Introduction to the special issue on learning and computational game theory

Game theory is concerned with the decision making of utility-maximizing individuals in their interactions with one another and their environment. From its earliest days of study, researchers have recognized the important relationship between game theory and learning— using experience from past play to guide future decisions. Recently, there has been a surge in research that applies a computational perspective to learning in general-sum games. The editors have been involved with such projects: for example, deriving finite time bounds on learning algorithms known to converge to game-theoretic equilibria in the limit (Greenwald, Li, & Marks, 2006); and developing computationally efficient models of strategic interactions (Kearns, Littman, & Singh, 2001). Our purpose in editing this special issue on computational issues that pertain to learning in games was to provide an opportunity for sharing results in this rapidly growing area at the intersection of computer science and economics. When facing an unknown opponent, learning plays a central role. As such, there are many ways of applying machine-learning techniques to games. As eloquently argued by Shoham, Powers, and Grenager (2007), it is critical for research in this area to be geared towards solving a precise problem, and that the criteria for judging the success of the work be clearly stated. We selected five articles that followed these important guidelines. Each of the contributions in the special issue spells out what information is available to the individual players (their own actions, the actions of others, utilities of all players, identity of the other players, etc.), how their performance is to be judged (utility of the player, social utility, convergence to equilibrium, stability of learned behavior, etc.), the model of uncertainty (randomized payoffs, noise in action perception, stochastic action effects, etc.), the relevant equilibrium concepts, and any computational concerns.