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

Wojciech Olszewski ()
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Wojciech Olszewski: Department of Economics, Northwestern University, Evanston, Illinois 60208

Mathematics of Operations Research, 2022, vol. 47, issue 3, 2333-2343

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.

Keywords: Primary: 37C25; 91A26; secondary: 47H10; iterations; fixed points; best-response dynamics (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:3:p:2333-2343

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