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

Bara Kim; Jeongsim Kim

doi:10.1016/j.jmaa.2019.07.004

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

Bara Kim, Jeongsim Kim

Department of Mathematics

Research output: Contribution to journal › Article

1 Citation (Scopus)

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 language	English
Journal	Journal of Mathematical Analysis and Applications
DOIs	https://doi.org/10.1016/j.jmaa.2019.07.004
Publication status	Published - 2019 Jan 1

Keywords

Lottery Blotto game
Nash equilibrium
Weighted majority

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2019.07.004

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Kim, B., & Kim, J. (2019). Existence of a unique Nash equilibrium for an asymmetric lottery Blotto game with weighted majority. Journal of Mathematical Analysis and Applications. https://doi.org/10.1016/j.jmaa.2019.07.004

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