Multiagent Resource Allocation with Sharable Items
Stéphane Airiau, Ulle Endriss
Abstract:
We study a particular multiagent resource allocation problem with
indivisible, but sharable resources. In our model, the utility of an
agent for using a bundle of resources is the difference between the
value the agent would assign to that bundle in isolation and a
congestion cost that depends on the number of agents she has to share
each of the resources in her bundle with. The valuation function
determining the value and the delay function determining the
congestion cost can be agent-dependent. When the agents that share a
resource also share control over that resource, then the current users
of a resource will require some compensation when a new agent wants to
join them using the resource. For this scenario of shared control, we
study the existence of distributed negotiation protocols that lead to
a social optimum. Depending on constraints on the valuation functions
(mainly modularity), on the delay functions (such as convexity), and
on the structural complexity of the deals between agents, we prove
either the existence of a sequences of deals leading to a social
optimum or the convergence of all sequences of deals to such an
optimum. We also analyse the length of the path leading to such
optimal allocations. For scenarios where the agents using a resource
do not have shared control over that resource (i.e., where any agent
can use any resource she wants), we study the existence of pure Nash
equilibria, i.e., allocations in which no single agent has an
incentive to add or drop any of the resources she is currently
holding. We provide results for modular valuation functions, we
analyse the length of the paths leading to a pure Nash equilibrium,
and we relate our findings to results from the literature on
congestion games