Comparative statics in non-cooperative games via transfinitely iterated play

Abstract Tarski's fixed point theorem establishes the existence of a Nash equilibrium when (a) each player's lattice of strategies is complete and (b) the composite best response function is isotone. Suppose the composite best response function is also isotone in one of the underlying parameters. Then our transfinite variant of iterated best response play is shown to “converge” and to produce an unambiguous comparative statics analysis. The efficacy of this approach is demonstrated with three examples.

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