Economic efficiency requires interaction

Abstract

We study the necessity of interaction between individuals for obtaining approximately efficient economic allocations. We view this as a formalization of Hayek's classic point of view that focuses on the information transfer advantages that markets have relative to centralized planning. We study two settings: combinatorial auctions with unit demand bidders (bipartite matching) and combinatorial auctions with subadditive bidders. In both settings we prove that non-interactive protocols require exponentially larger communication costs than do interactive ones, even ones that only use a modest amount of interaction.

Welfare Maximization with Limited Interaction

“…The bipartite matching problem is clearly a very basic one and obviously models a host of situations beyond the economic one that was the direct motivation of [DNO14] and of this paper. Despite having been widely studied, even its algorithmic status is not well understood, and it is not clear whether a nearly-linear time algorithm exists for it.…”

“…In parallel computation, a major open problem is whether bipartite matching can be solved in deterministic parallel poly-logarithmic time with a polynomial number of processors (Randomized parallel algorithms for the problem [MVV87,KUW85] have been known for over 25 years). It was suggested in [DNO14] that studying the problem in the communication complexity model is an approach that might lead to algorithmic insights as well. The bipartite matching problem has been studied in various other multi-party models that focus on communication as well.…”

“…The classic auction of [DGS86] -that may be viewed as a simple Walrasian-like market process for this setting -can be implemented as to find an approximately optimal allocation where each player needs only send O(log n) bits of communication (on the average). The question considered by [DNO14] was whether such a low communication burden suffices without using multiple rounds of interaction. As a lower bound, they proved that a non-interactive protocol, i.e.…”

“…The natural question at this point is whether there are r-round protocols with better approximation factors that still use n o(1) bits of communication per player. This question was left open in [DNO14], where it was pointed out that it was even open whether the exactly optimal matching can be found by 2-round protocols that use O(log n) bits of communication per player. We answer this open problem by proving lower bounds for any fixed number of rounds.…”

“…We show that even if the allowable perround bandwidth of each agent is n ε(r) , the approximation ratio of any r-round (randomized) protocol is no better than Ω(n 1/5 r+1 ), implying an Ω(log log n) lower bound on the rate of convergence of the market to equilibrium. Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of combinatorial auctions, for which the only known lower bound is for simultaneous (r = 1) protocols [DNO14]. …”