Nonlinear programming and stationary strategies in stochastic games

Jerzy A. Filar, Todd A. Schultz

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Pages (from-to)243-247
Number of pages5
JournalMathematical Programming
Issue number2
StatePublished - Mar 1 1986
Externally publishedYes


  • Nonlinear Programming
  • Stationary Strategies
  • Stochastic Games
  • Undiscounted Rewards

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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