Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition

2024/07/05 by Décamps, Jean-Paul, Gensbittel, Fabien, Mariotti, Thomas
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2407.04878

Abstract

We prove the existence of a Markov-perfect equilibrium in randomized stopping times for a model of the war of attrition in which the underlying state variable follows a homogenous linear diffusion. The proof uses the fact that the space of Markovian randomized stopping times can be topologized as a compact absolute retract, which in turn enables us to use a powerful fixed-point theorem by Eilenberg and Montgomery. We illustrate our results with an example of a war of attrition that admits a mixed-strategy Markov-perfect equilibrium but no pure-strategy Markov-perfect equilibrium.

Related

• Mixed-Strategy Equilibria in the War of Attrition under Uncertainty
• On the existence of Markovian randomized equilibria in Dynkin games of war-of-attrition-type
• Markovian randomized equilibria for general Markovian Dynkin games in discrete time
• On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems
• Symmetric Equilibria in Stochastic Timing Games