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sidenav header backgroundCCER讨论稿：N-Player War of Attrition with Complete Information
发布日期：2022-03-24 03:29 来源：
E2022004 2022-03-24
Hao Wang
Abstract
This paper considers a standard war of attrition game in which N heterogeneous players complete for N −K prizes. Each player can win at most one prize. When K = 1 (the base model), the game may have an equilibrium in which the strategies follow exponential distributions. The equilibrium surely exists when N = 2, but may not exist when N ≥ 3. In the equilibrium, a weaker player behaves ‘tougher’ and is more likely to win. All players receive an expected payoff of zero. The equilibrium, if exists, is the unique equilibrium in which the strategies follow atomless distributions and have supports of the entire time horizon. The game also has many partially degenerate equilibria, in which the game ends immediately with a probability. When K ≥ 2, there may exist nondegenerate equilibria in which K−1 players exit immediately. The model can be extended to cases where winners’ payoffs depend on which players exit, or where players face randomly arriving ‘defeats’. The findings can be applied to an all-pay auction with ascending bids and complete information.
Keywords: All-pay auction, Complete information, Interdependent valuation, Memoryless strategy, War of attrition
JEL codes: D74, H41, L13
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出版物展开 / 收起
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sidenav header backgroundCCER讨论稿：N-Player War of Attrition with Complete Information
发布日期：2022-03-24 03:29 来源：
E2022004 2022-03-24
Hao Wang
Abstract
This paper considers a standard war of attrition game in which N heterogeneous players complete for N −K prizes. Each player can win at most one prize. When K = 1 (the base model), the game may have an equilibrium in which the strategies follow exponential distributions. The equilibrium surely exists when N = 2, but may not exist when N ≥ 3. In the equilibrium, a weaker player behaves ‘tougher’ and is more likely to win. All players receive an expected payoff of zero. The equilibrium, if exists, is the unique equilibrium in which the strategies follow atomless distributions and have supports of the entire time horizon. The game also has many partially degenerate equilibria, in which the game ends immediately with a probability. When K ≥ 2, there may exist nondegenerate equilibria in which K−1 players exit immediately. The model can be extended to cases where winners’ payoffs depend on which players exit, or where players face randomly arriving ‘defeats’. The findings can be applied to an all-pay auction with ascending bids and complete information.
Keywords: All-pay auction, Complete information, Interdependent valuation, Memoryless strategy, War of attrition
JEL codes: D74, H41, L13
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