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… - John Harsanyi

In the period 1965 - 69, the U.S. Arms Control and Disarmament Agency employed a group of about ten young game theorists as consultants. It was as a member of this group that I developed the simpler approach, already mentioned, to the analysis of I-games. I realized that a major problem in arms control negotiations is the fact that each side is relatively well informed about its own position with respect to various variables relevant to arms control negotiations, such as its own policy objectives, its peaceful or bellicose attitudes toward the other side, its military strength, its own ability to introduce new military technologies, and so on - but may be rather poorly informed about the other side's position in terms of such variables. I came to the conclusion that finding a suitable mathematical representation for this particular problem may very well be a crucial key to a better theory of arms control negotiations, and indeed to a better theory of all I-games.

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.

Early in 1954 I was appointed Lecturer in Economics at the University of Queensland in Brisbane. Then, in 1956, I was awarded a Rockefeller Fellowship, enabling me and Anne to spend two years at Stanford University, where I got a Ph.D. in economics, whereas Anne got an M.A. in psychology. I had the good fortune of having Ken Arrow as advisor and as dissertation supervisor. I benefitted very much from discussing many finer points of economic theory with him. But I also benefitted substantially by following his advice to spend a sizable part of my Stanford time studying mathematics and statistics. These studies proved very useful in my later work in game theory.