Geodesic
A generalized model of the Colonel Blotto stochastic game
Diskretnaya Matematika, Tome 34 (2022) no. 3, pp. 136-154

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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. 
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     author = {V. V. Kharlamov},
     title = {A generalized model of the {Colonel} {Blotto} stochastic game},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
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     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_3_a9/}
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V. V. Kharlamov. A generalized model of the Colonel Blotto stochastic game. Diskretnaya Matematika, Tome 34 (2022) no. 3, pp. 136-154. http://geodesic.mathdoc.fr/item/DM_2022_34_3_a9/