Structural stability implies robustness to bounded rationality.

*(English)*Zbl 0996.91078Summary: The introduction of a small amount of bounded rationality into a model sometimes has little effect and sometimes has a dramatic impact on predicated behavior. Here the authors call a model robust to bounded rationality if small deviations from rationality result only in small changes in the equilibrium set. They also say that a model is structurally stable if the equilibrium set (given fully rational agents) varies continuously with the parameter values of the model.

It is easy to see that when the equilibrium set is discontinuous, bounded rationality can have a very large impact on behavior in the neighborhood of the discontinuity. They go further and show that it is only at such discontinuities that bounded rationality can have large effects. It follows that a model is robust to bounded rationality if and only if it is structurally stable. Thus, they can characterize which model will be robust to bounded rationality and which will not, independently of the exact form that the bounded rationality takes.

It is easy to see that when the equilibrium set is discontinuous, bounded rationality can have a very large impact on behavior in the neighborhood of the discontinuity. They go further and show that it is only at such discontinuities that bounded rationality can have large effects. It follows that a model is robust to bounded rationality if and only if it is structurally stable. Thus, they can characterize which model will be robust to bounded rationality and which will not, independently of the exact form that the bounded rationality takes.

##### MSC:

91B52 | Special types of economic equilibria |

91A26 | Rationality and learning in game theory |

91B64 | Macroeconomic theory (monetary models, models of taxation) |

90C47 | Minimax problems in mathematical programming |

91A40 | Other game-theoretic models |

91B06 | Decision theory |

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\textit{L. Anderlini} and \textit{D. Canning}, J. Econ. Theory 101, No. 2, 395--422 (2001; Zbl 0996.91078)

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