On the robustness of the competitive equilibrium: Utility-improvements and equilibrium points

We show that the set of competitive equilibrium points of a pure exchange economy are the equilibrium points of a broader class of better-response demands than the usual utility-maximizing demand functions. The better-response demands are derived from assigning weights to all commodity bundles with higher utility than the current commodity bundle, with the greatest weights being placed on the commodity bundles with the highest utility gain. The usual utility-maximizing demand functions are then those in which the weight on the utility-maximizing bundle is one. We also show that these better-response demands belong to a large class of response maps that are generated by monotonic transformations of the utility functions and/or monotonic transformations of the weights assigned to the commodity bundles.