Abstract of a talk presented at the UCLA Mathematics Department

# The Impact of Harsanyi, Nash and Selten in Modern
Economic Theory

David K. Levine

June 1995

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.

### References

J. Harsanyi [1967-8], "Games with Incomplete Information Played by Bayesian
Players," Management Science, 14, 159-82,320-34, 486-502

J. Nash [1951]: "Non-cooperative games," Annals of Mathematics, 54, 286-295.

R. Selten [1965]: "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.