BILINEAR PROGRAMMING AND STRUCTURED STOCHASTIC GAMES.

Jerzy A. Filab, Todd A. Schultz

Research output: Contribution to journalConference article

Abstract

Only this author abstract is provided: 'One step' algorithms are presented for two classes of structured stochastic games, namely those with additive rewards and transitions, and those which have switching controllers. Solutions to such classes of games under the 'average reward' criterion can be derived from optimal solutions to appropriate bilinear programs. The validity of using bilinear programming as a solution method follows from two preliminary theorems, the first of which is a complete classification of undiscounted stochastic games with optimal stationary strategies. The second of these preliminary theorems relaxes the conditions of the classification theorem for certain classes of stochastic games and provides the basis for the bilinear programming results. Analogous results hold for the discounted stochastic games with the above special structures.

Original languageEnglish (US)
Number of pages1
JournalProceedings - Annual Allerton Conference on Communication, Control, and Computing
StatePublished - Dec 1 1985

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N2 - Only this author abstract is provided: 'One step' algorithms are presented for two classes of structured stochastic games, namely those with additive rewards and transitions, and those which have switching controllers. Solutions to such classes of games under the 'average reward' criterion can be derived from optimal solutions to appropriate bilinear programs. The validity of using bilinear programming as a solution method follows from two preliminary theorems, the first of which is a complete classification of undiscounted stochastic games with optimal stationary strategies. The second of these preliminary theorems relaxes the conditions of the classification theorem for certain classes of stochastic games and provides the basis for the bilinear programming results. Analogous results hold for the discounted stochastic games with the above special structures.

AB - Only this author abstract is provided: 'One step' algorithms are presented for two classes of structured stochastic games, namely those with additive rewards and transitions, and those which have switching controllers. Solutions to such classes of games under the 'average reward' criterion can be derived from optimal solutions to appropriate bilinear programs. The validity of using bilinear programming as a solution method follows from two preliminary theorems, the first of which is a complete classification of undiscounted stochastic games with optimal stationary strategies. The second of these preliminary theorems relaxes the conditions of the classification theorem for certain classes of stochastic games and provides the basis for the bilinear programming results. Analogous results hold for the discounted stochastic games with the above special structures.

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