Further results on structural stability and robustness to bounded rationality

In this paper, we study the model of bounded rationality that has been studied in Anderlini and Canning (2001), Yu and Yu (2006), Yu et al. (2009) and Miyazaki and Azuma (2013). First, using a lower pseudocontinuous rationality function, we prove that the model is structurally stable and robust to ϵ-equilibria for almost all parameter values, and the structural stability implies robustness to bounded rationality. Second, by relaxing the assumption of compactness, if the feasible correspondence is compact-valued and continuous, and the rationality function is continuous, we show that the robustness to ϵ-equilibria implies structural stability. Third, using a lower semicontinuous rationality function, we prove that (λ,ϵ)-stability implies (λ,ϵ)-robustness. Finally, if the feasible correspondence is compact-valued and continuous, and the rationality function is continuous, we obtain that (λ,ϵ)-robustness implies (λ,ϵ)-stability.