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

72 Pages Posted: 1 Dec 2023

See all articles by Jean-Paul Decamps

Jean-Paul Decamps

University of Toulouse 1 - Toulouse School of Economics (TSE)

Fabien Gensbittel

University of Toulouse 1 - Toulouse School of Economics (TSE)

Thomas Mariotti

Universite de Toulouse 1 Capitole

Multiple version iconThere are 2 versions of this paper

Date Written: November 23, 2023

Abstract

We study a generic model of the war of attrition with symmetric information and stochastic payoffs that depend on a homogeneous linear diffusion. We first show that a player's mixed Markov strategy can be represented by an intensity measure over the state space together with a subset of the state space over which the player concedes with probability 1. We then show that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, these intensity measures must be discrete, and characterize any such equilibrium through a variational system for the players' value functions. We illustrate these findings by revisiting the standard model of exit in a duopoly under uncertainty and construct a mixed-strategy Markov-perfect equilibrium in which attrition takes place on path despite firms having different liquidation values. We show that firms' stock prices comove negatively over the attrition zone and exhibit resistance and support patterns documented by technical analysis.

Keywords: War of Attrition, Mixed-Strategy Equilibrium, Uncertainty.

JEL Classification: C61, D25, D83.

Suggested Citation

Decamps, Jean-Paul and Gensbittel, Fabien and Mariotti, Thomas, The War of Attrition under Uncertainty: Theory and Robust Testable Implications (November 23, 2023). Available at SSRN: https://ssrn.com/abstract=4642426 or http://dx.doi.org/10.2139/ssrn.4642426

Jean-Paul Decamps (Contact Author)

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

1, Esplanade de l'Université
31080 Toulouse Cedex 06
France

Fabien Gensbittel

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

Thomas Mariotti

Universite de Toulouse 1 Capitole ( email )

2 Rue du Doyen-Gabriel-Marty
Toulouse, 31042
France

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