Follow-the-Regularized-Leader Routes to Chaos in Routing Games

We study the emergence of chaotic behavior of Follow-the-Regularized Leader (FoReL) dynamics in games. We focus on the effects of increasing the population size or the scale of costs in congestion games, and generalize recent results on unstable, chaotic behaviors in the Multiplicative Weights Update dynamics to a much larger class of FoReL dynamics. We establish that, even in simple linear non-atomic congestion games with two parallel links and \emph{any} fixed learning rate, unless the game is fully symmetric, increasing the population size or the scale of costs causes learning dynamics to becomes unstable and eventually chaotic, in the sense of Li-Yorke and positive topological entropy. Furthermore, we prove the existence of novel non-standard phenomena such as the coexistence of stable Nash equilibria and chaos in the same game. We also observe the simultaneous creation of a chaotic attractor as another chaotic attractor gets destroyed. Lastly, although FoReL dynamics can be strange and non-equilibrating, we prove that the time average still converges to an \emph{exact} equilibrium for any choice of learning rate and any scale of costs

Heuristics and Biases in Travel Mode Choice

. This study applies experimental methods to analyze travel mode choice. Two different scenarios are considered. In the first scenario, subjects have to decide whether to commute by car or by metro. Metro costs are fixed, while car costs are uncertain and determined by the joint effect of casual events and traffic congestion. In the second scenario, subjects have to decide whether to travel by car or by bus, both modes in which costs are determined by the combination of chance and congestion. Subjects receive feedback information on the actual travel times of both modes. We find that individuals exhibit a marked preference for cars, are inclined to confirm their first choice and demonstrate travel mode stickiness. We conclude that travel mode choice is subject to heuristics and biases that lead to robust deviations from rational choice.travel mode choice, learning, information, heuristics, cognitive biases.

Potential games with continuous player sets

game theory

The Hughes model for pedestrian dynamics and congestion modelling

In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation and a first order conservation law, and it intends to approximate the flow of a large pedestrian group aiming to reach a target as fast as possible, while taking into account the congestion of the crowd. We propose an efficient semi-Lagrangian scheme (SL) to approximate the solution of the PDE system and we investigate the macroscopic effects of different penalization functions modelling the congestion phenomena.Comment: 6 page

Heuristics and Biases in Travel Mode Choice

This study applies experimental methods to analyze travel mode choice. Two different scenarios are considered. In the first scenario, subjects have to decide whether to commute by car or by metro. Metro costs are fixed, while car costs are uncertain and determined by the joint effect of casual events and traffic congestion. In the second scenario, subjects have to decide whether to travel by car or by bus, both modes in which costs are determined by the combination of chance and congestion. Subjects receive feedback information on the actual travel times of both modes. We find that individuals exhibit a marked preference for cars, are inclined to confirm their first choice and demonstrate travel mode stickiness. We conclude that travel mode choice is subject to heuristics and biases that lead to robust deviations from rational choicetravel mode choice, learning, information, heuristics, cognitive biases

Metastability of Asymptotically Well-Behaved Potential Games

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take time exponential in the number of players. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e., players do not go too far from it) for a super-polynomial number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics. We identify a class of potential games, called asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship of several convergence measures for Markov chains