A dynamic theory of zero-sum two-person games
| Autor: | G.R Mon |
|---|---|
| Rok vydání: | 1970 |
| Předmět: |
Computer Science::Computer Science and Game Theory
Recursion Applied Mathematics Stochastic game Markov process Conditional probability distribution Function (mathematics) Expected value Measure (mathematics) symbols.namesake symbols State-transition equation Mathematical economics Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 29(2):392-411 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/0022-247x(70)90087-9 |
| Popis: | In this paper the theory of a class of zero-sum two-person ( P and E ) stochastic finite state game problems is presented. The state transition process is assumed to be Markovian and hence is governed by a conditional probability distribution function in terms of which the state transition equation and payoff functional are expressed. The players attempt to “min-max” the expected value of a payoff functional by choosing an optimal pair of strategies—namely, a pair of behavioral strategies that satisfies a particular double inequality. The application of Bellman's optimality principle leads to necessary conditions for the optimality of a pair of strategies and a recursion equation for the optimal expected payoff vector. Two cases are considered: games in which each player can measure the state perfectly, and games in which the measurements are corrupted by noise. In both cases optimal feedback decision sequences are obtained; in the case of noisy measurements, decisions are conditioned on the previous measurement histories of each player. A simple two-stage pursuit problem is solved. The theory is shown to be closely related to the static theory of J. Von Neumann and O. Morgenstern [16], first published in 1944. However, it is pointed out that the present theory may result in substantial savings in computation time and cost. |
| Databáze: | OpenAIRE |
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