Rationalizability in general situations

Chen, Yi‐Chun; Luo, Xiao; Qu, Chen

doi:10.1007/s00199-015-0882-y

Cited by 11 publications

(4 citation statements)

References 49 publications

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“…Given a state of the world θ, a mechanism Γ induces a game of complete information among the agents. In this paper we assume (correlated) rationalizability as our solution concept in the sense of Brandenburger and Dekel (1987) (also see Chen et al (2016), Bernheim (1984), and Pearce (1984)). Given a mechanism Γ and a state of the world θ, we denote by R i (Γ, θ) the set of rationalizable strategies for agent i and R(Γ, θ) = R 1 (Γ, θ) × R 2 (Γ, θ) .…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…The use of stochastic integer game may not be entirely satisfactory and studying rationalizable implementation without relying on such games is a natural question to address. A step in this direction is Chen et al (2016) who, in economic environments, study rationalizable implementation of a SCF and Jain and Lombardi (2019) who study, in economic environments, virtual rationalizable implementation of SCCs.…”

Section: Role Of Snti Condition T and Stochastic Mechanismmentioning

confidence: 99%

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Rationalizable Implementation of Social Choice Correspondences

Jain

2019

SSRN Journal

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A social choice correspondence (SCC) F is a mapping which associates with every state θ ∈ Θ a non empty subset of a set of outcomes. F is implementable in rationalizable strategies provided that there exists a mechanism such that for each state θ, the support of its set of rationalizable outcomes is equal to the socially desirable set F (θ). We find that r-monotonicity is a necessary condition for the rationalizable implementation of F . When there are at least three agents and F satisfies certain auxiliary conditions, r-monotonicity is also sufficient for rationalizable implementation. Finally, we show that a SCC which is never single valued is rationalizably implementable if and only if it satisfies r-monotonicity.

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Section: Notation and Definitionsmentioning

confidence: 99%

Section: Role Of Snti Condition T and Stochastic Mechanismmentioning

confidence: 99%

Rationalizable Implementation of Social Choice Correspondences

Jain

2019

SSRN Journal

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“…In mathematics, a topology which is closed under arbitrary intersection is often called an Alexsandroff topology (see, for example, Pacuit (2017), Vickers (1989), and the references therein). 13 Within the framework of this paper, the fact that a topology (which represents information) is closed under arbitrary intersection corresponds to the arbitrary conjunction ability.…”

Section: Information and Topologymentioning

confidence: 99%

Epistemic foundations for set-algebraic representations of knowledge

Fukuda

2019

Journal of Mathematical Economics

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“…The probabilistic and nonprobabilistic beliefs have been discussed in Perea (2014). Chen et al (2016) extend rationalizability beyond the probabilistic beliefs and expected utility maximization. The non-expected utility models have also been examined in Jungbauer and Ritzberger (2011) and Beauchêne (2016).…”

Section: Introductionmentioning

confidence: 99%

Rationalizable strategies in games with incomplete preferences

Kokkala¹,

Berg

Virtanen

et al. 2018

Theory Decis

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This paper introduces a new solution concept for games with incomplete preferences. The concept is based on rationalizability and it is more general than the existing ones based on Nash equilibrium. In rationalizable strategies, we assume that the players choose nondominated strategies given their beliefs of what strategies the other players may choose. Our solution concept can also be used, e.g., in ordinal games where the standard notion of rationalizability cannot be applied. We show that the sets of rationalizable strategies are the maximal mutually nondominated sets. We also show that no new rationalizable strategies appear when the preferences are refined, i.e., when the information gets more precise. Moreover, noncooperative multicriteria games are suitable applications of incomplete preferences. We apply our framework to such games, where the outcomes are evaluated according to several criteria and the payoffs are vector valued. We use the sets of feasible weights to represent the relative importance of the criteria. We demonstrate the applicability of the new solution concept with an ordinal game and a bicriteria Cournot game.

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Rationalizability in general situations

Cited by 11 publications

References 49 publications

Rationalizable Implementation of Social Choice Correspondences

Rationalizable Implementation of Social Choice Correspondences

Epistemic foundations for set-algebraic representations of knowledge

Rationalizable strategies in games with incomplete preferences

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