Approximate Equilibria in Non-constant-sum Colonel Blotto and Lottery Blotto Games with Large Numbers of Battlefields

Abstract : In the Colonel Blotto game, two players with a fixed budget simultaneously allocate their resources across n battlefields to maximize the aggregate value gained from the battlefields where they have the higher allocation. Despite its long-standing history and important applicability, the Colonel Blotto game still lacks a complete Nash equilibrium characterization in its most general form-the non-constant-sum version with asymmetric players and heterogeneous battlefields. In this work, we propose a simply-constructed class of strategies-the independently uniform strategies-and we prove them to be approximate equilibria of the non-constant-sum Colonel Blotto game; moreover, we also characterize the approximation error according to the game's parameters. We also introduce an extension called the Lottery Blotto game, with stochastic winner-determination rules allowing more flexibility in modeling practical contexts. We prove that the proposed strategies are also approximate equilibria of the Lottery Blotto game.
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https://hal.archives-ouvertes.fr/hal-02315698
Contributor : Dong Quan Vu <>
Submitted on : Monday, October 14, 2019 - 4:40:12 PM
Last modification on : Friday, October 25, 2019 - 1:21:30 AM

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  • HAL Id : hal-02315698, version 1
  • ARXIV : 1910.06559

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Dong Quan Vu, Patrick Loiseau, Alonso Silva. Approximate Equilibria in Non-constant-sum Colonel Blotto and Lottery Blotto Games with Large Numbers of Battlefields. 2019. ⟨hal-02315698⟩

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