Assume that i q; m; p depends only on pair-wise price di¤erences; this property can be derived from a consumer choice model with quasi-linear preferences in money. where 1 n is a vector of ones of length n: Also, assume that the FOC is su¢ cient to characterize a unique equilibrium for any symmetric cost structure. Let i m; p denote the corresponding vector specifying the probabilities over di¤...

If the smooth vector fields X1,…,Xm and their commutators span tangent space at every point in Ω⊆RN for any fixed m≤N, then we establish full interior regularity theory of quasi-linear equations ∑i=1mXi⁎Ai(X1u,…,Xmu)=0 with p-Laplacian type growth condition. In other words, show that a weak solution equation is locally C1,α.

In this paper, we establish the regularized gap function for a class of mixed parametric vector quasi- equilibrium problems (briefly, (MPVQEP)y). Then an error bound is also provided (MPVQEP)g via under suitable assumptions. Some examples are given to illustrate our results. Our main results extend and differ from those corresponding ones in current literatures.