Value theory without symmetry

Abstract

We investigate quasi-values of finite games – solution concepts that satisfy the axioms of Shapley (1953) with the possible exception of symmetry. Following Owen (1972), we define “random arrival'', or path, values: players are assumed to “enter'' the game randomly, according to independently distributed arrival times, between 0 and 1; the payoff of a player is his expected marginal contribution to the set of players that have arrived before him. The main result of the paper characterizes quasi-values, symmetric with respect to some coalition structure with infinite elements (types), as random path values, with identically distributed random arrival times for all players of the same type. General quasi-values are shown to be the random order values (as in Weber (1988) for a finite universe of players). Pseudo-values (non-symmetric generalization of semivalues) are also characterized, under different assumptions of symmetry.