A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution

We consider the allocation problem of infinitely divisible resources with at least three agents. For this problem, Thomson (Games and Economic Behavior, 52: 186-200, 2005) and Dogan (Games and Economic Behavior, 98: 165-171, 2016) propose "simple" but not "procedurally fair" game forms which implement the "no-envy" solution in Nash equilibria. By contrast, Galbiati (Economics Letters, 100: 72-75, 2008) constructs a procedurally fair but not simple game form which implements the no-envy solution in Nash equilibria. In this paper, we design a both simple and procedurally fair game form which implements the no-envy solution in Nash equilibria