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 › peer-review

3 Citations (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
Pages (from-to)	1403-1415
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	479
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2019.07.004
Publication status	Published - 2019 Nov 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

Cite this

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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.",

keywords = "Lottery Blotto game, Nash equilibrium, Weighted majority",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: We are grateful to the reviewer for valuable comments and suggestions, which greatly improved this paper. B. Kim's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1A2B4012676 ). J. Kim's research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2017R1D1A1B03029542 ). Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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N2 - 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.

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.

KW - Lottery Blotto game

KW - Nash equilibrium

KW - Weighted majority

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

Abstract

Keywords

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