The complexity of deciding reachability properties of distributed negotiation schemes

Distributed negotiation schemes offer one approach to agreeing an allocation of resources among a set of individual agents. Such schemes attempt to agree a distribution via a sequence of locally agreed ‘deals’–reallocations of resources among the agents–ending when the result satisfies some accepted criteria. Our aim in this article is to demonstrate that some natural decision questions arising in such settings can be computationally significantly harder than questions related to optimal clearing strategies in combinatorial auctions. In particular we prove that the problem of deciding whether it is possible to progress from a given initial allocation to some desired final allocation via a sequence of “rational” steps is pspace-complete.