the decision maker does not necessarily learn the state of the world. For example, if the decision maker only learns what the outcome is, then all she knows is that the actual state is one of the (possibly several) states that yield the observed outcome under the chosen action. We refer to this situation as imperfect ex-post information. We show that, given a choice between more information and less information, the decision maker prefers the latter. We also extend the framework to encompass the possibility of less than the extreme degree of pessimism that characterizes the minimax regret criterion.

Link to the Open Access published paper: https://doi.org/10.1016/j.rie.2022.09.006



86. Giacomo Bonanno, "Rational play in extensive-form games", Games, Vol. 13, Issue 6,  2022  
Abstract.
We argue in favor of a departure from the equilibrium approach in game theory towards the less ambitious goal of describing only the actual behavior of rational players. The notions of Nash equilibrium and its refinements require a specification of the players’ choices and beliefs not only along the equilibrium play but also at counterfactual histories. We discuss an alternative - - counterfactual-free -- approach that focuses on choices and beliefs along the actual play, while being silent on choices and beliefs at unreached histories. Such an approach was introduced in an earlier paper that considered only perfect-information games. Here we extend the analysis to general extensive-form games (allowing for imperfect information) and put forward a behavioral notion of self-confirming play, which is close in spirit to the literature on self-confirming equilibrium. We also extend, to general extensive-form games, the characterization of rational play that is compatible with pure-strategy Nash equilibrium.

Link to the Open Access published paper:  https://www.mdpi.com/2073-4336/13/6/72


2023

87. Giacomo Bonanno,  "The Material Conditional is sufficient to model deliberation",  Erkenntnis, Vol 88, Issue 1, 2023, pp. 325-349;  published online 23 February 2021

Abstract.

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 familiar examples and both qualitative and probabilistic beliefs are considered. Issues such as common-cause cases and ‘Egan-style’ cases are discussed.

To download the pre-print version in pdf format click here:  MC.pdf

Link to the published paper: https://link.springer.com/article/10.1007%2Fs10670-020-00357-7  or   https://rdcu.be/cfJre                


88. Giacomo Bonanno,  "Characterization of AGM belief contraction in terms of conditionals",  In: Rineke Verbrugge (Editor): Proceedings Ninetheenth conference on Theoretical Aspects of Rationality and Knowledge (TARK 2023),  Electronic Proceedings in Theoretical Computer Science 379, pp. 142–156, 2023.

Abstract.

We provide a semantic characterization of AGM belief contraction based on frames consisting of a Kripke belief relation and a Stalnaker-Lewis selection function. The central idea is as follows. Let K be the initial belief set and K-A be the contraction of K by the formula A; then B belongs to the set K-A if and only if, at the actual state, the agent believes B and believes that if not-A is (were) the case then B is (would be) the case.

Link to the Open Access published paper: https://cgi.cse.unsw.edu.au/~eptcs/paper.cgi?TARK2023:4938   


2024

89. Giacomo Bonanno, "A Kripke-Lewis semantics for belief update and belief revision",  Artificial Intelligence,  In Press, published online 29 November 2024.  

Abstract.

We provide a new characterization of both belief update and belief revision in terms of a Kripke-Lewis semantics. We consider frames consisting of a set of states, a Kripke belief relation and a Lewis selection function. Adding a valuation to a frame yields a model. Given a model and a state, we identify the initial belief set K with the set of formulas that are believed at that state and  we identify either the updated belief set or the revised belief set, prompted by the input represented by formula A, as the set of formulas that are the consequent of conditionals that (1) are believed at that state and (2) have A as antecedent. We show that this class of models characterizes both the Katsuno-Mendelzon (KM) belief update functions and the AGM belief revision functions, in the following sense: (1) each model gives rise to a partial belief function that can be completed into a full KM/AGM update/revision function, and (2) for every KM/AGM update/revision function there is a model whose associated belief function coincides with it. The difference between update and revision can be reduced to two semantic properties that appear in a stronger form in revision relative to update, thus confirming the finding by Peppas et al. (1996) that, "for a fixed theory K, revising K is much the same as updating K".  It is argued that the proposed semantic characterization brings into question the common interpretation of belief revision and update as change in beliefs in response to new information.

To download the pre-print version in pdf format click here:  UpdRev.pdf

Link to the publisher: https://authors.elsevier.com/a/1kD3I-c5fZEY        
 




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