Egalitarian Allocations and Convexity

Abstract

In the Inverse Set, relative to the Shapley Value of a non-convex cooperative game, we derive a procedure to find out a convex game in which the Egalitarian Allocation is a coalitional rational value. The procedure depends on the relationship between two parameters called the Convexity Threshold and the Coalitional Rationality Threshold. Some examples follow and illustrate the procedure. We discussed a similar problem for other efficient values, the Shapley Value and the Egalitarian Nonseparable Contribution, in earlier work.