Existence of a unique Nash equilibrium for an asymmetric lottery Blotto game with weighted majority

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticle

Abstract

We consider an asymmetric lottery Blotto game with two agents and n items, where both agents wish to maximize their probability of winning a majority value of all n items. Duffy and Matros [2] showed that if there exists a Nash equilibrium, then the equilibrium is unique, and it is found in an explicit expression. They also provided sufficient conditions for the existence of a Nash equilibrium in the cases of n=3 and n=4. In this paper, we prove that the lottery Blotto game always has a unique Nash equilibrium for any value of n.

Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
DOIs
Publication statusPublished - 2019 Jan 1

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Lottery
Nash Equilibrium
Game
Maximise
Sufficient Conditions

Keywords

  • Lottery Blotto game
  • Nash equilibrium
  • Weighted majority

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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AB - We consider an asymmetric lottery Blotto game with two agents and n items, where both agents wish to maximize their probability of winning a majority value of all n items. Duffy and Matros [2] showed that if there exists a Nash equilibrium, then the equilibrium is unique, and it is found in an explicit expression. They also provided sufficient conditions for the existence of a Nash equilibrium in the cases of n=3 and n=4. In this paper, we prove that the lottery Blotto game always has a unique Nash equilibrium for any value of n.

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