Multiagent resource allocation with sharable items: simple protocols and Nash equilibria

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 valuation of that bundle and a congestion cost (or delay), a figure formed by adding up the individual congestion costs of each resource in the bundle. The valuation and the delay can be agent-dependent. When the agents that share a resource also share the resource's control, the current users of a resource will require some compensation when a new agent wants to use the resource. We study the existence of distributed protocols that lead to a social optimum. Depending on constraints on the valuation functions (mainly modularity), on the delay functions (e.g., convexity), and the structural complexity of the deals between agents, we prove either the existence of some sequences of deals or the convergence of all sequences of deals to a social optimum. When the agents do not have joint control over the resources (i.e., they can use any resource they want), we study the existence of pure Nash equilibria. We provide results for modular valuation functions and relate them to results from the literature on congestion games.