Simple Negotiation Schemes for Agents with Simple Preferences: Sufficiency, Necessity and Maximality
Yann Chevaleyre, Ulle Endriss, Nicolas Maudet
Abstract:
Simple Negotiation Schemes for Agents with Simple Preferences:
Sufficiency, Necessity and Maximality
Yann Chevaleyre, Ulle Endriss, Nicolas Maudet
Abstract:
We investigate the properties of an abstract negotiation framework
where agents autonomously negotiate over allocations of indivisible
resources. In this framework, reaching an allocation that is optimal
may require very complex multilateral deals. Therefore, we are
interested in identifying classes of valuation functions such that any
negotiation conducted by means of deals involving only a single
resource at a time is bound to converge to an optimal allocation
whenever all agents model their preferences using these functions. In
the case of negotiation with monetary side payments amongst
self-interested but myopic agents, the class of modular valuation
functions turns out to be such a class. That is, modularity is a
sufficient condition for convergence in this framework. We also show
that modularity is not a necessary condition. Indeed, there can be no
condition on individual valuation functions that would be both
necessary and sufficient in this sense. Evaluating conditions
formulated with respect to the whole profile of valuation functions
used by the agents in the system would be possible in theory, but
turns out to be computationally intractable in practice. Our main
result shows that the class of modular functions is maximal in the
sense that no strictly larger class of valuation functions would still
guarantee an optimal outcome of negotiation, even when we permit more
general bilateral deals. We also establish similar results in the
context of negotiation without side payments.