Fair Allocations and Distortion of Utilities: A Note

Given two agents with von Neumann-Morgenstern utilities who wish to divide n commodities, consider the two-person non-cooperative game with strategies consisting of concave, increasing von Neumann-Morgenstern utility functions and whose outcomes are fair allocations to the commodity division problem determined by the strategies used. It is shown that any equal income competitive equilibrium allocation for the true utilities is a Nash equilibrium outcome for the non-cooperative game.