A general solution concept for two-person, zero-sum games

Kindler, Jürgen

doi:10.1007/bf00934634

Cited by 11 publications

(7 citation statements)

References 9 publications

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“…Aside: Under a topology of pointwise convergence in lotteries, Theorem 1 generalizes to infinite states spaces and infinite, closed options sets O by using Theorem 2.1 of Kindler (1983) to replace Pearce's use of von Neumann's Minimax Theorem, which does not generalize to infinite games. But then the mixed strategies needed with Kindler's result are merely finitely additive, rather than countably additive.…”

Section: Distinguishing Sets Of Probabilities By Their Coherent Choicmentioning

confidence: 98%

Coherent choice functions under uncertainty

2009

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We discuss several features of coherent choice functions-where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertaintywhere only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the "shape" or "connectedness" of the sets of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almoststate-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility.

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Section: Distinguishing Sets Of Probabilities By Their Coherent Choicmentioning

confidence: 98%

Coherent choice functions under uncertainty

2009

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“…For the effects of finite additivity on the value of two-person zero sum games, see Maitra and Sudderth (1993), Maitra and Sudderth (1998), Yanovskaya (1970), Kindler (1983) and Schervish and Seidenfeld (1996). For similar studies on non-zero sum games, see Marinacci (1997), Harris et al (2005) and Capraro and Scarsini (2013).…”

Section: Interplay Between Set Theory and Game Theorymentioning

confidence: 99%

Catch games: the impact of modeling decisions

Flesch

Vermeulen²,

Zseleva³

2018

Int J Game Theory

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We examine the guarantee levels of the players in a type of zero sum games. We show how these levels depend on the sigma algebras that are being employed on the players' action spaces. We further argue that guarantee levels may therefore also depend on set theoretic considerations. Additionally, we calculate the guarantee levels for finitely additive strategies. The solutions of catch games essentially differ among these setups. We find optimal strategies for almost all cases. Keywords Infinite games • Two-person zero sum games • Countably additive strategies • Sigma algebras • Set theory • Finitely additive strategies We would like to thank Miklós Pintér and William Sudderth for their helpful comments, and the Dutch institute NWO (Grant no. 040.11.495) for providing the financial support for William's visit to Maastricht. We also thank an associate editor and two anonymous reviewers for their useful suggestions.

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“…Relating to our second pair of notions, taking a fixed order of integration as the expected payoff has been analyzed before by Heath and Sudderth (1972), and Sudderth (1993, 1998). Yanovskaya (1970) and Kindler (1983) consider the double integral as an expected payoff only when different orders of integration yield the same expected payoff. For all other strategy profiles, i.e.…”

Section: Related Literaturementioning

confidence: 99%

Zero-sum games with charges

Flesch

Vermeulen

Zseleva

2017

Games and Economic Behavior

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A general solution concept for two-person, zero-sum games

Cited by 11 publications

References 9 publications

Coherent choice functions under uncertainty

Coherent choice functions under uncertainty

Catch games: the impact of modeling decisions

Zero-sum games with charges

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