Stable and Metastable Contract Networks1

We consider a hypergraph ( I,C ), with possible multiple (hyper)edges and loops, in which the vertices i ∈ I are interpreted as agents , and the edges c ∈ C as contracts that can be concluded between agents. The preferences of each agent i concerning the contracts where i takes part are given by use of a choice function f i possessing the so-called path independent property. In this general setup we introduce the notion of stable network of contracts.​The paper contains two main results. The first one is that a general problem on stable systems of contracts for $(I,C,f)$ is reduced to a set of special ones in which preferences of agents are described by use of so-called \emph{weak orders}, or utility functions. However, for a special case of this sort, the stability may not exist. Trying to overcome this trouble when dealing with such special cases, we introduce a weaker notion of \emph{metastability} for systems of contracts. Our second result is that a metastable system always exists