An application of Ramsey theorem to stopping games

Eran Shmaya; Eilon Solan; Nicolas Vieille

doi:10.1016/S0899-8256(02)00539-0

An application of Ramsey theorem to stopping games

Eran Shmaya, Eilon Solan^*, Nicolas Vieille

^*Corresponding author for this work

Managerial Economics, Decision Sciences and Operations

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We prove that every two-player nonzero-sum deterministic stopping game with uniformly bounded payoffs admits an E-equilibrium, for every E > 0. The proof uses Ramsey Theorem that states that for every coloring of a complete infinite graph by finitely many colors there is a complete infinite subgraph which is monochromatic.

Original language	English (US)
Pages (from-to)	300-306
Number of pages	7
Journal	Games and Economic Behavior
Volume	42
Issue number	2
DOIs	https://doi.org/10.1016/S0899-8256(02)00539-0
State	Published - Feb 2003

Keywords

Equilibrium payoff
Nonzero-sum stopping games
Ramsey Theorem

ASJC Scopus subject areas

Finance
Economics and Econometrics

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10.1016/S0899-8256(02)00539-0

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abstract = "We prove that every two-player nonzero-sum deterministic stopping game with uniformly bounded payoffs admits an E-equilibrium, for every E > 0. The proof uses Ramsey Theorem that states that for every coloring of a complete infinite graph by finitely many colors there is a complete infinite subgraph which is monochromatic.",

keywords = "Equilibrium payoff, Nonzero-sum stopping games, Ramsey Theorem",

author = "Eran Shmaya and Eilon Solan and Nicolas Vieille",

note = "Funding Information: We thank Noga Alon, David Gilat, Abraham Neyman, and Sylvain Sorin for their time and suggestions. The second author acknowledges the financial support of the TMR Network, FMRX.CT96.0055.",

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AU - Shmaya, Eran

AU - Solan, Eilon

AU - Vieille, Nicolas

N1 - Funding Information: We thank Noga Alon, David Gilat, Abraham Neyman, and Sylvain Sorin for their time and suggestions. The second author acknowledges the financial support of the TMR Network, FMRX.CT96.0055.

PY - 2003/2

Y1 - 2003/2

N2 - We prove that every two-player nonzero-sum deterministic stopping game with uniformly bounded payoffs admits an E-equilibrium, for every E > 0. The proof uses Ramsey Theorem that states that for every coloring of a complete infinite graph by finitely many colors there is a complete infinite subgraph which is monochromatic.

AB - We prove that every two-player nonzero-sum deterministic stopping game with uniformly bounded payoffs admits an E-equilibrium, for every E > 0. The proof uses Ramsey Theorem that states that for every coloring of a complete infinite graph by finitely many colors there is a complete infinite subgraph which is monochromatic.

KW - Equilibrium payoff

KW - Nonzero-sum stopping games

KW - Ramsey Theorem

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JO - Games and Economic Behavior

JF - Games and Economic Behavior

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ER -

An application of Ramsey theorem to stopping games

Abstract

Keywords

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