Values of Non-atomic Games I: The Axiomatic Approach

The value of an n-person game, n finite, is a function that associates to each player a number that, intuitively speaking, represents an a priori opinion of what it is worth to him to play in the game. Games with a continuum of players have recently attracted considerable attention as models for mass phenomena in economics and game theory. The paper extends the definition of value to certain classes of games with a continuum of players, and investigates the properties of the concept so defined.