Advances in Value Theory

Publisher Summary This chapter describes value as a central concept in game theory and discusses its applications. The value of a game to a player is best viewed as a priori evaluation of his expected payoffs. The Shapley value and its generalizations have been extensively studied and continue to be the focus of much research, both theoretically as well as in applications. The chapter discusses recent advances in the study of the various value concepts. As it is well known, the standard axioms determining the Shapley value are efficiency; symmetry or equal treatment (which means that identical players have equal values); additivity (the value of the sum of two games is the sum of the values of the two games); and finally, null player (the value of a player who never contributes anything is zero). In a recent paper, it has been shown that one may replace the last two axioms—additivity and null player—with the following requirement: The value of a player depends only on his marginal contributions.

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