Optimal Robustness under Uncertainty

A. Robustness concern has been long reflected in the decision models under uncertainty since the maxmin expected utility theory. All the models set the degree of robustness concern as fixed across all the payoff profiles. However, a decision maker’s robustness concern may well changes when the certainty part or the unit scale of a payoff profile changes. This paper introduces formally a decision maker’s robustness order, and characterize together a general class of robustness order and preference order over all the payoff profiles. The preference order has the feature of ranking the payoff profiles using the optimal degree of robustness. The optimal robustness level is endogenous and can change with the certainty part of a payoff profile and its unit scale.