On the existence of Markovian randomized equilibria in Dynkin games of war-of-attrition-type

2024/06/14 by Sören Christensen, Christensen, Sören, Boy Schultz +1
Decision Sciences · Engineering · Mathematics · #91A15 (Secondary) #91A55 (Primary) 60G40 #FOS: Mathematics #Game Theory and Applications #Markov Chains and Monte Carlo Methods #Military Defense Systems Analysis #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2406.09820

openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In optimal stopping problems, a Markov structure guarantees Markovian optimal stopping times (first exit times). Surprisingly, there is no analogous result for Markovian stopping games once randomization is required. This paper addresses this gap by proving the existence of Markov-perfect equilibria in a specific type of stopping game - a general nonzero-sum Dynkin games of the war-of-attrition type with underlying linear diffusions. Our main mathematical contribution lies in the development of appropriate topologies for Markovian randomized stopping times. This allows us to establish the existence of equilibria within a tractable and interpretable class of stopping times, paving the way for further analysis of Markovian stopping games.

Related

• Markovian randomized equilibria for general Markovian Dynkin games in discrete time
• General Markovian randomized equilibrium existence and construction in zero-sum Dynkin games for diffusions
• Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition
• On Dynkin Games with Unordered Payoff Processes
• Equilibrium in Two-Player Non-Zero-Sum Dynkin Games in Continuous Time