On Groves Mechanisms for Costly Inclusion

We investigate Groves mechanisms for economies where (i) a social outcome specifies a group of winning agents, and (ii) a cost function associates each group with a monetary cost. Infeasible groups and revenue-generating groups are modeled using infinite costs and negative costs, respectively. First, we introduce a novel condition for cost functions, inclusion cost coverage, and prove that there are Groves mechanisms such that the agents cover the costs through voluntary payments if and only if the cost function satisfies this condition, in which case variants of the pivot mechanisms are such mechanisms (Theorem 1). Second, we establish that there are envy-free Groves mechanisms if and only if the cost function is convex and symmetric, in which case variants of the pivot mechanisms are such mechanisms (Theorem 2). It follows directly that whenever production efficient and envy-free allocations can be implemented in dominant strategies, this can moreover be done while funding production through voluntary payments. We discuss a variety of applications and additional topics.