VALUES OF NON-ATOMIC GAMES, IV: THE VALUE AND THE CORE
RAND CORP SANTA MONICA CA
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The value of an n-person game 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. A non-atomic game is a special kind of infinite-person game, in which no individual player has significance. The relationship between the value and another solution concept is developed. The core of a game is the set of outcomes that, intuitively speaking, no coalition of players can improve upon. The core is a basic concept that has been studied widely by both game theorists and economists. The main object of the present paper is to prove that under suitable assumptions, the core of a non-atomic game consists of a single outcome, and that this outcome coincides with the value. The assumptions superadditivity and homogeneity of degree 1 are satisfied in many cases of interest, including a basic economic application.
- Operations Research