Décamps, Jean-Paul, Gensbittel, Fabien and Mariotti, Thomas (2023) The War of Attrition under Uncertainty: Theory and Robust Testable Implications. TSE Working Paper, n. 22-1374, Toulouse

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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.

Item Type: Monograph (Working Paper)
Language: English
Date: 22 November 2023
Place of Publication: Toulouse
Uncontrolled Keywords: War of Attrition, Mixed-Strategy Equilibrium, Uncertainty.
JEL Classification: C61 - Optimization Techniques; Programming Models; Dynamic Analysis
D83 - Search; Learning; Information and Knowledge; Communication; Belief
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 18 Oct 2022 07:37
Last Modified: 04 Nov 2024 12:24
OAI Identifier: oai:tse-fr.eu:127448
URI: https://publications.ut-capitole.fr/id/eprint/46363
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