Game theory is a theory of strategic interaction. That is to say, it is a theory of rational behavior in social situations in which each player has t… - John Harsanyi

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.

If somebody prefers an income distribution more favorable to the poor for the sole reason that he is poor himself, this can hardly be considered as a genuine value judgment on social welfare.

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.