Abstract of a talk presented at the UCLA Mathematics Department
David K. Levine
Recently three game theorists, J. Harsanyi, J. Nash and R. Selten, shared the Nobel prize in economics. This talk describes their major ideas and the impact they have had in economics.
Nash defined the notion of a noncooperative (or Nash) equilibrium, and proved existence in mixed strategies. Selten refined this notion to the recursive notion of subgame perfect equilibrium and the closely related notion of trembling hand perfection. Harsanyi defined the notion of a Bayesian equilibrium, in which players lack of information about the game they are playing is encapsulated in a player's "type."
These ideas have been influential in the study of games by economists during the 1980s. Four major areas in which this impact has been felt are in the study of bargaining, reputation and repeated games, signalling, and mechanism design. The outlines of the theory in each of these areas will be briefly examined, and the role of Nash, perfect and Bayesian equilibrium discussed.
J. Harsanyi [1967-8], "Games with Incomplete Information Played by Bayesian Players," Management Science, 14, 159-82,320-34, 486-502
J. Nash : "Non-cooperative games," Annals of Mathematics, 54, 286-295.
R. Selten : "Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragentragheit," Zeitschrift fur die gesamte Staatswissenschaft, 12, 201-324.
© David K. Levine. You are free to make use of this document, provided you provide proper attribution.