Games with Incomplete Information Played by “Bayesian” Players, I–III Part I. The Basic Model

Abstract

The paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation, such as the payoff functions, the strategies available to various players, the information other players have about the game, etc. However, each player has a subjective probability distribution over the alternative possibilities.

Received June 1965, revised June 1966, accepted August 1966, and revised June 1967.

Parts II and III of “Games with Incomplete Information Played by ‘Bayesian’ Players” will appear in subsequent issues of Management Science: Theory.

The original version of this paper was read at the Fifth Princeton Conference on Game Theory, in April, 1965. The present revised version has greatly benefitted from personal discussions with Professors Michael Maschler and Robert J. Aumann, of the Hebrew University, Jerusalem; with Dr. Reinhard Selten, of the Johann Wolfgang Goethe University, Frankfurt am Main; and with the other participants of the International Game Theory Workshop held at the Hebrew University in Jerusalem, in October-November 1965. I am indebted to Dr. Maschler also for very helpful detailed comments on my manuscript.

This research was supported by Grant No. GS-722 of the National Science Foundation as well as by a grant from the Ford Foundation to the Graduate School of Business Administration, University of California. Both of these grants were administered through the Center for Research in Management Science, University of California, Berkeley. Further support has been received from the Center for Advanced Study in the Behavioral Sciences, Stanford.