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Existence of a unique Nash equilibrium for an asymmetric lottery Blotto game with weighted majority
- Authors
- Kim, Bara; Kim, Jeongsim
- Issue Date
- 1-11월-2019
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Lottery Blotto game; Nash equilibrium; Weighted majority
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.479, no.1, pp.1403 - 1415
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Volume
- 479
- Number
- 1
- Start Page
- 1403
- End Page
- 1415
- ISSN
- 0022-247X
- 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. (C) 2019 Elsevier Inc. All rights reserved.
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