We can regard the vector c_i as representing certain physical, social, and psychological attributes of player i himself in that it summariz… - John Harsanyi

Following von Neumann and Morgenstern [7, p. 30], we distinguish between games with complete information, to be sometimes briefly called C-games in this paper, and games with incomplete information, to be called I-games. The latter differ from the former in the fact that some or all of the players lack full information about the "rules" of the game, or equivalently about its normal form (or about its extensive form). For example, they may lack full information about other players' or even their own payoff functions, about the physical facilities and strategies available to other players or even to themselves, about the amount of information the other players have about various aspects of the game situation, etc. In our own view it has been a major analytical deficiency of existing game theory that it has been almost completely restricted to C-games, in spite of the fact that in many real-life economic, political, military, and other social situations the participants often lack full information about some important aspects of the "game" they are playing.

In principle, every social situation involves strategic interaction among the participants. Thus, one might argue that proper understanding of any social situation would require game-theoretic analysis. But in actual fact, classical economic theory did manage to sidestep the game-theoretic aspects of economic behavior by postulating perfect competition, i.e., by assuming that every buyer and every seller is very small as compared with the size of the relevant markets, so that nobody can significantly affect the existing market prices by his actions.

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.
In most of the paper it is assumed that these probability distributions entertained by the different players are mutually "consistent," in the sense that they can be regarded as conditional probability distributions derived from a certain "basic probability distribution" over the parameters unknown to the various players. But later the theory is extended also to cases where the different players' subjective probability distributions fail to satisfy this consistency assumption.