Abstract: We study the behavior of a generalized Frank-Wolfe algorithm in constrained (stochastic) monotone variational inequality (MVI) problems. Recent years have seen many efforts in designing algorithms for solving constrained MVI problems due to their connections with optimization, machine learning, and equilibrium computation in games. The majority of work in this domain has focused on extensions of simultaneous gradient play, with particular emphasis on understanding the convergence properties of extragradient and optimistic gradient methods. In contrast, we study the performance of an algorithm drawn from another well-known class of optimization algorithms: Frank-Wolfe. We show that a generalized variant of this algorithm enjoys a fast $\mathcal{O}(T^{-1/2})$ last-iterate convergence in constrained MVI problems. By making connections between our generalized Frank-Wolfe with the well-known smoothed fictious-play (FP) from game theory, we also derive a finite-sample convergence rate for smoothed FP in zero-sum matrix games. Furthermore, we show that a stochastic variant of generalized Frank-Wolfe in MVI problems also converges in a last-iterate sense albeit at a slower $\mathcal{O}(T^{-1/6})$ rate of convergence.