Vickrey-Clarke-Groves Payments Research Articles

Electronic service matching: Failure of incentive compatibility in Vickrey auctions

We consider pricing schemes for matching customers and providers on double-sided markets for electronic services. While existing second-best solutions are incentive compatible, the associated payment functions are difficult to implement in real-world settings. Based on the Vickrey–Clarke–Groves (VCG) and the k-pricing mechanism, we propose two straightforward payment schemes that offer a practical alternative to the second-best solution. Our experiments provide evidence that the VCG payments fail to implement incentive compatibility. This failure is due to the interdependency of the participants’ utilities.

Strategy-Proof Pricing for Cloud Service Composition

The on-demand provisions of cloud services create a service market, where users can dynamically select services based on such attractive criteria as price and quality. An intuitive model of a service market is a reverse auction. In the first price auction, however, a service that is cheaper and provides better quality is not necessarily selected. This causes undesirable outcomes both for users and service providers. A possible solution is the Vickrey-Clarke-Groves (VCG) mechanism, where the dominant strategy for a service provider is to report the true cost of his service. In spite of this desirable property, implementing the VCG mechanism for service composition suffers from computational cost. The calculation of payments to service providers based on the VCG mechanism requires iterative service selection, even though each service selection can be NP-hard. Approximation algorithms cannot be applied because approximate solutions do not assure the desirable property of the VCG mechanism. Thus, we model VCG payments for service markets and propose a dynamic programming (DP)-based algorithm for service selection and VCG payment calculation. Our proposed algorithm solves service selection in quasi-polynomial time and gives an exact solution. Moreover, we extend it and focus on the iterative service selection process for VCG payment calculation to improve its performance. Our series of experiments show that our proposed algorithm solves practical scale service composition.

Implementation with interdependent valuations

It is well known that the ability of the Vickrey–Clarke–Groves (VCG) mechanism to implement efficient outcomes for private value choice problems does not extend to interdependent value problems. When an agent’s type affects other agents’ utilities, it may not be incentive compatible for him to truthfully reveal his type when faced with VCG payments. We show that when agents are informationally small, there exist small modifications to the VCG transfers that restore incentive compatibility. We further show that truthful revelation is an approximate ex post equilibrium. Last, we show that in replicated settings, aggregate payments sufficient to induce truthful revelation go to zero.

Better redistribution with inefficient allocation in multi-unit auctions

For the problem of allocating one or more items among a group of competing agents, the Vickrey–Clarke–Groves (VCG) mechanism is strategy-proof and efficient. However, the VCG mechanism is not strongly budget balanced: in general, value flows out of the system of agents in the form of VCG payments, which reduces the agents' utilities. In many settings, the objective is to maximize the sum of the agents' utilities (taking payments into account). For this purpose, several VCG redistribution mechanisms have been proposed that redistribute a large fraction of the VCG payments back to the agents, in a way that maintains strategy-proofness and the non-deficit property. Unfortunately, sometimes even the best VCG redistribution mechanism fails to redistribute a substantial fraction of the VCG payments. This results in a low total utility for the agents, even though the items are allocated efficiently. In this paper, we study strategy-proof allocation mechanisms that do not always allocate the items efficiently. It turns out that by allocating inefficiently, more payment can sometimes be redistributed, so that the net effect is an increase in the sum of the agents' utilities.Our objective is to design mechanisms that are competitive against the first-best mechanism in terms of the agents' total utility. We first study multi-unit auctions with unit demand. We characterize the family of linear allocation mechanisms. We propose an optimization technique for simultaneously finding a linear allocation mechanism and a payment redistribution rule, which together are optimal. With the help of this technique, we also analytically characterize several competitive mechanisms, which are based on burning units and partitioning the agents into groups. Finally, we extend the definition of linear allocation mechanisms and the optimization technique to general multi-unit auctions.

Vickrey-reserve auctions and an equilibrium equivalence

This paper characterizes the class of combinatorial auctions that have a particular form of Nash equilibrium. We refer to this class as Vickrey-reserve auctions. In such auctions, bidders pay at least their Vickrey–Clarke–Groves payments. A specific strategy profile studied by Bernheim and Whinston [Bernheim, B.D., Whinston, M., 1986. Menu auctions, resource allocation and economic influence. Quarterly Journal of Economics 101, 1–31] is a Nash equilibrium of every Vickrey-reserve auction even in the presence of complementarities, and it implements an outcome in the bidder-optimal core.

VCG Redistribution with Gross Substitutes

For the problem of allocating resources among multiple strategic agents, the well-known Vickrey-Clarke-Groves (VCG) mechanism is efficient, strategy-proof, and it never incurs a deficit. However, in general, under the VCG mechanism, payments flow out of the system of agents, which reduces the agents' utilities. VCG redistribution mechanisms aim to return as much of the VCG payments as possible back to the agents, without affecting the desirable properties of the VCG mechanism. Most previous research on VCG redistribution mechanisms has focused on settings with homogeneous items and/or settings with unit-demand agents. In this paper, we study VCG redistribution mechanisms in the more general setting of combinatorial auctions. We show that when the gross substitutes condition holds, we are able to design mechanisms that guarantee to redistribute a large fraction of the VCG payments.

Sequential Pivotal Mechanisms for Public Project Problems

It is well-known that for several natural decision problems no budget balanced Groves mechanisms exist. This has motivated recent research on designing variants of feasible Groves mechanisms (termed as ‘redistribution of VCG (Vickrey-Clarke-Groves) payments)' that generate reduced deficit. With this in mind, we study sequential mechanisms and consider optimal strategies that could reduce the deficit resulting under the simultaneous mechanism. We show that such strategies exist for the sequential pivotal mechanism of the well-known public project problem. We also exhibit an optimal strategy with the property that a maximal social welfare is generated when each player follows it. Finally, we show that these strategies can be achieved by an implementation in Nash equilibrium.

Worst-case optimal redistribution of VCG payments in multi-unit auctions

For allocation problems with one or more items, the well-known Vickrey–Clarke–Groves (VCG) mechanism (aka Clarke mechanism, Generalized Vickrey Auction) is efficient, strategy-proof, individually rational, and does not incur a deficit. However, it is not (strongly) budget balanced: generally, the agents' payments will sum to more than 0. We study mechanisms that redistribute some of the VCG payments back to the agents, while maintaining the desirable properties of the VCG mechanism. Our objective is to come as close to budget balance as possible in the worst case. For auctions with multiple indistinguishable units in which marginal values are nonincreasing, we derive a mechanism that is optimal in this sense. We also derive an optimal mechanism for the case where we drop the non-deficit requirement. Finally, we show that if marginal values are not required to be nonincreasing, then the original VCG mechanism is worst-case optimal.

Incentive-compatible, budget-balanced, yet highly efficient auctions for supply chain formation

We address the mechanism design problem of supply chain formation—the problem of negotiation mechanisms to coordinate the buying and selling of goods in multiple markets across a supply chain. Because effective negotiation strategies can be difficult to design for supply chains, we focus on incentive-compatible (IC) auctions, in which the agents' dominant strategy is to simply report their private information truthfully. Unfortunately, with two-sided negotiation, characteristic of supply chains, it is impossible to simultaneously achieve perfect efficiency, budget balance, and individual rationality with incentive compatibility. To resolve this problem, we introduce auctions that explicitly discard profitable trades, thus giving up perfect efficiency to maintain budget balance, incentive compatibility, and individual rationality. We use a novel payment rule based on Vickrey–Clarke–Groves payments, but adapted to our allocation rule. The first auction we present is incentive compatible when each agent desires only a single bundle of goods; the auction correctly knows all agents' bundles of interest, but the monetary valuations are private to the agents. We introduce extensions to maintain incentive compatibility when the auction does not know the agents' bundles of interest. We establish a good worst case bound on efficiency when the bundles of interest are known, which also applies in some cases when the bundles are not known. Our auctions produce higher efficiency for a broader class of supply chains than any other incentive-compatible, individually rational (IR), and budget-balanced (BB) auction we are aware of.