Contents
1 What is game theory? 2 Definitions of games 3 Dominance 4 Nash equilibrium 5 Mixed strategies 6 Extensive games with perfect information 7 Extensive games with imperfect information 8 Zero-sum games and computation 9 Bidding in auctions 10 Further reading 4 6 8 12 17 22 29 33 34 38

This is the draft of an introductory survey of game theory, prepared for the Encyclopedia of Information Systems, Academic Press, to appear in 2002.

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Glossary
Backward induction Backward induction is a technique to solve a game of perfect information. It first considers the moves that are the last in the game, and determines the best move for the player in each case. Then, taking these as given future actions, it proceeds backwards in time, again determining the best move for the respective player, until the beginning of the game is reached. Common knowledge A fact is common knowledge if all players know it, and know that they all know it, and so on. The structure of the game is often assumed to be common knowledge among the players. Dominating strategy A strategy dominates another strategy of a player if it always gives a better payoff to that player, regardless of what the other players are doing. It weakly dominates the other strategy if it is always at least as good. Extensive game An extensive game (or extensive form game) describes with a tree how a game is played. It depicts the order in which players make moves, and the information each player has at each decision point. Game A game is a formal description of a strategic situation. Game theory Game theory is the formal study of decision-making where several players must make choices that potentially affect the interests of the other players.

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Mixed strategy A mixed strategy is an active randomization, with given probabilities, that determines the player’s decision. As a special case, a mixed