Simple adaptive strategies. From regret-matching to uncoupled dynamics. With the collaboration of Yakov Babichenko, Amotz Cahn, Yishay Mansour and David Schmeidler (Q2868742)

This book is a collection of papers of several authors (Sergiu Hart, Andreu Mas-Colell, Yakov Babichenko, Amotz Cahn, Yishay Mansour and David Schmeidler) published in very prestigious journals in the field of game theory during the last two decades. The common theme in them starts from the problem of using Nash equilibria as a solution concept in games. The epistemic conditions for the choice of Nash strategies are very demanding, as shown by \textit{R. J. Aumann} and \textit{A. Brandenburger} [Econometrica 63, No. 5, 1161--1180 (1995; Zbl 0841.90125)]. The notion of correlated equilibrium [\textit{R. J. Aumann}, J. Math. Econ. 1, 67--96 (1974; Zbl 0297.90106); Econometrica 55, 1--18 (1987; Zbl 0633.90094)] seems more appropriate as a solution. The articles in this book analyze the ways in which these two solutions notions may or not obtain in learning processes seen as adequate adaptive and simple procedures to adjust the choices made in previous plays. A particular strategy, regret matching, is analyzed in particular. It involves the choice of the actions that the players regret the most not having chosen in a previous play and has the important epistemic feature that it disregards the goals and reasons for choice of the other players (the dynamics under this strategy is thus uncoupled). Because of the latter property the dynamics under regret matching not converge to the class of Nash equilibria. They yield, instead, the set of correlated equilibria of the stage game. The analysis of how these two results are obtained, negative one and positive the other, involves many fine details, rigorously covered in the book.