zbMATH — the first resource for mathematics

Equilibrium in strategic interaction: The contributions of John C. Harsanyi, John F. Nash and Reinhard Selten. (English) Zbl 0912.90285
Summary: We review the three laureates’ main contributions to noncooperative game theory. Our emphasis is on the foundations and background of the equilibrium concepts that nowadays are routinely applied in economics. To provide a proper perspective, we start in Section II by reviewing the relationship between games and economic theory and by paraphrasing the desiderata for a theory of strategic interaction from the founding fathers of game theory, John von Neumann and Oskar Morgenstern. In Section III we introduce the Nash equilibrium concept, discuss Nash’s existence proofs and his attempts to arrive at a unique solution, and briefly review his work on bargaining theory. Section IV is devoted to Selten’s concepts of subgame perfection and perfect equilibrium. Section V considers Harsanyi’s approach to games with incomplete information. In Section VI we briefly discuss the main elements of Harsanyi’s and Selten’s theory of equilibrium selection, in particular the concept of risk dominance and the tracing procedure.
The material in Sections II–VI rests on the interpretation of Nash equilibrium as a necessary requirement for prescriptions based on a theory of rational behavior in strategic interactions. According to this interpretation, the game is played exactly once, and the players are rational decision makers. An alternative interpretation, first formulated in Nash’s unpublished doctoral thesis (1950), is discussed in Section VII. In this interpretation, the game is played over and over again by players who need not be rational and who are randomly drawn from large populations. This interpretation (until recently largely unknown) is relevant to the current literature on learning and social evolution in games. Section VIII concludes by looking back at von Neumann’s and Morgenstern’s desiderata for a theory of strategic interaction.

91A10 Noncooperative games
91A12 Cooperative games
91A35 Decision theory for games
91B06 Decision theory
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
Full Text: DOI