Nonlinear programming and stationary strategies in stochastic games

Jerzy A. Filar; Todd A. Schultz

doi:10.1007/BF01580590

Nonlinear programming and stationary strategies in stochastic games

Jerzy A. Filar, Todd A. Schultz

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We show that an undiscounted stochastic game possesses optimal stationary strategies if and only if a global minimum with objective value zero can be found to an appropriate nonlinear program with linear constraints. This nonlinear program arises as a method for solving a certain bilinear system, satisfaction of which is also equivalent to finding a stationary optimal solution for the game. The objective function of the program is a nonnegatively valued quadric polynomial.

Original language	English (US)
Pages (from-to)	243-247
Number of pages	5
Journal	Mathematical Programming
Volume	34
Issue number	2
DOIs	https://doi.org/10.1007/BF01580590
State	Published - Mar 1986
Externally published	Yes

Keywords

Nonlinear Programming
Stationary Strategies
Stochastic Games
Undiscounted Rewards

ASJC Scopus subject areas

Software
General Mathematics

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10.1007/BF01580590

Cite this

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abstract = "We show that an undiscounted stochastic game possesses optimal stationary strategies if and only if a global minimum with objective value zero can be found to an appropriate nonlinear program with linear constraints. This nonlinear program arises as a method for solving a certain bilinear system, satisfaction of which is also equivalent to finding a stationary optimal solution for the game. The objective function of the program is a nonnegatively valued quadric polynomial.",

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author = "Filar, {Jerzy A.} and Schultz, {Todd A.}",

year = "1986",

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AU - Schultz, Todd A.

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AB - We show that an undiscounted stochastic game possesses optimal stationary strategies if and only if a global minimum with objective value zero can be found to an appropriate nonlinear program with linear constraints. This nonlinear program arises as a method for solving a certain bilinear system, satisfaction of which is also equivalent to finding a stationary optimal solution for the game. The objective function of the program is a nonnegatively valued quadric polynomial.

KW - Nonlinear Programming

KW - Stationary Strategies

KW - Stochastic Games

KW - Undiscounted Rewards

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Nonlinear programming and stationary strategies in stochastic games

Abstract

Keywords

ASJC Scopus subject areas

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