Pure strategy Nash Equilibrium in 2-contestant generalized lottery Colonel Blotto games

Xinmi Li and Jie Zheng

Journal of Mathematical Economics, 2022, vol. 103, issue C

Abstract: We consider a large class of 2-contestant Colonel Blotto games, for which the budget and valuation are both asymmetric between players and the contest success functions are in Tullock form with battle-specific discriminatory power in (0,1] and battle-and-contestant-specific lobbying effectiveness. We prove the existence of pure strategy Nash Equilibrium of the game through a direct equilibrium characterization approach. We examine some important equilibrium properties. Among them, the rate of equilibrium rent dissipation ratio between the two contestants is constant across all the battles, and the payoff dominance relationship is impossible between any two distinct equilibria. Furthermore, we provide two sets of sufficient conditions, one for symmetric valuations and the other for asymmetric valuations, under each of which the equilibrium of the game is unique. Our study contributes to a better understanding regarding the existence, uniqueness, characterization and properties of equilibria in Blotto games.

Keywords: Tullock contest; Multi-battle contest; Colonel Blotto game; Equilibrium characterization; Existence and uniqueness of equilibrium (search for similar items in EconPapers)
JEL-codes: D72 D74 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:103:y:2022:i:c:s0304406822000970

DOI: 10.1016/j.jmateco.2022.102771

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