Equilibrium in an asymmetric war of attrition with a fight option

Bara Kim and Geofferey Jiyun Kim

Defence and Peace Economics, 2025, vol. 36, issue 8, 1197-1213

Abstract: We develop an asymmetric incomplete-information continuous-time two-player war-of-attrition game with a fight option. We show that there exists a unique Bayesian Nash equilibrium without a non-credible threat. Under the equilibrium, either the game stops immediately with a resignation of a player, or costly attrition remains. Moreover, a critical time when a fight transpires exists unless a player resigns prior to that time. It is remarkable that the attrition phenomenon appears under the equilibrium of our model with the fight option, despite asymmetries of the players and the fight option that ceases the game if chosen. This can provide a clue for explaining the attrition phenomenon that frequently arises in conflicts of the real world.

Date: 2025
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DOI: 10.1080/10242694.2025.2463971

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