Mechanism design for resource allocation in networks with intergroup competition and intragroup sharing

TL;DR

This paper introduces a novel mechanism for resource allocation in networks with intergroup competition and intragroup sharing, ensuring social welfare maximization, individual rationality, and feasibility off equilibrium.

Contribution

It proposes a new mechanism that achieves full Nash implementation, individual rationality, and feasibility off equilibrium using a radial projection allocation scheme.

Findings

Ensures social welfare maximization at all Nash equilibria.

Achieves feasibility of allocations even off equilibrium.

Provides a method for strong budget balance with minimal message space increase.

Abstract

We consider a network where strategic agents, who are contesting for allocation of resources, are divided into fixed groups. The network control protocol is such that within each group agents get to share the resource and across groups they contest for it. A prototypical example is the allocation of data rate on a network with multicast/multirate architecture. Compared to the unicast architecture (which is a special case), the multicast/multirate architecture can result in substantial bandwidth savings. However, design of a market mechanism in such a scenario requires dealing with both private and public good problems as opposed to just private goods in unicast. The mechanism proposed in this work ensures that social welfare maximizing allocation on such a network is realized at all Nash equilibria (NE) i.e., full implementation in NE. In addition it is individually rational, i.e., agents have an incentive to participate in the mechanism. The mechanism, which is constructed in a quasi-systematic way starting from the dual of the centralized problem, has a number of useful properties. Specifically, due to a novel allocation scheme, namely "radial projection", the proposed mechanism results in feasible allocation even off equilibrium. This is a practical necessity for any realistic mechanism since agents have to "learn" the NE through a dynamic process. Finally, it is shown how strong budget balance at equilibrium can be achieved with a minimal increase in message space as an add-on to a weakly budget balanced mechanism.