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A Result on Convergence of Sequences of Iterations with Applications to Best-Response Dynamics

Author

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  • Wojciech Olszewski

    (Department of Economics, Northwestern University, Evanston, Illinois 60208)

Abstract

The result that says the sequence of iterations x k + 1 = f ( x k ) converges if f : [ 0 , 1 ] → [ 0 , 1 ] is an increasing function has numerous applications in elementary economic analysis. I generalize this simple result to some mappings f : S ⊂ [ 0 , 1 ] n → S . The applications of the new result include the convergence of the best-response dynamics in the general version of the Crawford and Sobel model and in some versions of the Hotelling and Tiebout models.

Suggested Citation

  • Wojciech Olszewski, 2022. "A Result on Convergence of Sequences of Iterations with Applications to Best-Response Dynamics," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 2333-2343, August.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:3:p:2333-2343
    DOI: 10.1287/moor.2021.1210
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    References listed on IDEAS

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    1. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64(5), pages 416-416.
    2. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
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