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Stochastic Games on Markov Processes with Final Sequence of States
Authors: Alexandru Lazari
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Abstract
In this paper a class of stochastic games, defined on Markov processes with final sequence of states, is investigated. In these games each player, knowing the initial distribution of the states, defines his stationary strategy, represented by one proper transition matrix. The game is started by first player and, at every discrete moment of time, the stochastic system passes to the next state according to the stra\-tegy of the current player. After the last player, the first player acts on the system evolution and the game continues in this way until, for the first time, the given final sequence of states is achieved. The player who acts the last on the system evolution is considered the winner of the game. In this paper we prove that the distribution of the game duration is a homogeneous linear recurrence and we determine the initial state and the generating vector of this recurrence. Based on these results, we develop polynomial algorithms for determining the main probabilistic characteristics of the game duration and the win probabilities of players. Also, using the signomial and geometric programming approaches, the optimal cooperative strategies that minimize the expectation of the game duration are determined.Moldova State University,
60 Mateevici str., Chi¸ sin˘ au,
Republic of Moldova, MD−2009.
E-mail:
60 Mateevici str., Chi¸ sin˘ au,
Republic of Moldova, MD−2009.
E-mail:
Fulltext
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Contents
- Regular, Intra-regular and Duo Γ-Semirings
- Some Properties of Meromorphic Solutions of Logarithmic Order to Higher Order Linear Difference Equations
- Forbidden Set of the Rational Difference Equation xn+1 = xnxn-k/(axn-k+1 + xnxn-k+1xn-k)
- A New Characterization of Curves in Euclidean 4-Space $\mathbb{E}^{4}$
- Solvability of the boundary value problem for the equation of transition processes in semiconductors with a fractional time derivative
- On the inverse operations in the class of preradicals of a module category, I
- Some Homomorphic Properties of Multigroups
- Stochastic Games on Markov Processes with Final Sequence of States
- Application of the Fast Automatic Differentiation for Calculation of Gradients of Material's Bulk Modulus and Shear Modulus
