Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation

• Published in: Games and economic behavior Vol. 75; no. 2; pp. 788 - 808
• Main Authors: Marden, Jason R., Shamma, Jeff S.
• Format: Journal Article
• Language: English
• Published: Duluth Elsevier Inc 01.07.2012; Academic Press
• Subjects: Algorithms; Asymptotic methods; Computational methods; Distributed control; Equilibrium selection; Equilibrium theory; Game theory; Information economics; Learning; Linear models; Markov analysis; Pay-off; Potential games; Stochastic models; Studies; Distributed control; Potential games; Equilibrium selection; C72; C61
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2012.03.006

Log-linear learning is a learning algorithm that provides guarantees on the percentage of time that the action profile will be at a potential maximizer in potential games. The traditional analysis of log-linear learning focuses on explicitly computing the stationary distribution and hence requires a highly structured environment. Since the appeal of log-linear learning is not solely the explicit form of the stationary distribution, we seek to address to what degree one can relax the structural assumptions while maintaining that only potential function maximizers are stochastically stable. In this paper, we introduce slight variants of log-linear learning that provide the desired asymptotic guarantees while relaxing the structural assumptions to include synchronous updates, time-varying action sets, and limitations in information available to the players. The motivation for these relaxations stems from the applicability of log-linear learning to the control of multi-agent systems where these structural assumptions are unrealistic from an implementation perspective. ► We analyze variants of the learning process known as log-linear learning. ► We consider synchronous moves, constrained moves, and payoff measurements. ► Under suitable variants, potential function maximizers remain stochastically stable. ► Proofs use resistance trees methods, and not an explicit stationary distribution.