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

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  • Li, Xinmi
  • Zheng, Jie

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.

Suggested Citation

  • Li, Xinmi & Zheng, Jie, 2022. "Pure strategy Nash Equilibrium in 2-contestant generalized lottery Colonel Blotto games," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    • Handle: RePEc:eee:mateco:v:103:y:2022:i:c:s0304406822000970
    DOI: 10.1016/j.jmateco.2022.102771
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    1. Anbarci, Nejat & Cingiz, Kutay & Ismail, Mehmet S., 2023. "Proportional resource allocation in dynamic n-player Blotto games," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 94-100.

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    More about this item

    Keywords

    Tullock contest; Multi-battle contest; Colonel Blotto game; Equilibrium characterization; Existence and uniqueness of equilibrium;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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