Chaotic congestion games

We analyze a class of congestion games where two agents must send a finite amount of goods from an initial location to a terminal one. To do so the agents must use resources which are costly and costs are load dependent. In this context we assume that the agents have limited computational capability and they use a gradient rule as a decision mechanism. By introducing an appropriate dynamical system, which has the steady state exactly at the unique Nash equilibrium of the static congestion game, we investigate the dynamical behavior of the game. We provide a local stability condition in terms of the agents' reactivity and the nonlinearity of the cost functions. In particular we show numerically that there is a route to complex dynamics: a cascade of flip-bifurcation leading to periodic cycles and finally to chaos.