Paper Info
Title
Computing the Lp-strong nash equilibrium looking for cooperative stability in multiple agents markov games
Abstract
The notion of collaboration implies that related agents interact with each other looking for cooperative stability. This notion consents agents to select optimal strategies and to condition their own behavior on the behavior of others in a strategic forward looking manner. In game theory the collective stability is a special case of the Nash equilibrium called strong Nash equilibrium. In this paper we present a novel method for computing the Strong L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -Nash equilibrium in case of a metric state space for a class of time-discrete ergodic controllable Markov chains games. We first present a general solution for the Lp-norm for computing the Strong L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -Nash equilibrium and then, we suggest an explicit solution involving the norms L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . For solving the problem we use the extraproximal method. We employ the Tikhonov's regularization method to ensure the convergence of the cost-functions to a unique equilibrium point. The method converges in exponential time to a unique Strong L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -Nash equilibrium. A game theory example illustrates the main results.
Year
DOI
Venue
2015
10.1109/ICEEE.2015.7357926
2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)
Keywords
Field
DocType
Lp-strong Nash equilibrium,cooperative stability,multiple agents Markov games,optimal strategy,game theory,metric state space,time-discrete ergodic controllable Markov chains game,strong Lp-Nash equilibrium,Tikhonov's regularization method,convergence,cost-function,exponential time
Correlated equilibrium,Strong Nash equilibrium,Mathematical optimization,Mathematical economics,Epsilon-equilibrium,Computer science,Best response,Symmetric equilibrium,Equilibrium selection,Solution concept,Nash equilibrium
Conference
Citations 
PageRank 
References 
0
0.34
9
Authors
3
Name
Order
Citations
PageRank
Kristal K. Trejo1293.24
Julio B. Clempner29120.11
Alexander S. Poznyak335863.68