The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games

Khan, M. Ali; Rath, Kali P.; Sun, Yeneng

doi:10.1007/s00182-005-0004-3

Cited by 52 publications

(32 citation statements)

References 11 publications

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“…Balder and Rustichini (1994) extended these results to games with an infinite set of players. Other interesting purification results can be found in Khan et al (2006).…”

Section: Introductionmentioning

confidence: 89%

The ex ante -core for normal form games with uncertainty

Askoura¹,

Sbihi

Tikobaini

2013

Journal of Mathematical Economics

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In this paper we study the existence of the α−core for an n−person game with incomplete information. We follow a Milgrom-Weber-Balder formulation of a game with incomplete information. The players adopt behavioral strategies represented by Young measures. The game unrolls in one step at the ex ante stage. In this context, the mixed-extensions of the utility functions are not quasi-concave, and as a result the classical Scarf's theorem cannot be applied. An approximation argument is used to overcome this lack of concavity.

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“…Balder and Rustichini (1994) extended these results to games with an infinite set of players. Other interesting purification results can be found in Khan et al (2006).…”

Section: Introductionmentioning

confidence: 89%

The ex ante -core for normal form games with uncertainty

Askoura¹,

Sbihi

Tikobaini

2013

Journal of Mathematical Economics

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“…For some recent applications to game theory of the classical result of Dvoretzky-Wald-Wolfowitz in [1, Theorem 4], see [5]. Finally, we note that with the choice of appropriate mappings, the results in [8] should also extend to nowhere countably generated measure spaces using the technique employed here.…”

Section: Each ν ∈ M(a) and U ∈ C(a) This Function Is Jointly Continumentioning

confidence: 96%

Purification and saturation

Loeb

Sun

2009

Proc. Amer. Math. Soc.

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Abstract. This paper illustrates the general technique established in 1984 by Hoover and Keisler for extending certain types of results from atomless Loeb measure spaces to measure spaces that we shall call "nowhere countably generated". The Hoover-Keisler technique is applied here to further extend the authors' 2006 generalization of a theorem of Dvoretzky, Wald and Wolfowitz on the purification of measure-valued maps. The authors' 2006 result was first extended to these more general spaces by K. Podczeck in 2007; he used new results in functional analysis produced for that purpose. This paper demonstrates that, in general, such extensions follow from the Hoover-Keisler technique. Moreover, adaptations of counterexamples from earlier papers show that the extension obtained here holds only for nowhere countably generated spaces.

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“…Thus, Items 1 and 2 guarantee that if the mixed strategy f is a Nash equilibrium, so is its strong purification, which is a pure strategy. See Section 3 of Khan et al (2006) for more discussion.…”

Section: Finite Games With Incomplete Informationmentioning

confidence: 99%

“…A unified approach by applying DWW Theorem to purification problems in games with finite players is presented in Khan et al (2006). More precisely, Khan et al establish a stronger purification result that, in the above games with diffused and incomplete information, any mixed strategy (not necessarily an equilibrium) has a strong purification (see Definition 4 below).…”

Section: Introductionmentioning

confidence: 99%

“…Finally, as an application of Theorem 1, following Khan et al (2006), we study in Section 4 the problem of purification for mixed strategies in game theoretic models as in Milgrom and Weber (1985). We show that every mixed strategy has many strong purifications in such a finite-player game with a general Polish action space (not necessarily compact), and with a diffused, conditionally independent incomplete information structure, and even with discontinuous payoff functions.…”

Section: Introductionmentioning

confidence: 99%

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Purification, saturation and the exact law of large numbers

Wang

2010

Econ Theory

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Purification results are important in game theory and statistical decision theory. The purpose of this paper is to prove a general purification theorem that generalizes many earlier results. The key idea of our proof is to make use of the exact law of large numbers. As an application, we show that every mixed strategy in games with finite players, general action spaces and diffused, conditionally independent incomplete information has many strong purifications.JEL classification: C60 · C70

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The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games

Abstract: DWW theorem, Atomless, Mixed and pure strategies equilibria, Randomization, Purification, C07, DO5,

Cited by 52 publications

References 11 publications

The ex ante -core for normal form games with uncertainty

The ex ante -core for normal form games with uncertainty

Purification and saturation

Purification, saturation and the exact law of large numbers

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