Polynomial games and sum of squares optimization

Author

Parrilo, Pablo A.

Author_Institution

Lab. for Inf. & Decision Syst., Massachusetts Inst. of Technol., Cambridge, MA

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

2855

Lastpage

2860

Abstract

We study two-person zero-sum games, where the payoff function is a polynomial expression in the actions of the players. This class of games was introduced by Dresher, Karlin, and Shapley in 1950. We show that the value of the game, and the corresponding optimal strategies, can be obtained by solving a single semidefinite programming problem. In addition, we show how the results extend, with suitable modifications, to a general class of semialgebraic games

Keywords

game theory; optimisation; polynomials; optimal strategy; payoff function; polynomial games; semialgebraic games; semidefinite programming problem; sum of squares optimization; zero-sum games; Control systems; Game theory; Laboratories; Linear programming; Mathematical model; Minimax techniques; Nash equilibrium; Polynomials; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377261

Filename

4178056

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2484296