Unpredictable Dynamics in Congestion Games : Memory Loss Can Prevent Chaos

We study the dynamics of simple congestion games with two resources where a continuum of agents behaves according to a simplified version of Experience-Weighted Attraction algorithm. The dynamics is characterized by the intensity of choice capturing rationality of the total population of agents and a discount factor capturing a type of memory loss where past outcomes matter exponentially less than the recent ones. Finally, our system adds a third parameter, which captures the asymmetry of the cost functions of the two resources. We show that for any discount factor the system will be destabilized for a sufficiently large intensity of choice, but dependent on the asymmetry of costs, and its relation to the discount factor, the system will stay predictable or become unpredictable and chaotic. Moreover, as memory loss increases the chaotic regime will give place to the attracting periodic orbit of period 2