Games played by Exponential Weights Algorithms

Many machine learning algorithms used for prediction or decision-making are designed to optimize the behavior of a single agent facing an unknown environment. However, with the increasing use of these algorithms in various fields and the complexity of the problems at hand, interaction between these algorithms, designed for an agent unconscious of other players, have become common. This raises a natural question: where will these interactions lead? Our paper contributes to the large literature on learning algorithms in games. Precisely, we analyze the day to day behavior of the exponential weights (EW) algorithm with constant learning rates, when applied independently by all the players in a finite game. The EW algorithm ([15, 10, 5, 3]) is one of the most popular and widely studied algorithm with applications in various domains and contexts: computational geometry, optimization, operations research, online statistical decision-making, machine learning (we refer to [4, 14, 2] for a general account on the subject).