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Further results on structural stability and robustness to bounded rationality

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  • Yu, Jian
  • Yang, Zhe
  • Wang, Neng-Fa

Abstract

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.

Suggested Citation

  • Yu, Jian & Yang, Zhe & Wang, Neng-Fa, 2016. "Further results on structural stability and robustness to bounded rationality," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 49-53.
    • Handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:49-53
    DOI: 10.1016/j.jmateco.2016.09.009
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    References listed on IDEAS

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    1. Loi, Andrea & Matta, Stefano, 2015. "Increasing complexity in structurally stable models: An application to a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 20-24.
    2. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    3. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    4. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    5. Miyazaki, Yusuke & Azuma, Hiromi, 2013. "(λ,ϵ)-stable model and essential equilibria," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 85-91.
    6. Anderlini, Luca & Canning, David, 2001. "Structural Stability Implies Robustness to Bounded Rationality," Journal of Economic Theory, Elsevier, vol. 101(2), pages 395-422, December.
    7. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    8. Miyazaki, Yusuke, 2014. "A remark on topological robustness to bounded rationality in semialgebraic models," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 33-35.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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