The existence of a strong solution of time-dependent quasi-variational inequalities is examined. The initial-value problem (y′(t)+A(t; y(t); y(t))-f,x(t)-y(t))H≥0 a.e. on (0, T), y(t)∈L y(t) for all t∈[0, T], y(0) = y0 is considered for all x∈C(0, T; H) with x(t)∈L y(t) and A(t; y; y)∈∂yφ(t; z; y)|z = y. The result shows the existence of the equilibria of a constrained non-cooperative game. An
... [Show full abstract] application to the Walras equilibrium of a nonstationary compactified economy is provided, and parabolic quasi-variational inequalities in noncylindrical domains are presented.