Memory loss can prevent chaos in games dynamics

Abstract

Recent studies have raised concerns on the inevitability of chaos in congestion games with large learning rates. We further investigate this phenomenon by exploring the learning dynamics in simple two-resource congestion games, where a continuum of agents learns according to a simplified experience-weighted attraction algorithm. The model is characterized by three key parameters: a population intensity of choice (learning rate), a discount factor (recency bias or exploration parameter), and the cost function asymmetry. The intensity of choice captures agents’ economic rationality in their tendency to approximately best respond to the other agent’s behavior. The discount factor captures a type of memory loss of agents, where past outcomes matter exponentially less than the recent ones. Our main findings reveal that while increasing the intensity of choice destabilizes the system for any discount factor, whether the resulting dynamics remains predictable or becomes unpredictable and chaotic depends on both the memory loss and the cost asymmetry. As memory loss increases, the chaotic regime gives place to a periodic orbit of period 2 that is globally attracting except for a countable set of points that lead to the equilibrium. Therefore, memory loss can suppress chaotic behaviors. The results highlight the crucial role of memory loss in mitigating chaos and promoting predictable outcomes in congestion games, providing insights into designing control strategies in resource allocation systems susceptible to chaotic behaviors.