Utility-based two-stage models with fairness concern

This paper studies the impact of social comparison and fairness concerns on the efficiency of a two-stage process. The decision maker of each stage cares about not only the absolute score of his efficiency, but also the relative status when comparing with the other. By incorporating the utility theory and the concept of fairness, an efficiency-based Neumann-Morgenstern cardinal utility is defined to compose of basic utility from his self-efficiency and additional utility from the fairness concern of the other's efficiency. Utility-based two-stage models are proposed to optimize the utilities of the stages rather than only the efficiencies instead. We characterize the concern of fairness as advantageous and disadvantageous inequity based on equitable outcome comparison. By investigating the non-cooperating relationship between two stages, we show that the stage dominating the process has the incentive to optimize his efficiency without ignoring that of the other, which is contrary to the conventional situation. In addition, the coefficients of equitable outcome and inequity significantly affect the efficiencies of both stages. We further investigate the cooperation between two stages and find that the efficiencies of the stages vary with the coefficients of unfairness perceptions. Numerical analysis verifies the validity of the proposed models and identifies the impacts of the coefficients of equitable outcome and inequity on the stages' and overall efficiencies.