A characterization of the existenceof optimal dominant strategy mechanisms

This paper provides two theorems which characterize the domains of valuation functions for which there exist Pareto efficient and truth dominant strategy mechanisms (balanced Groves mechanisms). Theorem 1 characterizes the existence of balanced Groves mechanisms for a general class of valuation functions. Theorem 2 provides new balance-permitting domains of valuation functions by reducing the problem of solving partial differential equations to the problem of solving a polynomial function. It shows that a balanced Groves mechanism exists if and only if each valuation function in the family under consideration can be obtained by solving a polynomial function with order less than $n-1$, where n is the number of individuals.