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 will converge in the sense that both the average action vector will converge to a Nash equilibrium and that the utility of each player will converge to her utility in that Nash equilibrium. We show that many natural games are indeed socially con- cave games. Speci cally, we show that linear Cournot com- petition 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 dynamics might diverge for linear resource allocation games, and is known to diverge for linear Cournot competition. For the TCP congestion games we show that \near" the equilib- rium the games are socially-concave, and using our general methodology we show the convergence of a speci c regret minimization dynamics.