Subjectivity and correlation in randomized strategies

Aumann, Robert J.

doi:10.1016/0304-4068(74)90037-8

Cited by 1,312 publications

(948 citation statements)

References 11 publications

(15 reference statements)

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“…However, NE-solutions render a lot of the refined or modified principles of optimality, allowing to smooth differences in utility and equity [2], [10], [11]. Mainly, they are principles of Pareto equilibrium [2], [6], [8], [10], [13], [14], Mertens-stable equilibrium [15], trembling hand perfect equilibrium [16], proper equilibrium [17], [18], correlated equilibrium [19], sequential equilibrium [20], [21], quasi-perfect equilibrium [18], [22], [23], perfect Bayesian equilibrium [18], [20], [24], [25], quantal response equilibrium [26], [27], self-confirming equilibrium [28], [29], strong Nash equilibrium [30], [31], Markov perfect equilibrium [32], [33]. The question is only to find NEsolutions as fast as possible.…”

Section: Noncooperative Game Modelsmentioning

confidence: 99%

Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

Romanuke

2015

Electrical, Control and Communication Engineering

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-The paper suggests a method of obtaining an approximate solution of the infinite noncooperative game on the unit hypercube. The method is based on sampling uniformly the players' payoff functions with the constant step along each of the hypercube dimensions. The author states the conditions for a sufficiently accurate sampling and suggests the method of reshaping the multidimensional matrix of the player's payoff values, being the former player's payoff function before its sampling, into a matrix with minimally possible number of dimensions, where also maintenance of one-to-one indexing has been provided. Requirements for finite NE-strategy from NE (Nash equilibrium) solution of the finite game as the initial infinite game approximation are given as definitions of the approximate solution consistency. The approximate solution consistency ensures its relative independence upon the sampling step within its minimal neighborhood or the minimally decreased sampling step. The ultimate reshaping of multidimensional matrices of players' payoff values to the minimal number of dimensions, being equal to the number of players, stimulates shortened computations.

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Section: Noncooperative Game Modelsmentioning

confidence: 99%

Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

Romanuke

2015

Electrical, Control and Communication Engineering

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“…The notion of correlated equilibrium was introduced by Aumann [2]. A non-technical introduction motivating the notion of cheap talk is given in Farrell and Rabin [8].…”

Section: Related Workmentioning

confidence: 99%

“…In the basic case of two-player games, a Nash equilibrium (NE) constitutes of two independent plans of action, one for each player, such that no player can unilaterally benefit by deviating from her own plan. The NE solution concept was subsequently generalized by Aumann [2], who allowed players to pick their actions in a correlated way. Correlated equilibria (CE) are in many cases preferable over NE, in part because they can potentially guarantee higher utility to the players.…”

Section: Introductionmentioning

confidence: 99%

Limits on the Power of Cryptographic Cheap Talk

Hubáček

Nielsen

Rosen

2013

Advances in Cryptology – CRYPTO 2013

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We revisit the question of whether cryptographic protocols can replace correlated equilibria mediators in two-player strategic games. This problem was first addressed by Dodis, Halevi and Rabin (CRYPTO 2000), who suggested replacing the mediator with a secure protocol and proved that their solution is stable in the Nash equilibrium (NE) sense, provided that the players are computationally bounded.We show that there exist two-player games for which no cryptographic protocol can implement the mediator in a sequentially rational way; that is, without introducing empty threats. This explains why all solutions so far were either sequentially unstable, or were restricted to a limited class of correlated equilibria (specifically, those that do not dominate any NE, and hence playing them does not offer a clear advantage over playing any NE).In the context of computational NE, we classify necessary and sufficient cryptographic assumptions for implementing a mediator that allows to achieve a given utility profile of a correlated equilibrium. The picture that emerges is somewhat different than the one arising in semi-honest secure two-party computation. Specifically, while in the latter case every functionality is either "complete" (i.e., implies Oblivious Transfer) or "trivial" (i.e., can be securely computed unconditionally), in the former there exist some "intermediate" utility profiles whose implementation is equivalent to the existence of one-way functions.

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“…Technically, the requirements for a Bayes/Nash equilibrium under the veil of uncertainty imply that the distribution ρ(s i ,s -i ) should be a correlated equilibrium (Aumann, 1974(Aumann, , 1987.…”

Section: We Define Rational Institutional Design Under the Veil Of Unmentioning

confidence: 99%

“…The institutional arrangements we consider are self-enforcing in the sense that every country gains from following rules based on correlating strategies, which are not the same as mixed strategies and need not be a Nash equilibrium (Arce, 1997;Aumann, 1974Aumann, , 1987Skryms, 1996).…”

Section: Introductionmentioning

confidence: 99%

Transnational public goods: strategies and institutions

Arce

Sandler

2001

European Journal of Political Economy

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Weaker-link and better-shot public goods are prevalent in examples of transnational collective action. Instances include dike building, atmospheric monitoring, cyberspace virus control, deforestation, disease control, and peacekeeping. This paper analyzes essential game-theoretic features of such public goods, which allow correlated strategies to provide Pareto-improving alternatives to Nash equilibria. Correlation is justified as providing a formal structure for the veil of uncertainty and political leadership. Weaker-link and better-shot public goods differ in terms of the appropriate institutional design. We also consider the consequences of diminishing returns on game forms and institutional prescriptions.JEL classification: H41, D70.

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Subjectivity and correlation in randomized strategies

Cited by 1,312 publications

References 11 publications

Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

Limits on the Power of Cryptographic Cheap Talk

Transnational public goods: strategies and institutions

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