On the convergence of regret minimization dynamics in concave games

We study a general sub-class of concave games, which we call socially concave games. We show that if each player follows any no-external regret minimization procedure then the dynamics converges in the sense that both the average action vector converges to a Nash equilibrium and that the utility of each player converges to her utility in that Nash equilibrium. We show that many natural games are socially concave games. Specifically, we show that linear Cournot competition and linear resource allocation games are socially-concave games, and therefore our convergence result applies to them. In addition, we show that a simple best response dynamic might diverge for linear resource allocation games, and is known to diverge for a linear Cournot competition. For the TCP congestion games we show that "near" the equilibrium these games are socially-concave, and using our general methodology we show convergence of specific regret minimization dynamics.

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Eyal Even-Dar, Yishay Mansour, Uri Nadav
• Keywords: Algorithms, Concave Games, Linear Resource Allocation, Resource Allocation Games, STOC 2009