Complete Characterization of Acceptable Game Forms by Effectivity Functions

Bezalel Peleg ()

Discussion Paper Series from Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem

Abstract: Acceptable game forms were introduced in Hurwicz and Schmeidler (1978). Dutta (1984) 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 (i) it belongs to some Nash consistent game forms; and (ii) it satisfies an extra simple condition (our (3.1) or (4.2)). (Nash consistent game forms have already been characterized by their effectivity functions in Peleg et al. (2001).) As a corollary of our characterization we show that every acceptable game form violates minimal liberalism.

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Date: 2002-01
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Published as "Representation of effectivity functions by acceptable game forms: A complete characterization" in Social Sciences, 2004, vol. 47, pp. 275-287

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