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Consider a M-player game in strategic form $G=(X_1,\mathrm{\cdots },X_M,g_1,\mathrm{\cdots },g_M)$ where the set $X_i$ is a closed interval of real numbers and the payoff function $g_i$ is concave and differentiable with respect to the variable $x_i\in X_i$, for any $i=1,\mathrm{\cdots },M$. The aim of this paper is to find appropriate conditions on the payoff functions under the well-posedness with respect to the related variational inequality is equivalent to the formulation of the Tykhonov well-posedness in a game context. The idea of the proof is to appeal to a third equivalence, which...