*(Please note: the copyright of these publications
belongs to the publisher; the files made available for download on this
web page contain the Working Paper version of the paper. These files cannot
be copied or posted on the web without permission of the copyright holder.)*

Most of the files that can be downloaded are in .pdf format

[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, ]

** To download this paper in pdf format click
here: JET_85.pdf**

2. Giacomo Bonanno, "Vertical differentiation with Cournot competition",

** To download this paper in
pdf format click here: EN1986.pdf**

** To download this paper in
pdf format click here: metro_1986.pdf**

** To download this paper in
pdf format click here: en_it_1986.pdf**

5. Giacomo Bonanno, "Location choice, product proliferation and entry deterrence",

** To download this paper in
pdf format click here: RES_87.pdf**

** Reprinted in: J. Barkley Rosser,
Jr.(Ed.), Complexity in Economics, The International Library of
Critical**

** To download this paper in
pdf format click here: aep_1987.pdf**

7. Giacomo Bonanno, "Oligopoly equilibria when firms have local knowledge of demand",

** To download this paper in
pdf format click here: IER_1988.pdf.pdf**

** To download this paper in
pdf format click here: JIE_1988.pdf**

** To download this paper in
pdf format click here: QJE_1988.pdf**

** To download this paper in
pdf format click here: IJIO_1988.pdf**

** To download this paper in
pdf format click here: EJOR_1988.pdf**

** To download this paper in
pdf format click here: TD_1988.pdf**

13. Giacomo Bonanno, "Sudden and surprising changes of attitude during negotiations",

** To download this paper in
pdf format click here: EN_1989.pdf**

14. Giacomo Bonanno (with D. Brandolini, Eds.),

** To download this paper in
pdf format click here: JES_1990.pdf**

16. Giacomo Bonanno, "Concorrenza imperfetta nella teoria dell'equilibrio economico generale", in S. Zamagni (Ed.),

** To download this paper in
pdf format click here: EAP_1991.pdf**

19. Giacomo Bonanno, "Set-theoretic equivalence of extensive-form games",

** To download this paper in
pdf format click here: IJGT_1992.pdf**

** To download this paper in
pdf format click here: TD_1992.pdf**

** To download this paper in
pdf format click here: EN_1992_aw.pdf**

** To download this paper in
pdf format click here: MSS_1992.pdf**

** To download this paper in
pdf format click here: EN_1992_piv.pdf**

24. Giacomo Bonanno, "The logical representation of extensive games",

** To download this paper in
pdf format click here: ijgt93.pdf**

** To download this paper in
pdf format click here: EL_1993.pdf**

** To download this paper in
pdf format click here: EN_1993.pdf**

27. Giacomo Bonanno, "Reply to Vilks",

** To download this paper in
pdf format click here: EAP_1994.pdf**

** To download this paper in
pdf format click here: RE_1994.pdf**

29. Giacomo Bonanno, Review of Cristina Bicchieri’s "Rationality and Coordination",

** To download this paper in
pdf format click here: EAP_review.pdf**

** To download this paper in
pdf format click here: EN_1995_SE.pdf**

**31. Giacomo Bonanno, "Modeling production with
Petri Nets", Economic Notes, 1995, 25 (2), pp. 263-292.**

*Abstract*

The purpose of this paper is to bring to the attention of economists a tool of analysis, known as Petri nets, which was developed in the computer science literature. Although, from a purely formal point of view, Petri nets are not a new tool, they do seem to provide a new perspective on models of production. First of all, the graph-theoretic representation of Petri nets makes it possible to see things that would be hard to detect from a purely algebraic formulation of the same problem. Secondly, the formal definition of a Petri net allows one to introduce a wedge between the notions of input and output (to a production process) and the notion of commodity. Among the inputs to (and outputs of) a production process one can include states of nature, logical conditions, etc. This enables us to show that one of the assumptions which is usually considered to be inherent to linear models of production, namely the absence of external economies and diseconomies among processes, can be dispensed with. We also show that Petri nets do not require another assumption normally associated with activity analysis, namely that of constant returns to scale. Finally, Petri nets allow a simple analysis of the problem of what commodity vectors can be obtained from a given vector of initial resources.

**To download this paper in pdf formatclick here:
EN_1995_PN.pdf**

**32. Giacomo Bonanno, "On the logic of common
belief", Mathematical Logic Quarterly, 1996, 42, 305-311.**

*Abstract*

We provide an axiomatization of the notion of common belief (knowledge) that makes use of no rules of inference (apart from Modus Ponens and Necessitation) and highlight the property of the set of accessibility relations that characterizes each axiom.

** To download this paper in
pdf format click here: ** **MLQ_1996.pdf**

**33. Giacomo Bonanno (with P. Battigalli), "The
logic of belief persistence", Economics and Philosophy,**

** To download this paper in
pdf format click here: ** **EAP_1997.pdf**

**34. Giacomo Bonanno (with P. Battigalli), "Synchronic
information, knowledge and common knowledge**
** in extensive
games", in M. Bacharach, L.A. Gérard-Varet, P. Mongin and H. Shin
(Eds.),**
* Epistemic
logic and the theory of games and decisions*, Kluwer Academic, 1997,
pp. 235-263.

** Reprinted in:
Research
in Economics, 53 (1), March 1999, pp.77-99.**

*Abstract*

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular information partition for each player and show that it captures the notion of maximum information in the sense that it is the finest within the class of information partitions that satisfy four natural properties. Using this notion of “maximum information” we are able to provide an alternative characterization of the meet of the information partitions.

** To download
this paper in pdf format click here: extensive.pdf**
**Download the Journal version from the publisher's
web site:** http://www.idealibrary.com/links/doi/10.1006/reec.1998.0183/pdf

**35. Giacomo Bonanno
,
“A note on the subtleties of Bayesian inference”, Economic Notes,
1997, 26 (3), 477-486.**

*Abstract*

Bayesian theory asserts that the beliefs formed by a rational individual in response to new information must be derived from the original beliefs by conditioning on the information. Information is represented by a set of possible states. A state, in turn, ought to represent a complete description of the world. Once the states have been described accurately, application of Bayes’ rule is a non-problematic and mechanical procedure. However, if the states have not been described fully and correctly, then inference based on Bayes’ rule will typically be incorrect. We illustrate this with the help of a case discussed by Nalebuff.

** To download
this paper in pdf format click here: EN_1997.pdf**

**36. Giacomo Bonanno (with K. Nehring), "On
the logic and role of negative introspection of common belief",**
* Mathematical
Social Sciences*, 35, 1998, 17-36.

*Abstract*

Negative Introspection of common belief and its characterizing conditions help provide epistemic foundations for game-theoretic solution concepts. We show this for correlated equilibrium under incomplete information as well as backward induction in a class of extensive games.

** To download
this paper in pdf format click here: neg_int.pdf**

**37. Giacomo Bonanno (with B. Haworth), "Intensity
of competition and the choice between product**
** and process
innovation", International Journal of Industrial Organization, 16(4),
495-510, 1998.**

*Abstract*

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 (Bertrand) or less intense (Cournot) competition. We find that there are cost-reducing innovations that are pursued under Cournot but not under Bertrand competition. The second is whether the regime of competition affects a firm’s choice between product and process innovation. We show that for the high quality firm, whenever there is a difference between the choice made by a Bertrand competitor and the choice made by a Cournot competitor, the former opts for product innovation, while the latter prefers process innovation. For the low-quality firm the result is reversed.

** To download this paper
in pdf format click here: Innovate.pdf**

**38. Giacomo Bonanno (with K. Nehring), "Assessing
the Truth Axiom under incomplete information",**
* Mathematical
Social Sciences*, 36, 1998, 3-29.

*Abstract*

** To download this paper
in pdf format click here: truth.pdf**

**39. Giacomo Bonanno (with K. Nehring), “Understanding
Common Priors under Incomplete Information”,**
** in: Itzhak
Gilboa (ed.), Theoretical aspects of rationality and knowledge (TARK
1998), Morgan Kaufman,**

** To download
this paper in pdf format click here: TARK
98.pdf** also here: ACM_dig_lib

**40. Giacomo Bonanno (with K. Nehring), “On
Stalnaker's notion of strong rationalizability and Nash**
** equilibrium
in perfect information games”, Theory and Decision, 1998, 45, pp.
291-295.**

*Abstract*

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 equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to the set of profiles that survive the iterative deletion of inferior profiles.

** To download
this paper in pdf format click here: Staln.pdf**

**41. Giacomo Bonanno (with P. Battigalli), "Synchronic
information, knowledge and common knowledge**
** in extensive
games", Research in Economics, 53 (1), March 1999, pp.77-99.**

*Abstract*

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular information partition for each player and show that it captures the notion of maximum information in the sense that it is the finest within the class of information partitions that satisfy four natural properties. Using this notion of “maximum information” we are able to provide an alternative characterization of the meet of the information partitions.

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

**42. Giacomo Bonanno (with K. Nehring), ““Varieties
of interpersonal compatibility of beliefs” in: Jelle Gerbrandy,**
** Maarten Marx,
Maarten de Rijke and Yde Venema (Eds.), “Essays dedicated to Johan van
Benthem on the**
** occasion of
his 50th birthday”, Amsterdam University Press, Vossiuspers series,
Amsterdam, 1999.**

*Abstract*

The logic of common belief does not always reflect the logic of individual beliefs. In particular, the Negative Introspection property fails at the common belief level, that is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. Indeed Negative Introspection of common belief involves restrictions on individual beliefs of an intersubjective nature. We consider a number of interpersonal restrictions on beliefs and study their relationship. We also characterize Negative Introspection of common belief in terms of interpersonal properties of individual beliefs. All the results are proved syntactically.

*Abstract*

We provide a self-contained, selective overview of the literature on the role of knowledge and beliefs in game theory. We focus on recent results on the epistemic foundations of solution concepts, including correlated equilibrium, rationalizability in dynamic games, forward and backward induction.

[Note: this is a 94-page paper. The pdf file is 1.2MB and might take a while to download. On the other hand, the postscript file is much too large (15MB!) and there is no point making it avaliable for downloading]

*Abstract*

The Common Prior Assumption (CPA) is central to the economics of information and the foundations of game theory. Recent contributions (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned its meaningfulness in situations of incomplete information where there is no ex ante stage and the primitives of the model are the individuals’ belief hierarchies. We address this conceptual issue by providing characterizations of two local versions of the CPA which are in terms of the primitives and, therefore, do not involve a counterfactual and problematic ex ante stage. The characterizations involve three notions: Comprehensive Agreement, no error of beliefs and common belief in no error. Comprehensive Agreement is defined as the absence of “agreement to disagree” about any aspect of beliefs; it is a generalization of Aumann’s (1976) notion of agreement. The entire analysis is carried out locally, that is, with reference to the “true state” (which represents the actual profile of belief hierarchies) and does not rely on the Truth Axiom for individual beliefs. The results are also applied to the problem of generalizing the notion of Bayesian updating to single-person, intertemporal situations without perfect recall and without given information partitions.

If you prefer to download the paper as a postscript file click here: common.ps

**45. Giacomo Bonanno (with K. Nehring), “Common
belief with the logic of individual belief ",
Mathematical Logic Quarterly,**

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 (the negative introspection
axiom). 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.

**46. Giacomo Bonanno (with K. Nehring), “Intersubjective
Consistency of Knowledge and Belief ” in: Martina Faller,**
** Stefan Kaufmann
and Marc Pauly (Eds.): Formalizing the Dynamics of Information,
CSLI Publications,**

*Abstract.*

We consider interactive epistemic
models where individuals are described by both their “knowledge” and their
“beliefs”. Three intersubjective consistency conditions are examined: Intersubjective
Caution (if an individual believes something to be common belief then he
knows it to be common belief), Truth of Common Belief (only true facts
are commonly believed) and Qualitative Agreement. These conditions are
employed in characterizations of the following properties which describe
either the extent of intersubjective truth and/or the logic of common
belief: common belief in no error, common knowledge of common belief, negative
introspection of common belief, coincidence of common knowledge and common
belief, and collapse of individual belief and knowledge. We also discuss
to what extent the** **the three fundamental conditions can be viewed
as intersubjective rationality conditions.

If you prefer to download the paper as a postscript file click here: cb&ck.ps

**47. Giacomo Bonanno, “Prediction
in branching time logic”,
Mathematical
Logic Quarterly, 47 (2), May 2001, pp. 239-247.**

*Abstract.*

When we make a non-trivial prediction about the future we select, among
the conceivable future descriptions of the world, those that appear to
us to be most plausible. Within a branching-time framework we capture this
by means of two binary relations, <_{c} and <_{p}.
If t_{1} and t_{2 }are two different times, we interpret
t_{1} <_{c} t_{2} as saying that t_{2}
is in the *conceivable* future of t_{1}, while t_{1}
<_{p} t_{2} is interpreted to mean that t_{2}
is in the *predicted * future of t_{1}. We propose the
following notion of "consistency of predictions''. Suppose that at t_{1}
some future instant t_{2} is predicted to occur, then (a) every
time instant t on the *unique* path from t_{1} to t_{2}
should also be predicted at t_{1} and (b) the prediction of t_{2}
should continue to hold at every such t. We provide a modal system of temporal
logic which gives a sound and complete axiomatization of this notion of
consistency.

If you prefer to download the paper as a

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.

If you prefer to download the paper as a

49. Giacomo Bonanno, “Branching Time Logic, Perfect Information Games and Backward Induction”,Games and Economic Behavior, 36 (1), July 2001, pp. 57-73.

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**

If
you prefer to download the paper as a postscript file click here: bi_logic.ps

**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 NotesI 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

If you prefer to download the paper as a postscript file click here:information.ps

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

descriptionof the behavior of rational individuals who recognize each other's rationality and reasoning abilities, and (2) game theory as an internally consistentrecommendationto 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

If you prefer to download the paper as a postscript file click here: Rimini.ps

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

If you prefer to download the paper as a postscript file click here: Loft5.ps

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:Memory.pdf

If you prefer to download the paper as a postscript file click here: Memory.ps

Link to the journal article: http://ipsapp009.kluweronline.com/IPS/frames/toc.aspx?J=5187&I=51#

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/26Link 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 (andKnowledge, 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: vNM.pdf

Also available at:http://repositories.cdlib.org/postprints/24Link to the journal article: http://journals.kluweronline.com/article.asp?PIPS=5256223orhttp://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 (andKnowledge, 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: 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.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.

Abstract.

To download the paper in pdf format click here: 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)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

Abstract.purestrategies. 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

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.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.

Abstract.

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

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

Abstract.

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.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

Abstract.W, a collectionCof subsets ofW(representing possible choice sets) and a functionffromCinto the set of subsets ofW(representing choices made). A choice frame is rationalizable if there exists a total pre-orderRonWsuch that, for everyEinC,f(E) coincides with the best elements ofErelative toR. We re-interpret choice structures in terms of belief revision. An interpretation is obtained by adding a valuation that assigns to every atompthe subset ofWat whichpis 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-consistentif and only ifit 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.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

Editors' abstract.

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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 theSage Handbook of Philosophy of the Social Scienceedited by Ian C Jarvie and Jesus Zamora-Bonilla, Sage Publications, 2011, 322-338.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.

Abstract.

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Link to publisher's site for the handbook: http://www.uk.sagepub.com/booksProdDesc.nav?contribId=512629&prodId=Book232751#tabview=toc67. 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.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.

Abstract.

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", inFundamental Economics[Ed. Mukul Majmdar], inEncyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, EOLSS Publishers, Oxford, UK, 2011.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.

Abstract.

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

201269. Giacomo Bonanno, "Belief Change in Branching Time: AGM-consistency and Iterated Revision",DOI: 10.1007/s10992-011-9202-6)Journal of Philosophical Logic,Volume 41, Issue 1, 2012, 201-236.

(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.

Abstract.

To download the pre-print version in pdf format click here: plausibility.pdfLink to the journal article: http://www.springerlink.com/content/77748356775w6477/

201370. 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)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.

Abstract.

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.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 (

Abstract.w,t). Each statewspecifies the entire play of the game and, for every instantt, (w,t) specifies the history that is reached at that instant (in statew). A player is said to be active at (w,t) if the history reached in statewat datetis 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 actiona", for every available actiona. 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 statewis "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.pdfLink to the journal article: http://www.sciencedirect.com/science/article/pii/S0899825612001856

201472. 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)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.

Abstract.

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 421-449Johan 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.

Abstract.

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.Contents1. 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.pdfLink to the publisher: http://www.cambridge.org/us/academic/subjects/philosophy/philosophy-science/prisoners-dilemma?format=PB

Reasoning about strategies and rational play in dynamic games

76. Giacomo Bonanno, "", 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.pdfLink to the publisher: http://link.springer.com/chapter/10.1007/978-3-662-48540-8_2

2016"AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium",

77. Giacomo Bonanno,

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.

To download the pre-print version in pdf format click here:PBEII.pdfLink to the publisher: http://link.springer.com/article/10.1007/s00182-015-0506-6

78. Giacomo Bonanno,"Exploring the gap between perfect Bayesian equilibrium and sequential equilibrium",

Games,November 2016, 7(4), 35, pp. 1-23.

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.pdfLink to the publisher:

http://www.mdpi.com/2073-4336/7/4/35/

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