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

Wojciech Olszewski

doi:10.1287/moor.2021.1210

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

Wojciech Olszewski^*

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	2333-2343
Number of pages	11
Journal	Mathematics of Operations Research
Volume	47
Issue number	3
DOIs	https://doi.org/10.1287/moor.2021.1210
State	Published - Aug 2022

Keywords

best-response dynamics
fixed points
iterations

ASJC Scopus subject areas

General Mathematics
Computer Science Applications
Management Science and Operations Research

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10.1287/moor.2021.1210

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abstract = "The result that says the sequence of iterations xk+1 f (xk) 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.",

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author = "Wojciech Olszewski",

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AB - The result that says the sequence of iterations xk+1 f (xk) 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.

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

Abstract

Keywords

ASJC Scopus subject areas

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