the theory of learning in games - drew fudenberg

[...]... model The first part of this book will examine these three dynamics, the connection between them, and some of their variants, in the setting of one-shot simultaneous-move games Our focus will be on the long run behavior of the systems in various classes of games, in particular on whether the system will converge to a Nash equilibrium, and, if so, which equilibrium will be selected The second part of the. .. examine similar questions in the setting of general extensive form games The third and final part of the 10 book will discuss what sorts of learning rules have desirable properties, from both the normative and descriptive points of view 1.4 Cournot Adjustment To give the flavor of the type of analyses the book considers, we now develop the example of Cournot adjustment by firms, which is perhaps the. .. replaced when they fail This makes lock -in more comprehensible; but limits the applicability of the models Another point is that under the perfect foresight interpretation, lock -in models do not sound like a story of learning Rather they are a story of dynamics in a world where learning is irrelevant because players know just what they need to do to compute their optimal actions.10 10 Maskin and Tirole... them The section is not intended as an introduction to game theory; readers who would like a more leisurely or detailed treatment should look elsewhere.11 Instead, we try to highlight those aspects of “standard” game theory that will be of most importance in this book, and to focus on those problems in game theory for which learning theory has proven helpful in analyzing In a one-shot simultaneous-move... result relates best-response correspondences of general games to those of zero-sum games in two-player, two-action games 14 Note that the “zero” in “zero-sum” is unimportant; what matters is that the payoffs have a constant sum 19 Proposition 1.2 : Every 2x2 game for which the best-response correspondences have a unique intersection that lies in the interior of the strategy space is best-response equivalent... once the state gets sufficiently close to it The appendix reviews the relevant theory of the stability of dynamical systems for this and other examples 1.6 Cournot Process with Lock -In We argued above that interpreting Cournot adjustment as a model of learning supposes that the players are pretty dim-witted: They choose their actions to maximize against the opponent's last period play It is as if they... simultaneous-move adjustment process, and in fact is the process that Cournot actually studied 9 There is another variant on the timing of moves that is of interest: instead of firms taking turns, suppose that each period, one firm is chosen at random and given the opportunity to change its output, while the output of the other remains locked in Then once again if firms are impatient, the equilibrium... action, and thus in the long run obtain the payoff of a “Stackelberg leader.” Most of learning theory abstracts from such repeated game considerations by explicitly or implicitly relying on a model in which the incentive to try to alter the future play of opponents is small enough to be negligible One class of models of this type is one in players are locked in to their choices, and the discount factors... focus on finite games, in which each player has only finitely many available alternatives Our basic setting will be one in which a group of players i = 1,K , I play a stage game against one another The first half of the book will discuss the simplest kind of stage game, namely oneshot simultaneous move games This section reviews the basic theory of simultaneousmove games, and introduces the notation... Matching Models This book is about learning, and if learning is to take place players must play either the same or related games repeatedly so that they have something to learn about So far, most of the literature on learning has focused on repetitions of the same game, and not on the more difficult issue of when two games are “similar enough” that the results of one may have implications for the other.4 . dynamics, the connection between them, and some of their variants, in the setting of one-shot simultaneous-move games. Our focus will be on the long run behavior of the systems in various classes of games, . y0 w0 h2" alt="" 1 1. Introduction 1.1. Introduction This book is about the theory of learning in games. Most of non-cooperative game theory has focused on equilibrium in games, especially Nash. think that learning models have some relevance to real-world situations. To focus our thinking, we will begin by limiting attention to two-player games. The natural starting for the study of learning