A generalized model of the Colonel Blotto stochastic game
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Viktor V. Kharlamov
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.
Originally published in Diskretnaya Matematika (2022) 34, №3, 136–154 (in Russian).
Acknowledgement
The author is deeply grateful to A. V. Shklyaev for constant support of the work. The author thanks the anonymous reviewers for their comments which allowed us to significantly improve the text.
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Funding: The study was supported by a grant from the Russian Scientific Foundation No. 19-11-00111, https://rscf.ru/project/19-11-00111/.
References
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Articles in the same Issue
- Frontmatter
- On the relationship between local affinities of a Boolean function and some types of its degeneracy
- A generalized model of the Colonel Blotto stochastic game
- Logical extensions of the parametric closure operator
- Short conditional complete diagnostic tests for circuits under one-type constant faults of gates
- Approximation of vectorial functions over finite fields and their restrictions to linear manifolds by affine analogues
Articles in the same Issue
- Frontmatter
- On the relationship between local affinities of a Boolean function and some types of its degeneracy
- A generalized model of the Colonel Blotto stochastic game
- Logical extensions of the parametric closure operator
- Short conditional complete diagnostic tests for circuits under one-type constant faults of gates
- Approximation of vectorial functions over finite fields and their restrictions to linear manifolds by affine analogues
