Extremal Behaviour in Multiagent Contract Negotiation

TL;DR

This paper analyzes resource reallocation in multiagent negotiations, showing that implementing certain reallocations can require exponentially many rational deals, especially with limited agent participation.

Contribution

It demonstrates that some resource reallocations in multiagent systems may need exponentially many steps to implement under rationality constraints, highlighting complexity issues.

Findings

Reallocations can require exponential rational deals in the number of resources.

Single deals involving multiple agents can achieve complex reallocations.

Limited agent participation restricts the realizability of certain reallocations.

Abstract

We examine properties of a model of resource allocation in which several agents exchange resources in order to optimise their individual holdings. The schemes discussed relate to well-known negotiation protocols proposed in earlier work and we consider a number of alternative notions of rationality covering both quantitative measures, e.g. cooperative and individual rationality and more qualitative forms, e.g. Pigou-Dalton transfers. While it is known that imposing particular rationality and structural restrictions may result in some reallocations of the resource set becoming unrealisable, in this paper we address the issue of the number of restricted rational deals that may be required to implement a particular reallocation when it is possible to do so. We construct examples showing that this number may be exponential (in the number of resources m), even when all of the agent utility functions are monotonic. We further show that k agents may achieve in a single deal a reallocation requiring exponentially many rational deals if at most k-1 agents can participate, this same reallocation being unrealisable by any sequences of rational deals in which at most k-2 agents are involved.