Summary: Consider a \(M\)-player game in strategic form \(G=(X_1,\dots,X_M,g_1,\dots,g_M)\) 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 \(i=1,\dots,M\). The aim of this paper is to find appropriate conditions on the payoff functions under which the well-posedness with respect to the related variational inequality is equivalent to the formulation of Tikhonov's well-posedness in a game context. The idea of the proof is to appeal to a third equivalence, which is the well-posedness of an appropriate minimum problem.