Equal-Budget Choice Equivalent Solutions in Exchange Economies

Abstract

Given a family of linear budget sets, an allocation is equal opportunity equivalent (Thomson, 1994) if there exists a common budget set such that each agent is indi¤erent between the bundle that he gets and the best bundle he can obtain in the choice set. We first study therobustness properties of equal opportunity equivalent correspondences with respect to change in preferences. We impose independence to irrelevant preference changes and connect this property with the implementation of rules via some game-theoretic solution concept. We provide an equivalence result with the equal-income Walrasian rule. Next, we study robustness with respect to change in the number of agents and derive a haracterization of the equal-income Walrasian rule. Our results provide additional justifications for the equal-division of resources as a first step toward fairness.microeconomics ;