Representation of effectivity functions by acceptable game forms: a complete characterization

Acceptable game forms were introduced in Hurwicz and Schmeidler [Econometrica 46 (1978) 1447]. Dutta [Econometrica 52 (1984) 1151] considered effectivity functions of acceptable game forms. This paper unifies and extends the foregoing two papers. We obtain the following characterization of the effectivity functions of acceptable game forms: An effectivity function belongs to some acceptable game form if and only if (i) it belongs to some Nash consistent game forms, and (ii) it satisfies an extra simple condition. (Nash consistent game forms have already been characterized by their effectivity functions in Peleg et al. [Mathematical Social Sciences 43 (2002) 267].) As a corollary of our characterization, we show that every acceptable game form violates minimal liberalism. (C) 2003 Elsevier B.V. All rights reserved.