We consider a network where strategic agents, who are contesting forallocation of resources, are divided into fixed groups. The network controlprotocol is such that within each group agents get to share the resource andacross groups they contest for it. A prototypical example is the allocation ofdata rate on a network with multicast/multirate architecture. Compared to theunicast architecture (which is a special case), the multicast/multiratearchitecture can result in substantial bandwidth savings. However, design of amarket mechanism in such a scenario requires dealing with both private andpublic good problems as opposed to just private goods in unicast. The mechanism proposed in this work ensures that social welfare maximizingallocation on such a network is realized at all Nash equilibria (NE) i.e., fullimplementation in NE. In addition it is individually rational, i.e., agentshave an incentive to participate in the mechanism. The mechanism, which isconstructed in a quasi-systematic way starting from the dual of the centralizedproblem, has a number of useful properties. Specifically, due to a novelallocation scheme, namely "radial projection", the proposed mechanism resultsin feasible allocation even off equilibrium. This is a practical necessity forany realistic mechanism since agents have to "learn" the NE through a dynamicprocess. Finally, it is shown how strong budget balance at equilibrium can beachieved with a minimal increase in message space as an add-on to a weaklybudget balanced mechanism.
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