IJPAM: Volume 22, No. 1 (2005)

MODELING PROPERTIES OF THE ENTROPY AS
A LYAPUNOV-LIKE UTILITY FUNCTION IN DPPN

Julio Clempner
Centro de Investigación en Computación (CIC)
Instituto Politécnico Nacional
Apartado Postal 75-476, C.P. 07738, Mexico City, MEXICO
e-mail: julio@k-itech.com


Abstract.The theoretical foundations for the definition of the Entropy as a Lypunov-like utility function are laid out in this paper. It allows the introduction of a formal framework for game representation called game entropy decision process Petri nets (GEDPPN). In game sense, we introduce the entropy-Lyapunov equilibrium point as an alternative definition to the Nash equilibrium point for games. The advantage of this approach is that fixed-point conditions for games are given by the definition of the vector entropy function. As a result, new properties related with the characterization of the Lyapunov-like function by the entropy are introduced. A formal treatment is presented.

Received: June 2, 2005

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

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 1