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12
Dynamic interactive epistemology
, 2004
"... The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various gametheoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive rea ..."
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Cited by 24 (1 self)
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The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various gametheoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive reasoning have been developed, most notably by Stalnaker [Econ. Philos. 12 (1996) 133– 163] and Battigalli and Siniscalchi [J. Econ. Theory 88 (1999) 188–230], and used to analyze rational play in extensive form games. But while the properties of Aumann structures are well understood, without a formal language in which belief and belief revision statements can be expressed, it is unclear exactly what are the properties of these dynamic models. Here we investigate this question by defining such a language. A semantics and syntax are presented, with soundness and completeness theorems linking the two.
Hypothetical Knowledge and Counterfactual Reasoning
 International Journal of Game Theory
, 1999
"... Abstract: Salmet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended informatio ..."
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Abstract: Salmet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information structures used to model it bear some resemblance to the way philosophers have used conditional logic to model counterfactuals, hypothetical knowledge cannot be reduced to conditional logic together with epistemic logic. Here it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator "> " and the knowledge operator "K", provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed. 1
Using Counterfactuals in KnowledgeBased Programming
 Distributed Computing
, 1998
"... : We show how counterfactuals can be added to the framework of knowledgebased programs of Fagin, Halpern, Moses, and Vardi [1995, 1997]. We show that counterfactuals allow us to capture in a natural way notions like minimizing the number of messages that are sent, whereas attempts to formalize these ..."
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Cited by 6 (3 self)
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: We show how counterfactuals can be added to the framework of knowledgebased programs of Fagin, Halpern, Moses, and Vardi [1995, 1997]. We show that counterfactuals allow us to capture in a natural way notions like minimizing the number of messages that are sent, whereas attempts to formalize these notions without counterfactuals lead to some rather counterintuitive behavior. We also show how knowledgebased programs with counterfactuals can capture subgameperfect equilibria in games of perfect information. 1 Introduction Knowledgebased programs, first introduced in [Halpern and Fagin 1989] and further developed by Fagin, Halpern, Moses, and Vardi [1995, 1997], are intended to provide a highlevel framework for the design and specification of protocols. Their key feature is that of allowing explicit tests for knowledge. Thus, a knowledgebased program might have the form if K(x = 0) then y := y + 1 else skip; where K(x = 0) should be read as "you know x = 0" and skip is the actio...
ObjectBased Unawareness: Theory and Applications
, 2009
"... In this paper and its companion paper, Board & Chung [4], we provide foundations for a model of unawareness that can be used to distinguish between what an agent is unaware of and what she simply does not know. At an informal level, this distinction plays a key role in a number of recent papers such ..."
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In this paper and its companion paper, Board & Chung [4], we provide foundations for a model of unawareness that can be used to distinguish between what an agent is unaware of and what she simply does not know. At an informal level, this distinction plays a key role in a number of recent papers such as Tirole [27] and Chung & Fortnow [6]. Here we provide a settheoretic (i.e. nonlinguistic) version of our framework. We use our objectbased unawareness structures to investigate two applications. The first application provides a justification for the contra proferentem doctrine of contract interpretation, under which ambiguous terms in a contract are construed against the drafter. Our second application examines speculative trade. We first generalize the classical No Trade Theorem to situations where agents are delusional but nevertheless satisfy a weaker condition called terminal partitionality. We then introduce the concepts of living in denial (i.e., agents believe, perhaps incorrectly, that there is nothing that they are unaware of) and living in paranoia (i.e., agents believe, perhaps incorrectly, that there is something that they are unaware of). We show that both living in denial and living in paranoid, in the absence of other forms of delusion, imply terminal partitionality, and hence the notrade theorem result obtains. This paper replaces an earlier working paper titled “ObjectBased Unawareness II: Applications”. Our companion paper, Board & Chung [4], replaces an earlier working paper titled “ObjectBased Unawareness”.
Logics of informational attitudes and informative actions
, 2010
"... There is an extensive literature focused on using logical methods to reason about communities of agents engaged in some form of social interaction. Much of the work builds upon existing logical frameworks developed by philosophers and computer scientists incorporating insights and ideas from philoso ..."
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There is an extensive literature focused on using logical methods to reason about communities of agents engaged in some form of social interaction. Much of the work builds upon existing logical frameworks developed by philosophers and computer scientists incorporating insights and ideas from philosophy (especially
Belief Revision in Games of Perfect Information
"... A syntactic formalism for the modeling of belief revision in perfect information games is presented that allows to define the rationality of a player's choice of moves relative to the beliefs he holds as his respective decision nodes have been reached. In this setting, true common belief in the stru ..."
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A syntactic formalism for the modeling of belief revision in perfect information games is presented that allows to define the rationality of a player's choice of moves relative to the beliefs he holds as his respective decision nodes have been reached. In this setting, true common belief in the structure of the game and rationality held before the start of the game does not imply that backward induction will be played. To derive backward induction, a "forward belief' condition is formulated in terms of revised rather than initial beliefs. Alternative notions of rationality as well as the use of knowledge instead of belief are also studied within this framework.
ObjectBased Unawareness II: Applications
, 2008
"... Board & Chung [3] propose a class of structures (OBU structures) designed to model agents ’ awareness of their own unawareness. In particular, OBU structures are capable of modeling an agent who is “not sure whether or not she is aware of everything”, without the implication that she does not know w ..."
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Board & Chung [3] propose a class of structures (OBU structures) designed to model agents ’ awareness of their own unawareness. In particular, OBU structures are capable of modeling an agent who is “not sure whether or not she is aware of everything”, without the implication that she does not know what she is aware of. 1 In Board & Chung [3] (henceforth BC), OBU structures were used to provide semantics for a language of firstorder modal logic; in this paper, we show that essentially the same structures can be interpreted without appeal to a formal language, creating a purely settheoretic model of unawareness. We prove characterization results which provide a precise description of the features of these structures, and then present two applications. The first application examines the legal interpretive doctrine verba fortius accipiuntur contra proferentem, which instructs judges to resolve any contractual ambiguity against the party who drafted the contract. We show that this doctrine systematically outperforms other doctrines when there is persistent asymmetric awareness between the contracting parties. The second application is to revisit a central result in Heifetz, Meier, and Schipper [16] (henceforth HMS). HMS claim that “unawareness can be interpreted as a special form of delusion”. However, surprisingly, they prove that the
Conditional belief types
, 2013
"... We study type spaces where a player’s type at a state is a conditional probability on the space. We axiomatize these type spaces using conditional belief operators, and examine three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certai ..."
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We study type spaces where a player’s type at a state is a conditional probability on the space. We axiomatize these type spaces using conditional belief operators, and examine three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certain of her beliefs. Second, echo, according to which the unconditional beliefs implied by the condition must be held given the condition. Third, determination, which says that the conditional beliefs are the unconditional beliefs that are conditionally certain. The echo axiom implies that conditioning on an event is the same as conditioning on the event being certain, which formalizes the standard informal interpretation of conditioning in probability theory. The echo axiom also implies that the conditional probability given an event is a prior of the unconditional probability. The gametheoretic application of our model, which we treat in the context of an example, sheds light on a number of basic issues in the analysis of extensive form games. Type spaces are closely related to the sphere models of counterfactual conditionals and to models of hypothetical knowledge, and we discuss these relationships in detail.