Game Theory for Computer Scientists-Noncooperative Games (Basic Theory)

Abstract

Game theory is a mathematical study of interaction among rational players. This tutorial presents an overview of noncooperative game theory, specifically games in normal-form. In noncooperative game theory in normal-form, multiple players independently and simultaneously select their actions so as to maximize their own utilities. The obtained utility of a player is determined by combination of her own action and the actions of other players. In noncooperative games, various equilibrium concepts have been developed to predict the result of a game. First, we introduce basic notations and equilibrium concepts in noncoperative games. If we explicitly represent a normal form game, the size of the representation grows exponentially as the number of players increases. Thus, we explain the algorithms/computational costs to efficiently find Nash equilibria in graphical games and congestion games, which have been proposed as concise representation schema. © 2012, Japan Society for Software Science and Technology. All rights reserved.