Signaling and mediation in games with common interests

Lehrer, Ehud; Rosenberg, Dinah; Shmaya, Eran

doi:10.1016/j.geb.2009.08.007

Cited by 75 publications

(98 citation statements)

References 15 publications

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“…9 In establishing the theorem, we will show constructively that if S is individually su¢ cient for S 0 and is a BCE random choice rule of (G; S), then we can use the BCE decision rule inducing and the Markov kernel establishing individual su¢ ciency to construct a BCE of (G; S 0 ) which induces ; this argument adapts an argument in Lehrer, Rosenberg, and Shmaya (2013). However, the results and arguments in Liu (2011) and Lehrer, Rosenberg, and Shmaya (2013) do not help prove the converse.…”

Section: An Immediate Corollary Of This Results Ismentioning

confidence: 95%

“…While Lehrer, Rosenberg, andShmaya (2010), (2013) are the closest works to ours, there is a large literature on the value of information in games, and we now discuss that work and its relation. Hirshleifer (1971) noted why information might be damaging in a many player context because it removed options to insure ex ante.…”

Section: Other Relations On Information Structures and Their Usesmentioning

confidence: 93%

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The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

Bergemann¹,

Morris

2013

SSRN Journal

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We de…ne and characterize a notion of correlated equilibrium for games with incomplete information, which we call Bayes correlated equilibrium: The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the information structure is characterized and shown to be equivalent to the set of Bayes correlated equilibria.A game of incomplete information can be decomposed into a basic game, given by actions sets and payo¤ functions, and an information structure. We introduce a partial order on many player information structures -which we call individual su¢ ciency -under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative de…nitions of correlated equilibrium in incomplete information games and of the partial order on information structures to others, including Blackwell's for the single player case.Keywords: Correlated equilibrium, incomplete information, robust predictions, information structure, su¢ ciency, Blackwell ordering.JEL Classification: C72, D82, D83.We acknowledge …nancial support through NSF Grants SES 0851200 and ICES 1215808. Earlier versions (Bergemann and Morris (2011)) were circulated under the title "Correlated Equilibrium in Games of Incomplete Information." We are grateful for discussions with Ben Brooks, with whom we are working on related projects, and to Hanming Fang and Ilya Segal, with whom we discussed related ideas for possible joint work in the past. We have bene…ted from comments from seminar participants and also from

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Section: An Immediate Corollary Of This Results Ismentioning

confidence: 95%

Section: Other Relations On Information Structures and Their Usesmentioning

confidence: 93%

The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

Bergemann¹,

Morris

2013

SSRN Journal

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“…We follow the formalization in Lehrer et al (2010Lehrer et al ( , 2013 and Bergemann and Morris (2015) that splits the Bayesian game in two components, so that strategic and informational aspects can be studied separately. First, we have a game with incomplete information G = I, Θ, ψ, (A i ) i∈I , (u i ) i∈I , where: I is a finite set of players, Θ is a finite set of states of nature, ψ ∈ ∆ (Θ) is a common prior with full support, and, for any player i, we have a finite set of actions A i , and a payoff function u i : A×Θ → R, where A = i∈I A i is the set of action profiles.…”

Section: Preliminariesmentioning

confidence: 99%

“…Lehrer et al (2010Lehrer et al ( , 2013 clarify epistemically the role of different assumptions and information structures and study their effect on equilibrium behavior. Bergemann and Morris (2015) introduce a further broader notion of correlated equilibrium, which they call Bayes correlated equilibrium, and which they show characterizes behavior robust to varying information structures.…”

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confidence: 99%

Bounded rationality and correlated equilibria

Germano

Zuazo-Garin

2016

Int J Game Theory

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We study an interactive framework that explicitly allows for nonrational behavior. We do not place any restrictions on how players' behavior deviates from rationality. Instead we assume that there exists a probability p such that all players play rationally with at least probability p, and all players believe, with at least probability p, that their opponents play rationally. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary probability p. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information, and they can be applied to observed frequencies of play to derive a measure p that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization.Keywords: strategic interaction, correlated equilibrium, robustness to bounded rationality, approximate knowledge, incomplete information, measure of rationality, experiments. JEL Classification: C72, D82, D83.

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“…But under this assumption, the "correlation" in interim correlated rationalizability is no longer relevant, and it is equivalent to interim independent rationalizability; the belief invariant Bayes correlated equilibrium reduces to the belief invariant Bayesian solution of Forges (2006) and Lehrer, Rosenberg, and Shmaya (2010); and Bayes correlated equilibrium reduces to the Bayesian solution of Forges (1993).…”

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confidence: 99%

Informational Robustness and Solution Concepts

Bergemann¹,

Morris

2014

SSRN Journal

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Consider the following "informational robustness" question: what can we say about the set of outcomes that may arise in equilibrium of a Bayesian game if players may observe some additional information? This set of outcomes will correspond to a solution concept that is weaker than equilibrium, with the solution concept depending on what restrictions are imposed on the additional information.We describe a uni…ed approach encompassing prior informational robustness results, as well as identifying the solution concept that corresponds to no restrictions on the additional information; this version of rationalizability depends only on the support of players'beliefs and implies novel predictions in classic economic environments of coordination and trading games.Our results generalize from complete to incomplete information the classical results in Aumann (1974Aumann ( , 1987 and Brandenburger and Dekel (1987) which can be (and were) given informational robustness interpretations. We discuss the relation between informational robustness and "epistemic" foundations of solution concepts.Jel Classification: C72, C79, D82, D83.Keywords: Incomplete Information, Informational Robustness, Bayes Correlated Equilibrium, Interim Corrrelated Rationalizability, Belief Free RationalizabilityWe acknowledge …nancial support from NSF ICES 1215808. We are grateful for discussions about an earlier version of this paper with

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Signaling and mediation in games with common interests

Cited by 75 publications

References 15 publications

The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

Bounded rationality and correlated equilibria

Informational Robustness and Solution Concepts

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