Varian, H., and MacKie-Mason, J. K. Generalized Vickrey auctions. Tech. rep., University of Michigan, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of prices after every round, conditions for withdrawing bids, etc. The rules are usually formulated such that the auction converges to some kind of optimality or game theoretic equilibrium. There are several CA protocols including AkBA [13] iBundle [2] and the Generalized Vickrey Auction [4]. For each of these protocols, the winner determination problem must be solved at every stage of the auction. Depending on the time between rounds and the number of bids, it may be impossible to use an optimal algorithm to solve the problem. An incremental algorithm fits nicely in such a situation ....

H. Varian and J.K. MacKie-Mason. "Generalized Vickrey Auctions". Technical report, University of Michigan, 1995.

.... This can be important when agents have hard valuation problems [15, 16] Furthermore, the auc tioneer only needs to generate explicit prices on a subset of bundles and often solves smaller winner determination problems than in the classic sealed bid bundle auction (the Generalized Vickrey Auction [23]) Also relevant, because the winner determination problem remains A P complete, is that the auction allows a tradeoff between performance and computation. Increasing the minimal bid increment can speedup termination and reduce the number of winner determination problems that the auctioneer must ....

Varian, H., and MacKie-Mason, J. K. Generalized Vickrey auctions. Tech. rep., University of Michigan, 1995.

....is said to weakly dominate all other strategies in the player s strategy set if, regardless of what he expects his opponents to do, this strategy always yields a payoff that is at least as good as any other of his strategies. 2. 1 Generalized Vickrey Auction The Generalized Vickrey Auction (GVA) [9] is a well known mechanism in economics which has the surprising and desirable property that each participant has a weakly dominant strategy to truthfully reveal his true values for all options. Informally, the GVA achieves this property, called incentive compatibility, by computing a payment for ....

H. Varian and J. MacKie-Mason. Generalized vickrey auctions. Technical report, Technical report, University of Michigan., 1995.

.... of this type; e.g. distributed scheduling (Wellman et al. 2000) supply chain (Walsh et al. 2000) course registration (Graves et al. 1993) airport scheduling (Rassenti et al. 1982) and air conditioning for an office building (Huberman Clearwater 1995) The Generalized Vickrey Auction (GVA) (Varian MacKie Mason 1995) has received wide attention in the literature, e.g. Wellman et al. 2000) and Hunsberger Grosz (2000) because of its incentive properties; truthful bidding is the optimal strategy for an agent in the GVA. The GVA solves the combinatorial allocation problem (CAP) Rothkopf et al. 1998; de Vries ....

Varian, H., and MacKie-Mason, J. K. 1995. Generalized Vickrey auctions. Technical report, University of Michigan.

....payments to sellers. man et al. 1998) Economic Properties. Vickrey payments are IR, because V (V Gammal ) by a simple feasibility argument, and also strategy proof. The proof of strategy proofness is omitted due to lack of space, but closely follows standard Vickrey proofs, for example see Varian MacKie Mason (1995). However, BB will often fail in an exchange, as we show in the next section. Vickrey Budget Balance: Success Failure Now that we have defined Vickrey payments in a combinatorial exchange, let us outline some cases in which BB is achieved and some cases in which BB fails. We will see that ....

Varian, H., and MacKie-Mason, J. K. 1995. Generalized Vickrey auctions. Tech. report, University of Michigan.

....of prices after every round, conditions for withdrawing bids, etc. The rules are usually formulated such that the auction converges to some kind of optimality or game theoretic equilibrium. There are several CA protocols including AkBA [13] iBundle [2] and the Generalized Vickrey Auction [4]. For each of these protocols, the winner determination problem must be solved at every stage of the auction. Depending on the time between rounds and the number of bids, it may be impossible to use an optimal algorithm to solve the problem. An incremental algorithm fits nicely in such a situation ....

H. Varian and J.K. MacKie-Mason. "Generalized Vickrey Auctions". Technical report, University of Michigan, 1995.

....of bids that can lead to arbitrarily bad outcomes when and the greedy algorithm is used. Agent Offer Divisible Agent 1 sell units at Yes Agent 2 buy 1 unit at Yes Agent 3 buy units at No 4.4.1. Generalized Vickrey Auction The well known Generalized Vickrey Auction (GVA) [20] extends the intuition gained from Vickrey s [39] original work,and results by Clarke [7] and Groves [16] in general allocation problems. The GVA is a direct revelation mechanism, but we include it here because in many cases agent types can be characterized in the form of offer correspondences. ....

Jeffrey K. MacKie-Mason and Hal R. Varian. Generalized Vickrey Auctions. Technical report, University of Michigan, July 1994.

....compute optimal resource allocations in competitive equilibrium. 1 We adjust prices retrospectively after an auction terminates towards prices that provide incentives for agents to bid truthfully. The goal is to compute the prices that agents would pay in the Generalized Vickrey Auction (GVA) (Varian MacKieMason 1995), a sealed bid auction for combinatorial resource allocation problems. The prices in the GVA provide strong truth revelation properties; truth revelation is a dominant strategy, optimal for a self interested agent for all strategies of other agents. When successful, in combination with proxy ....

Varian, H., and MacKie-Mason, J. K. 1995. Generalized Vickrey auctions. Tech. report, University of Michigan.

....theory (Papadimitriou Steiglitz 1982) that also suggests a useful methodology for the design and analysis of iterative auctions for other problems. iBundle has many computational advantages over the only other known optimal combinatorial auction, the Generalized Vickrey Auction (GVA) (Varian MacKie Mason 1995). As an iterative auction, agents can incrementally compute values for different bundles of items as prices change, and make new bids in response to bids from other agents. In comparison, the GVA is a sealed bid auction, in which agents first submit bids simultaneously, and then the auctioneer ....

Varian, H., and MacKie-Mason, J. K. 1995. Generalized Vickrey auctions. Technical report, University of Michigan.

....provided with closed form solutions to their local valuation problems, so 11 minimizing agent valuation work was not important. Problems associated with limited or costly computation in the auctioneer have received recent attention, in particular with respect to the generalized Vickrey auction [27]. Interesting recent work explores methods to introduce approximate solutions but retain the incentive compatibility property (such that truth telling remains optimal for self interested agents) 8, 9, 14] However, these methods still require that agents compute their values for all possible ....

Varian, H., and MacKie-Mason, J. K. 1995. Generalized Vickrey auctions. Technical report, University of Michigan.

....that the mechanism described is truthful and then discuss the complexity issues that render those auctions infeasible when k, the number of goods, is large. Generalized Vickrey Auctions (GVA s) appear to be part of the folklore of mechanism design. A general description of the GVA may be found in [5, 12]; we adopt a special case of it, one which does not allow for externalities. Given a vector D of declarations, the generalized Vickrey auction defines the allocation and payment policies as follows (notice that a Gamma1 (i) is the bundle allocated to i by allocation a, and that g i is defined ....

Jeffrey K. MacKie-Mason and Hal R. Varian. Generalized Vickrey auctions. Working paper, Un. of Michigan, July 1994.

....the mechanism described is truthful and then discuss the complexity issues that render those auctions infeasible when k, the number of goods, is large. Generalized Vickrey Auctions (GVAs) appear to be part of the folklore of mechanism design. A description of a more general type may be found in [9, 18]; we adopt a special case of it, one which does not allow for externalities. In a GVA, the allocation chosen maximizes the sum of the declared valuations of the bidders, each bidder receives a monetary amount that equals the sum of the declared valuations of all other bidders, and pays the ....

Jerey K. MacKie-Mason and Hal R. Varian. Generalized Vickrey auctions. Working paper, Un. of Michigan, July 1994.

....as long as each producer s bid represents a locally feasible combination of inputs and outputs. Moreover, this computes the allocation that optimizes value as reported 2 Although it is possible to define Generalized Vickrey payments that induce truth revelation as a dominant strategy [5], such a scheme will in general require subsidies in the supply chain context. The mechanism defined here is guaranteed to be budget balanced. It is an interesting open question whether alternative designs would have positive incentive properties. The fact that agent preferences have a very ....

J. K. MacKie-Mason and H. R. Varian. Generalized Vickrey auctions. Technical report, Dept. of Economics, Univ. of Michigan, July 1994.

....that is individually rational, ecient, and Bayesian incentive compatible for both buyers and sellers, that does not require outside subsidies. We next consider another relaxation of the theorems conditions, specifically the restriction to single unit bids. The Generalized Vickrey Auction (GVA) [8, 18] an extension of mechanisms developed by Vickrey [19] Clarke [2] and Groves [7] is incentive compatible for all bidders. 4 The GVA is a direct revelation mechanism [6] agents submit their reservation prices (equivalent to their utility functions under the independent private values model) as ....

Jerey K. MacKie-Mason and Hal R. Varian. Generalized Vickrey Auctions. Technical report, University of Michigan, July 1994.

....is individually rational, efficient, and Bayesian incentive compatible for both buyers and sellers, that does not require outside subsidies. We next consider another relaxation of the theorems conditions, specifically the restriction to single unit bids. The Generalized Vickrey Auction (GVA) [8, 18] an extension of mechanisms developed by Vickrey [19] Clarke [2] and Groves [7] is incentive compatible for all bidders. 4 The GVAisa direct revelation mechanism [6]# agents submit their reservation prices (equivalent to their utility functions under the independent private values model) ....

Jeffrey K. MacKie-Mason and Hal R. Varian. Generalized Vickrey Auctions. Technical report, UniversityofMichigan, July 1994.

....the design of incentive mechanisms is technically challenging, and is beyond the scope of this paper. We merely offer some observations on the possible shape of a good scheme. One important result originally due to Vickrey [31] and generalized to a much richer set of problems in Reference [30] lends some intuition for the problem. Vickrey proposed the second price auction: charge the winner of a single good auction the second highest bid. The bidder s announcement affects only when she wins, not how much she pays, and it can be shown that the bidder s dominant 2 The problem of ....

....preventing a cache from over reporting hits in a scheme in which servers pay for cache hits. Economics offers insight into the former problem ( bid shading ) but not the latter (fraud) 10 strategy is to bid her true valuation for the good being sold. The Varian MacKie Mason generalization [30] suggests that charging a server for each hit the valuation announced for the object that was most recently evicted might be incentive compatible. This would work if caching decisions were a one shot activity. Unfortunately it is not, and in this example, the server s bid would affect future ....

Hal Varian and Jeffrey K. MacKie-Mason. Generalized vickrey auctions. Technical report, Dept. of Economics, University of Michigan, July 1994.

....analysis characterizes the performance of multiple ascending single good auctions for the scheduling problem, and the prospects for combinatorial auctions. Neither is guaranteed to produce optimal solutions to all scheduling problems. Another mechanism, the Generalized Vickrey Auction (GVA) [35], does find efficient schedules for all of our problems. Although the main results are not new, we briefly present the GVA because it takes an important place in our spectrum of mechanisms for scheduling. We also provide a new result stronger properties for the GVA in a particular class of ....

....for agents other than j at the solution f . The residual payment P j could be any function of other agents reported valuations. However, we restrict attention here to the formula (11) Given this allocation rule, truthful bidding of the utility function, v j = v j , is a dominant strategy [35]. The GVA computes the optimal allocation based on the bids, and since all bids are truthful, the allocation is globally optimal. Example 8.1. Consider the setup of Example 7.2 (Table 6) If the agents truthfully report their value functions, the auction mechanism finds an optimal agents have ....

Hal R. Varian and Jeffrey K. MacKie-Mason. Generalized Vickrey auctions. Technical report, Department of Economics, University of Michigan, June 1994.

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Varian, H., and MacKie-Mason, J. K. Generalized Vickrey auctions. Tech. rep., University of Michigan, 1995.

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Varian, H., and MacKie-Mason, J. K. Generalized Vickrey auctions. Tech. rep., University of Michigan, 1995.

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H Varian and J K MacKie-Mason. Generalized Vickrey auctions. Technical report, University of Michigan, 1995.

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Varian, H., MacKie-Mason, J.K.: Generalized Vickrey auctions. Technical report, Dept. of Economics, University of Michigan (1994)

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H Varian and J K MacKie-Mason. Generalized Vickrey auctions. Technical report, University of Michigan, 1995.

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Varian, H., MacKie-Mason, J.K.: Generalized Vickrey auctions. Technical report, Dept. of Economics, University of Michigan (1994)

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Hal Varian and Jeffrey K. MacKie-Mason. Generalized Vickrey auctions. Technical report, Dept. of Economics, University of Michigan, July 1994.

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Varian, H., and MacKie-Mason, J. K. 1995. Generalized Vickrey auctions. Technical report, University of Michigan.

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