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Structural stability and robustness to bounded rationality for non-compact cases

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Abstract

We study the model M consisting of “general games” with noncompact action space, together with an associated abstract rationality function. We prove that M is structurally stable and robust to ϵ-equilibria for “almost all” parameters. As applications, we investigate structural stability and robustness to bounded rationality for noncooperative games, multiobjective optimizations and fixed point problems satisfying existence and some continuity conditions. Specifically, we introduce concrete rationality functions for such three kinds of problems with both payoffs and strategy sets, objective functions and domain spaces, and correspondence and domain spaces as parameters, respectively, and show the generic structural stability and robustness to bounded rationality for the corresponding model Ms.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, People’s Republic of China

    Jian Yu, Hui Yang & Chao Yu

Authors
  1. Jian Yu
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  2. Hui Yang
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  3. Chao Yu
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Correspondence to Hui Yang.

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Yu, J., Yang, H. & Yu, C. Structural stability and robustness to bounded rationality for non-compact cases. J Glob Optim 44, 149–157 (2009). https://doi.org/10.1007/s10898-008-9316-8

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  • DOI: https://doi.org/10.1007/s10898-008-9316-8

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