IJPAM: Volume 22, No. 2 (2005)

ONE-PLAYER DECISION PROCESS: TOWARDS A GAME
THEORY IMPLEMENTATION USING DPPN

Julio Clempner
Instituto Politecnico Nacional
Centro de Investigacion en Computación Av. Juan de Dios Batiz s/n
Casi esq. Miguel Othon de Mendizabal
Unidad Profesional, "Adolfo Lopez Meteos", Edificio CIC Col. Nueva Industrial Vallejo 07738, Mexico D.F., MEXICO
e-mail: julio@k-itech.com


Abstract.In this paper we introduce the Lyapunov equilibrium point as an alternative definition to the Nash equilibrium point for one-player games using decision process Petri nets. We prove that the concept of Lyapunov equilibrium coincides in this case with the concept of Nash equilibrium. The advantage of this approach is that fixed-point conditions for games are given by the definition of the Lypunov-like function. To the best of our knowledge the approach is to be a new application area in Petri Net theory (PN).

Received: June 2, 2005

AMS Subject Classification: 62C99, 91A35, 91B06, 93D005, 39A05, 39A11

Key Words and Phrases: decision process, decision process Petri nets, stability, Lyapunov methods, optimization, game theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 2