The War of Attrition under Uncertainty: Theory and Robust Testable Implications

Abstract

We study a symmetric-information war of attrition in which the players’ payoffs depend on exogenous market conditions that evolve according to a homogeneous linear diffusion. Using that a Markov strategy can be represented as a stopping region along with an intensity measure of stopping, we fully characterize mixed-strategy Markovperfect equilibria through a variational system for the players’ value functions. When players are asymmetric, in any such equilibrium each player randomizes at a discrete set of thresholds for market conditions. As a result, players may alternatively find themselves in a position of strength or weakness on the equilibrium path. Delayed concessions occur because a player currently in a position of weakness can hope for market conditions to reverse in his favor. In the standard duopoly model of exit under uncertainty, the firms’ stock prices and their return volatilities comove negatively over the attrition region and exhibit patterns documented by technical analysis.

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Reference

Jean-Paul Décamps, Fabien Gensbittel, and Thomas Mariotti, “The War of Attrition under Uncertainty: Theory and Robust Testable Implications”, TSE Working Paper, n. 22-1374, October 2022, revised June 2024.