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This article is cited in 1 scientific paper (total in 1 paper)
A generalized model of the Colonel Blotto stochastic game
V. V. Kharlamov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Abstract:
A generalized stochastic modification of the Colonel Blotto game, also known as the game of gladiators, is considered. In the original model, each of two players has a set of gladiators with given strengths. The battle of gladiator teams takes place through individual gladiator battles. In each fight, the probability of gladiator winning is proportional to its strength. Kaminsky et al. in 1984 had obtained a formula for the probability of winning in terms of weighted sums of exponential random variables. Here we provide an interpretation of this result from the Markov chains with continuous time point of view, and a more general statement of the problem is considered, for which a similar expression is obtained.
Keywords:
Colonel Blotto game, Markov chain, generalized Poisson process, nonhomogeneous exponential representation.
Received: 06.04.2021 Revised: 06.04.2022
Citation:
V. V. Kharlamov, “A generalized model of the Colonel Blotto stochastic game”, Diskr. Mat., 34:3 (2022), 136–154; Discrete Math. Appl., 33:6 (2023), 355–369
Linking options:
https://www.mathnet.ru/eng/dm1665https://doi.org/10.4213/dm1665 https://www.mathnet.ru/eng/dm/v34/i3/p136
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Abstract page: | 211 | Full-text PDF : | 57 | References: | 40 | First page: | 11 |
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