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February 2018 Nash equilibria of threshold type for two-player nonzero-sum games of stopping
Tiziano De Angelis, Giorgio Ferrari, John Moriarty
Ann. Appl. Probab. 28(1): 112-147 (February 2018). DOI: 10.1214/17-AAP1301

Abstract

This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not nonsingular boundary behaviour [in the sense of Itô and McKean (Diffusion Processes and Their Sample Paths (1974) Springer, page 108)]. We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also provide conditions sufficient for the uniqueness of the equilibrium in this class.

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Tiziano De Angelis. Giorgio Ferrari. John Moriarty. "Nash equilibria of threshold type for two-player nonzero-sum games of stopping." Ann. Appl. Probab. 28 (1) 112 - 147, February 2018. https://doi.org/10.1214/17-AAP1301

Information

Received: 1 August 2015; Revised: 1 November 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06873681
MathSciNet: MR3770874
Digital Object Identifier: 10.1214/17-AAP1301

Subjects:
Primary: 35R35 , 60G40 , 60J60 , 91A05 , 91A15

Keywords: free boundary problems , Nash equilibrium , Nonzero-sum Dynkin games , regular diffusions , smooth-fit principle

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2018
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