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 | |
| Publication status | Published - 2019 Jan 1 |
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Keywords
- Lottery Blotto game
- Nash equilibrium
- Weighted majority
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Existence of a unique Nash equilibrium for an asymmetric lottery Blotto game with weighted majority. / Kim, Bara; Kim, Jeongsim.
In: Journal of Mathematical Analysis and Applications, 01.01.2019.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Existence of a unique Nash equilibrium for an asymmetric lottery Blotto game with weighted majority
AU - Kim, Bara
AU - Kim, Jeongsim
PY - 2019/1/1
Y1 - 2019/1/1
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
UR - http://www.scopus.com/inward/record.url?scp=85068354108&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85068354108&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2019.07.004
DO - 10.1016/j.jmaa.2019.07.004
M3 - Article
AN - SCOPUS:85068354108
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
ER -