Bilinear programming and structured stochastic games

J. A. Filar, Todd Arthur Schultz

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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)
Pages (from-to)85-104
Number of pages20
JournalJournal of Optimization Theory and Applications
Volume53
Issue number1
DOIs
StatePublished - Apr 1 1987

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Bilinear Programming
Stochastic Games
Reward
Theorem
Controllers
Optimal Solution
Game
Controller
Programming
Stochastic games
Class

Keywords

  • Stochastic games
  • bilinear programming
  • stationary strategies

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

Bilinear programming and structured stochastic games. / Filar, J. A.; Schultz, Todd Arthur.

In: Journal of Optimization Theory and Applications, Vol. 53, No. 1, 01.04.1987, p. 85-104.

Research output: Contribution to journalArticle

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