Dynamics in Congestion Games

Game theoretic modeling and equilibrium analysis of congestion games have provided insights in the performance of Internet congestion control, road transportation networks, etc. Despite the long history, very little is known about their transient (non equilibrium) performance. In this paper, we are motivated to seek answers to questions such as how long does it take to reach equilibrium, when the system does operate near equilibrium in the presence of dynamics, e.g. nodes join or leave. In this pursuit, we provide three contributions in this paper. First, a novel probabilistic model to capture realistic behaviors of agents allowing for the possibility of arbitrariness in conjunction with rationality. Second, evaluation of (a) time to converge to equilibrium under this behavior model and (b) distance to Nash equilibrium. Finally, determination of trade-off between the rate of dynamics and quality of performance (distance to equilibrium) which leads to an interesting uncertainty principle. The novel technical ingredients involve analysis of logarithmic Sobolov constant of Markov process with time varying state space and methodically this should be of broader interest in the context of dynamical systems.