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