The Annals of Probability

Two-player nonZero–sum stopping games in discrete time

Eran Shmaya and Eilon Solan

Full-text: Open access

Abstract

We prove that every two-player nonzero–sum stopping game in discrete time admits an ɛ-equilibrium in randomized strategies for every ɛ>0. We use a stochastic variation of Ramsey’s theorem, which enables us to reduce the problem to that of studying properties of ɛ-equilibria in a simple class of stochastic games with finite state space.

Article information

Source
Ann. Probab., Volume 32, Number 3B (2004), 2733-2764.

Dates
First available in Project Euclid: 6 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1091813629

Digital Object Identifier
doi:10.1214/009117904000000162

Mathematical Reviews number (MathSciNet)
MR2078556

Zentralblatt MATH identifier
1079.60045

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 91A15: Stochastic games 91A05: 2-person games

Keywords
Stopping games Dynkin games stochastic games ɛ-equilibrium randomized stopping times

Citation

Shmaya, Eran; Solan, Eilon. Two-player nonZero–sum stopping games in discrete time. Ann. Probab. 32 (2004), no. 3B, 2733--2764. doi:10.1214/009117904000000162. https://projecteuclid.org/euclid.aop/1091813629


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