Comparing the best-reply strategy and mean-field games : the stationary case

Mean-field games (MFGs) and the best-reply strategy (BRS) are two methods of describing competitive optimisation of systems of interacting agents. The latter can be interpreted as an approximation of the respective MFG system. In this paper, we present an analysis and comparison of the two approaches in the stationary case. We provide novel existence and uniqueness results for the stationary boundary value problems related to the MFG and BRS formulations, and we present an analytical and numerical comparison of the two paradigms in some specific modelling situations

One Dimensional Asynchronous Cooperative Parrondo's Games

An analytical result and an algorithm are derived for the probability distribution of the one-dimensional cooperative Parrondo's games. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.Comment: 10 pages, 4 figures, submitted to Fluctuations and Noise Letter

Mean Field Games models of segregation

This paper introduces and analyses some models in the framework of Mean Field Games describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games, a large population limit is proved. For differential games with noise, the existence of solutions is established for the systems of partial differential equations of Mean Field Game theory, in the stationary and in the evolutive case. Numerical methods are proposed, with several simulations. In the examples and in the numerical results, particular emphasis is put on the phenomenon of segregation between the populations.Comment: 35 pages, 10 figure