Learning Equilibrium in Resource Selection Games

We consider a resource selection game with incomplete information about the resource-cost functions. All the players know is the set of players, an upper bound on the possible costs, and that the cost functions are positive and nondecreasing. The game is played repeatedly and after every stage each player observes her cost, and the actions of all players. For every E > 0 we prove the existence of a learning E-equilibrium, which is a profile of algorithms, one for each player such that a unilateral deviation of a player is, up to e not beneficial for her regardless of the actual cost functions. Furthermore, the learning eqUilibrium yields an optimal social cost.

[1]  M. Cripps.  The theory of learning in games. , 1999 .

[2]  Martin Gairing,et al.  Selfish routing with incomplete information , 2005, SPAA.

[3]  A. Roth,et al.  Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria , 1998 .

[4]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[5]  Moshe Tennenholtz,et al.  Learning equilibrium as a generalization of learning to optimize , 2007, Artif. Intell..

[6]  L. Shapley,et al.  Potential Games , 1994 .

[7]  Ronen I. Brafman,et al.  Optimal Efficient Learning Equilibrium: Imperfect Monitoring in Symmetric Games , 2005, AAAI.

[8]  Itai Ashlagi,et al.  Resource selection games with unknown number of players , 2006, AAMAS '06.

[9]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[10]  Ronen I. Brafman,et al.  Efficient learning equilibrium , 2004, Artificial Intelligence.

[11]  Ronen I. Brafman,et al.  R-MAX - A General Polynomial Time Algorithm for Near-Optimal Reinforcement Learning , 2001, J. Mach. Learn. Res..

[12]  Y. Narahari,et al.  Price of Anarchy of Network Routing Games with Incomplete Information , 2005, WINE.

[13]  Itai Ashlagi,et al.  Robust Learning Equilibrium , 2006, UAI.

[14]  Ronen I. Brafman,et al.  Optimal Efficient Learning Equilibrium : Imperfect Monitoring , 2005 .

[15]  Vincent Conitzer,et al.  AWESOME: A general multiagent learning algorithm that converges in self-play and learns a best response against stationary opponents , 2003, Machine Learning.

[16]  Michael L. Littman,et al.  Markov Games as a Framework for Multi-Agent Reinforcement Learning , 1994, ICML.

[17]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[18]  Keith B. Hall,et al.  Correlated Q-Learning , 2003, ICML.

[19]  Manuela M. Veloso,et al.  Rational and Convergent Learning in Stochastic Games , 2001, IJCAI.

[20]  Michael P. Wellman,et al.  Multiagent Reinforcement Learning: Theoretical Framework and an Algorithm , 1998, ICML.