Paper Info
Title
On Lyapunov Game Theory Equilibrium: Static And Dynamic Approaches
Abstract
This paper suggests a game theory problem in which any feasible solution is based on the Lyapunov theory. The problem is analyzed in the static and dynamic cases. Some properties of Nash equilibria such as existence and stability are derived naturally from the Lyapunov theory. Remarkable is that every asymptotically stable equilibrium point (Nash equilibrium point) admits a Lyapunov-like function and if a Lyapunov-like function exists it converges to a Nash/Lyapunov equilibrium point. We define a Lyapunov-like function as an Lp-norm from the multiplayer objective function to the utopia minimum as a cost function. We propose multiple metrics to find the Nash/Lyapunov equilibrium and the strong Nash/Lyapunov equilibrium. Finding a Nash/Lyapunov equilibrium is reduced to the minimization problem of the Lyapunov-like function. We prove that the equilibrium point properties of Nash and Lyapunov meet in game theory. In order to validate the contributions of the paper, we present a numerical example.
Year
DOI
Venue
2018
10.1142/S0219198917500335
INTERNATIONAL GAME THEORY REVIEW
Keywords
Field
DocType
Lyapunov games, Lyapunov equilibrium, Nash, strong Nash equilibrium
Minimization problem,Lyapunov function,Strong Nash equilibrium,Economics,Mathematical economics,Nash equilibrium point,Equilibrium point,Game theory,Nash equilibrium,Stability theory
Journal
Volume
Issue
ISSN
20
2
0219-1989
Citations 
PageRank 
References 
0
0.34
6
Authors
1
Name
Order
Citations
PageRank
Julio B. Clempner19120.11