Toward general robustness evaluation of incentive mechanism against bounded rationality

Abstract

An incentive mechanism is designed to achieve desired outcomes as Nash equilibrium, by assuming agents to be fully rational. Nevertheless, practical agents may violate this assumption for various reasons, causing mechanisms to fail. Thus, before deploying a mechanism in practice, it is crucial to quantitatively evaluate to what extent the Nash equilibrium can resist different kinds of bounded rationality, termed robustness. In this paper, focusing on Nash equilibrium, we first propose a general robustness formulation as the upper bound of the stable region of equilibrium strategies by generalizing existing bounded rationality models. We also show that different existing robustness formulations of Nash equilibrium can be derived from this general formulation, which verifies the soundness of our formulation. Then, we develop a robustness evaluation framework specifically for incentive mechanisms, of which the key component is the empirical stability test given a certain level of bounded rationality. Finally, the evaluation framework is validated on three typical but distinct incentive mechanisms, and the robustness computation results conform to our theoretical analysis. The comparison also offers us a good reference for making a proper selection among different designs.