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Memoryless-Strategy Equilibria of a N-Player War of Attrition Game with Complete Information

Wang Hao ()
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Wang Hao: China Center for Economic Research, National School of Development, Peking University, Beijing, China

The B.E. Journal of Theoretical Economics, 2025, vol. 25, issue 1, 137-164

Abstract: Consider a war of attrition game in continuous time with complete information, in which N ≥ 2 players compete for N − K prizes. I focus on the equilibria in which the strategies follow exponential distributions, which are memoryless. When K = 1, such an equilibrium can be explicitly characterized. The equilibrium certainly exists if N = 2. If N ≥ 3, it exists as long as the weakest player is not too weak compared to the average. If it exists, the equilibrium is unique under some conditions. When K ≥ 2, the game typically has nondegenerate equilibria in which K − 1 relatively weak players concede at the beginning. The model can be extended to the case in which the players have loser-dependent valuations. The model helps to solve a generalized exit game in a “nature oligopoly” and an all-pay auction with ascending bids.

Keywords: all-pay auction; complete information; loser-dependent valuation; N-player; war of attrition (search for similar items in EconPapers)
JEL-codes: D74 H41 L13 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/bejte-2024-0081

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