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We will constructively prove the existence of a Nashequilibrium in a finite strategic game with sequentially locally nonconstantpayoff functions. The proof is based on the existence of approximate Nashequilibria which is proved by Sperner's lemma. We follow the Bishop-styleconstructive mathematics.

Constructive Proof of the Existence of Nash Equilibrium in a Finite Strategic Game with Sequentially Locally Nonconstant Payoff Functions