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Mixed-Strategy Equilibria in the War of Attrition under Uncertainty

Jean-Paul Décamps, Fabien Gensbittel and Thomas Mariotti

No 22-1374, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: 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 (µ i , S i ), where µ 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 tops with probability 1. We then prove that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, the measures µ 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.

Keywords: War of Attrition; Mixed-Strategy Equilibrium; Uncertainty. (search for similar items in EconPapers)
JEL-codes: C61 D25 D83 (search for similar items in EconPapers)
Date: 2022-10
New Economics Papers: this item is included in nep-gth and nep-mic
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