Partitionable variational inequalities with applications to network and economic equilibria

In this paper, we describe a useful class of finite-dimensional variational inequalities which we call partitionable. These variational inequalities are characterized by state functions which can be thought of as nonlinear separable functions added to antisymmetric linear functions. In the case of partitionable variational inequalities, questions of the monotonicity and coercivity of the state function can be addressed by considering the monotonicity and coercivity of a series of lower-dimensional functions. These functions are generally simpler to investigate than the state function. In the applications, these lower-dimensional functions are usually the natural functions to consider. To demonstrate, we conclude the paper by reviewing several models in the recent literature which give rise to partitionable variational inequalities.