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We study the dynamics of simple congestion games with two resources where acontinuum of agents behaves according to a version of Experience-WeightedAttraction (EWA) algorithm. The dynamics is characterized by two parameters:the (population) intensity of choice $a>0$ capturing the economic rationalityof the total population of agents and a discount factor $\sigma\in [0,1]$capturing a type of memory loss where past outcomes matter exponentially lessthan the recent ones. Finally, our system adds a third parameter $b \in (0,1)$,which captures the asymmetry of the cost functions of the two resources. It isthe proportion of the agents using the first resource at Nash equilibrium, with$b=1/2$ capturing a symmetric network.  Within this simple framework, we show a plethora of bifurcation phenomenawhere behavioral dynamics destabilize from global convergence to equilibrium,to limit cycles or even (formally proven) chaos as a function of the parameters$a$, $b$ and $\sigma$. Specifically, we show that for any discount factor$\sigma$ the system will be destabilized for a sufficiently large intensity ofchoice $a$. Although for discount factor $\sigma=0$ almost always (i.e., $b\neq 1/2$) the system will become chaotic, as $\sigma$ increases the chaoticregime will give place to the attracting periodic orbit of period 2. Therefore,memory loss can simplify game dynamics and make the system predictable. Wecomplement our theoretical analysis with simulations and several bifurcationdiagrams that showcase the unyielding complexity of the population dynamics(e.g., attracting periodic orbits of different lengths) even in the simplestpossible potential games.

Unpredictable dynamics in congestion games: memory loss can prevent chaos