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15
Secrecy in multiagent systems
"... We introduce a general framework for reasoning about secrecy requirements in multiagent systems. Because secrecy requirements are closely connected with the knowledge of individual agents of a system, our framework employs the modal logic of knowledge within the context of the wellstudied runs and ..."
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Cited by 71 (6 self)
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We introduce a general framework for reasoning about secrecy requirements in multiagent systems. Because secrecy requirements are closely connected with the knowledge of individual agents of a system, our framework employs the modal logic of knowledge within the context of the wellstudied runs and systems framework. Put simply, “secrets ” are facts about a system that lowlevel agents are never allowed to know. The framework presented here allows us to formalize this intuition precisely, in a way that is much in the spirit of Sutherland’s notion of nondeducibility. Several wellknown attempts to characterize the absence of information flow, including separability, generalized noninterference, and nondeducibility on strategies, turn out to be special cases of our definition of secrecy. However, our approach lets us go well beyond these definitions. It can handle probabilistic secrecy in a clean way, and it suggests generalizations of secrecy that may be useful for dealing with resourcebounded reasoning and with issues such as downgrading of information.
Lexicographic probability, conditional probability, and nonstandard probability
 In Theoretical Aspects of Rationality and Knowledge: Proc. Eighth Conference (TARK 2001
, 2001
"... The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If coun ..."
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Cited by 24 (2 self)
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The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS’s are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS’s are equivalent to NPS’s. However, if the state space is infinite, NPS’s are shown to be more general than LPS’s. JEL classification numbers: C70; D80; D81; 1
Unawareness, Beliefs, and Speculative Trade
, 2009
"... We define a generalized statespace model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. We compare unawareness with probability zero belief. Applying our unawareness belief structures, we show that the common p ..."
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Cited by 7 (4 self)
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We define a generalized statespace model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. We compare unawareness with probability zero belief. Applying our unawareness belief structures, we show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized “Notrade” theorem according to which there can not be common certainty of strict preference to trade. Moreover, we show a generalization of the “Noagreeingtodisagree” theorem.
Conservative Belief and Rationality
, 2012
"... Brandenburger and Dekel have shown that common belief of rationality (CBR) characterizes rationalizable strategies, which are also characterized by a refinement of subjective correlated equilibrium called a posteriori equilibrium. It is possible that players ’ beliefs are incompatible, in the sense ..."
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Cited by 3 (3 self)
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Brandenburger and Dekel have shown that common belief of rationality (CBR) characterizes rationalizable strategies, which are also characterized by a refinement of subjective correlated equilibrium called a posteriori equilibrium. It is possible that players ’ beliefs are incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require players ’ beliefs to be conservative, in the sense that all players must ascribe the actual world positive probability. Aumann has shown that, under the common prior assumption (CPA), common belief of rationality characterizes strategies in the support of an objective correlated equilibrium. Under the CPA, without loss of generality, all players ’ beliefs can be assumed to be conservative. We consider the consequences of common convervative belief of rationality (CCBR), without the common prior assumption. We show that CCBR characterizes strategies in the support of a subjective correlated equilibrium where all players ’ beliefs have common support. We also In the Bayesian view of the world, each player has a subjective probability distribution (describing her
Epistemic game theory: complete information. The New Palgrave Dictionary of Economics,
, 2008
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Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic
, 2010
"... Aumann’s agreeing to disagree theorem is a central theorem of game theory. This result says that if two agents have a common prior, then they cannot agree (have common knowledge of their posteriors) to disagree (while these posteriors are not identical). This thesis looks at the agreeing to disagree ..."
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Cited by 2 (0 self)
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Aumann’s agreeing to disagree theorem is a central theorem of game theory. This result says that if two agents have a common prior, then they cannot agree (have common knowledge of their posteriors) to disagree (while these posteriors are not identical). This thesis looks at the agreeing to disagree theorem from the perspective of probabilistic dynamic epistemic logic. The first goal of the thesis is to establish a new connection between game theory and epistemic logic. We prove (local modelbased versions and global framebased versions of) several semantic agreement theorems, and show that these are natural formalizations of Aumann’s original result. We also provide axiomatizations of (dynamic) agreement logics, in which the first of these agreement theorems can be derived syntactically. The second goal is the further technical development of probabilistic dynamic epistemic logic. We mention three examples. First, to model the experiment dynamics, we enrich the probabilistic Kripke models with ‘experiment relations’, thus establishing a link with the dynamic epistemic logic of questions. Second,
SECRECY AND ANONYMITY IN INTERACTIVE SYSTEMS
, 2006
"... When building systems that guarantee confidentiality, system designers must first define confidentiality appropriately. Although researchers have proposed definitions of properties such as secrecy, anonymity, and privacy for a wide variety of system models, general definitions that are intuitive, wi ..."
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Cited by 1 (0 self)
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When building systems that guarantee confidentiality, system designers must first define confidentiality appropriately. Although researchers have proposed definitions of properties such as secrecy, anonymity, and privacy for a wide variety of system models, general definitions that are intuitive, widely applicable, and sufficiently formal have proven surprisingly elusive. The goal of this dissertation is to provide such a framework for systems that interact with multiple agents, emphasizing definitions of secrecy (to rule out unwanted information flows) and anonymity (to prevent observers from learning the identity of an agent who performs some action). The definitions of secrecy extend earlier definitions of secrecy and nondeducibility given by Shannon and Sutherland. Roughly speaking, one agent maintains secrecy with respect to another if the second agent cannot rule out any possibilities for the behavior or state of the first agent. These definitions are characterized syntactically, using a modal logic of knowledge. Definitions of anonymity are given, with respect to agents, actions, and observers, and are also stated in terms of a modal logic of knowledge. The general framework is shown
Ambiguous Language and Differences in Beliefs
"... Standard models of multiagent modal logic do not capture the fact that information is often ambiguous, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents ’ bel ..."
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Cited by 1 (1 self)
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Standard models of multiagent modal logic do not capture the fact that information is often ambiguous, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents ’ beliefs regarding whether or not there is ambiguity. We consider the impact of ambiguity on a seminal result in economics: Aumann’s result saying that agents with a common prior cannot agree to disagree. This result is known not to hold if agents do not have a common prior; we show that it also does not hold in the presence of ambiguity. We then consider the tradeoff between assuming a common interpretation (i.e., no ambiguity) and a common prior (i.e., shared initial beliefs). 1
Finite order implications of . . .
, 2003
"... I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that in finite models, the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any finite N and any finite parti ..."
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I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that in finite models, the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any finite N and any finite partitions model where priors have the same support, there is another finite partitions model with common priors which has the same n th order beliefs
Common Priors For LikeMinded Agents
, 2003
"... Two agents are likeminded when their beliefs are equal once conditioned on knowledge of both of their types. Assuming the existence of an outside observer that is commonly known to be likeminded and uninformative about the insiders, we derivetheexistenceofacommonprioramong the insiders, with the ou ..."
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Two agents are likeminded when their beliefs are equal once conditioned on knowledge of both of their types. Assuming the existence of an outside observer that is commonly known to be likeminded and uninformative about the insiders, we derivetheexistenceofacommonprioramong the insiders, with the outsiders beliefs (appropriately conditioned) serving as the common prior. A key advantage of likemindedness is its fully local definition, which allows to distinction between consistency of agent’s actual beliefs and of beliefs they merely view as possible. By later including agents ’ “epistemic attitudes ” among the primitives, we derive likemindedness from reasonableness judgments about each others attitudes. In this richer framework, one can model alternative conceptions of intersubjective rationality as constraints on such reasonableness judgements.