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Pré-Publication, Document De Travail Année : 2022

Mixed-Strategy Equilibria in the War of Attrition under Uncertainty

Résumé

We study a generic family of two-player continuous-time nonzero-sum stopping games modeling a war of attrition with symmetric information and stochastic payoffs that depend on an homogeneous linear diffusion. We first show that any Markovian mixed strategy for player $i$ can be represented by a pair $(\mu^i,S^i)$, where $\mu^i$ is a measure over the state space representing player $i$'s stopping intensity, and $S^i$ is a subset of the state space over which player $i$ stops with probability $1$. We then prove that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, the measures $\mu^i$ have to be essentially discrete, and we characterize any such equilibrium through a variational system satisfied by the players' equilibrium value functions. This result contrasts with the literature, which focuses on pure-strategy equilibria, or, in the case of symmetric players, on mixed-strategy equilibria with absolutely continuous stopping intensities. We illustrate this result by revisiting the model of exit in a duopoly under uncertainty, and exhibit a mixed-strategy equilibrium in which attrition takes place on the equilibrium path though firms have different liquidation values.
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Dates et versions

hal-03816389 , version 1 (16-10-2022)
hal-03816389 , version 2 (25-11-2023)
hal-03816389 , version 3 (12-07-2024)

Identifiants

Citer

Jean-Paul Décamps, Fabien Gensbittel, Thomas Mariotti. Mixed-Strategy Equilibria in the War of Attrition under Uncertainty. 2022. ⟨hal-03816389v1⟩
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