VCG-Kelly Mechanisms for Allocation of Divisible Goods: Adapting VCG Mechanisms to One-Dimensional Signals

Abstract

Abstract-The VCG-Kelly mechanism is proposed, which is obtained by composing the communication efficient, onedimensional signaling idea of Kelly with the VCG mechanism, providing efficient allocation for strategic buyers at Nash equilibrium points. It is shown that the revenue to the seller can be maximized or minimized using a particular one-dimensional family of surrogate valuation functions.

An Efficient Game Form for Unicast Service Provisioning

“…The mechanisms/game forms proposed in [26], [27], [37], [38] induce games that have multiple NE; these mechanisms are not budget-balanced even at equilibrium, and the allocations corresponding to the Nash equilibria are not always globally optimal ( that is these mechanisms do not implement in Nash equilibria the solution of the centralized unicast service provisioning problem). Our mechanism is not of the VCG-type, thus, it is philosophically different from those of [25]- [27], [31], [37], [38].…”

“…The game forms/mechanisms proposed in [31] and [25] induce games that establish the existence of a unique Nash equilibrium at which the allocation is globally optimal under some conditions; but these mechanisms are not budget-balanced even at equilibrium. The mechanisms/game forms proposed in [26], [27], [37], [38] induce games that have multiple NE; these mechanisms are not budget-balanced even at equilibrium, and the allocations corresponding to the Nash equilibria are not always globally optimal ( that is these mechanisms do not implement in Nash equilibria the solution of the centralized unicast service provisioning problem).…”

“…Most of the previous work on the unicast service provisioning problem in networks with general topology is based on Vickrey-Clark-Groves(VCG)-type mechanisms, [25]- [27], [31], [37]- [41]. The game forms/mechanisms proposed in [31] and [25] induce games that establish the existence of a unique Nash equilibrium at which the allocation is globally optimal under some conditions; but these mechanisms are not budget-balanced even at equilibrium.…”

“…they are not price-takers, they do not necessarily obey the rules of the mechanism but have to be induced to follow the rules). Within the context of wired networks, decentralized resource allocation mechanisms have been proposed and analyzed in [6], [8], [23]- [30] and [31]. A more detailed discussion of these references and comparison with the results of this paper will be presented in section I-C.…”

Leveraging Downlink for Optimal Uplink Rate Allocation: An Incentive Compatible Approach

“…However, when considering utility functions that do not have a homogenous component known to the base, the users need to report an entire function rather than a single value. It would be interesting to examine this work in the context of scalar VCG mechanisms, which implement problems in Nash equilibrium (rather than dominant strategies) but only require users to report a single parameter value (see [12], [13]). …”