Stable and metastable contract networks

TL;DR

This paper introduces a general framework for stable and metastable contract networks modeled as hypergraphs with agents and contracts, proving existence results for metastable systems and reducing stability problems to simpler preference structures.

Contribution

It generalizes the concept of stable contract networks to hypergraphs with complex preferences and establishes the existence of metastable systems, even when stable ones may not exist.

Findings

Stable networks can be reduced to simpler preference models.

Metastable systems always exist in the proposed framework.

Existence of stable systems is not guaranteed in all cases.

Abstract

We consider a hypergraph (I,C), with possible multiple (hyper)edges and loops, in which the vertices $i\in I$ are interpreted as agents, and the edges $c\in C$ 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 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 metastability for systems of contracts. Our second result is that a metastable system always exists.