Generalized Multidimensional Contests with Asymmetric Players: Equilibrium and Optimal Prize Design

Siyuan Fan, Zhonghong Kuang and Jingfeng Lu

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Abstract: We study $n$-dimensional contests between two players with heterogeneous effort costs, where each dimension (battle) is modeled as a Tullock contest. Prize-allocation rules are identity-independent, budget-balanced, and weakly increasing in the number of victories. Players' costs can be separable across battles or exhibit cross-battle externalities. We identify a tight sufficient condition under which a unique equilibrium exists and is in pure strategies, for all admissible prize-allocation rules and all degrees of player asymmetry. Under this condition, we characterize the effort-maximizing prize-allocation rule: the entire prize goes to the player who wins more battles than the opponent by at least a prespecified margin, and is split equally if neither player meets this threshold. In the symmetric-player case, the majority rule is optimal if $n$ is odd. Interestingly, cross-battle cost externalities do not change the optimal prize allocation rule in our setting.

Date: 2026-02, Revised 2026-03
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-spo
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