A new complementarity-based pricing game

Abstract

It is highly nontrivial to construct a multi-product demand function on the entire set of nonnegative prices, not to mention approximating the real market demands to a desirable accuracy. Thus, many decision-makers use incomplete demand functions which are defined only on a restricted domain. We will demonstrate the necessity of defining demand functions on the entire set of nonnegative prices, through some examples. Indeed, these examples show that incomplete demand functions may lead to inferior pricing models. Then we formulate a type of demand functions using a Nonlinear Complementarity. When the model of demand functions is incorporated into the best response problem of each producer/seller involved, it leads to a complementarity constrained pricing problem facing each producer/seller. Some basic properties of the pricing models are presented. In particular, we show that, under certain conditions, the complementarity constraints in this pricing model can be eliminated, tremendously simplifying computation and theoretical analyses.