W. E. Walsh, M. P. Wellman, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Proc 18th International Conference on Distributed Computing Systems (ICDCS), pages 612--621, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....totally to a single user. Even if an agent chooses to purchase an entire resource, we expect at some point that the resource will be partitioned, and it is that exchange that we are interested in analyzing. There has been a lot of research in analyzing combinatorial auctions for multi unit goods [7, 21, 26]. However, these methods are inappropriate for the goods we are considering because network and computational resources are rarely partitioned into well defined bundles that can be bid for in discrete quantities. Thus, we consider divisible or share auctions as a market mechanism. Though network ....

Wellman, M., W. Walsh, P. Wurman, and J. Mackie-Mason: 2001, `Auction protocols for decentralized scheduling'. Games and Economic Behavior 35, 271--303.

....Categories Subject Descriptors Intelligent agents, Multiagent systems. General Terms Economics. Keywords Bidding and bargaining agents. Electronic commerce market. 1. INTRODUCTION Recently, auction mechanisms have become a fundamental way of automating negotiation among agents [4,9,10,12]. The widespread research on automated auctions deals mostly with models in which price is the unique strategic dimension. However, in many situations, it is necessary to conduct negotiations on multiple attributes of a deal. For example, in task allocation, the attributes of a deal include ....

....(ascending) auction protocol, and we prove that, given some assumptions, they all converge to the same result. We also discuss which of the above variations is preferred for different types of environments. 2. RELATED WORK An auction is an efficient protocol for reaching agreements among agents [4,9,10,12]. There are several types of auctions which are used, including the English auction, first price sealed bid auction, second price sealed bid (Vickery) auction, and the Dutch auction [10] In this paper, we consider the first price sealed bid and the English auction. In the first price auction, ....

Walsh, W.E., Wellman, M. P., Wurman, P.R. and MacKie-Mason, J. K. Auction protocols for decentralized scheduling. In Proc. 18th International Conference on Distributed Computing Systems, 1998.

....will do just that. Thus, for example, congestion over some communication link in a network can be handled by auctioning the bandwidth of the link. This type of idea has indeed been applied in various forms both for low level resources like network bandwidth [17, 32, 30, 13] or computing resources [36, 38, 37, 14, 25, 27], and for many e commerce systems [2, 3, 1, 5, 4] Several researchers have considered the e ect of various computational considerations on the design of auctions: online behavior [16, 6] unbounded supply [8, 11, 6] computational complexity in combinatorial auctions [35, 18, 24, 31, 40] timing ....

W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), 1998.

....among tasks. Auctions lie in the core of these resource allocation systems. To allow bundled preferences in resource allocation problems could enhance resource utilization e# ciency in many real world domains, however, it increases computational complexity to find optimal solutions. Walsh et al. [12] outline the fundamental choices for auction based resource allocation schemes: a) Vickery auctions, b) combinatorial auctions, and (c) single resource auctions. In Vickery auctions, every resource requester has an incentive to report his true requirements to a centralized auction mechanism ....

W. Walsh, M. Wellman, P. Wurman, and J. MacKie-Mason. Auction protocols for decentralized scheduling. In Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998.

....The problem is formulated with mixed integer programming, with many domain specific optimizations. Bids are expressed by specifying a price to enter a line and a time window. The bidding language, which is similar to what we use in MAGNET, avoids use of discrete time slots. Time slots are used in [13], where a protocol for decentralized scheduling is proposed. The study is limited to scheduling a single resource. MAGNET agents deal with multiple resources. Walsh et al. [11] propose a protocol for combinatorial auctions for supply chain formation, using a game theoretical perspective. They allow ....

M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

....The problem is formulated with mixed integer programming, with many domain specific optimizations. Bids are expressed by specifying a price to enter a line and a time window. The bidding language, which is similar to what we use in MAGNET, avoids use of discrete time slots. Time slots are used in [25], where a protocol for decentralized scheduling is proposed. The study is limited to scheduling a single resource. MAGNET agents deal with multiple resources. Most work in supply chain management is limited to hierarchical modeling of the decision making process, which is inadequate for ....

M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

....In [25] a method is proposed to auction a shared track line for train scheduling. The problem is formulated with mixed integer programming, with many domain specific optimizations. Bids are expressed by specifying a price to enter a line and a time window. Time slots are used in [41], where a protocol for decentralized scheduling is proposed. The study is limited to scheduling a single resource. MAGNET agents deal with multiple resources. Most work in supply chain management is limited to hierarchical modeling of the decision making process, which is inadequate for ....

Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Je#rey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

....across items, including both complements and substitutes. To appear, the Stanford Institute for Theoretical Economics (SITE) 2002 Summer Work shop: The Economics of the Internet, June 25 June 29, 2002 The CAP has many interesting applications: in logistics [35, 54] in job shop scheduling [57]; for airport slot allocation [51] bandwidth allocation [24] multiagent planning [30] class registration [25] and resource allocation [34] Combi natorial auctions allow agents to bid for bundles of items, and express complex preferences that may include both synergies and complements. This ....

Michael P Wellman, William E Walsh, Peter R Wurman, and Jeff K MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271-303, 2001.

....mechanism. The rationale for this is that a market mechanism is a distributed coordination mechanism which facilitates efficient solutions with low communication needs. In particular, only prices for specific goods are communicated, keeping all other information private to the market participants [Wellman et al. 2001] . Additionally, a market facilitates a dynamic environment, where the market participants take actions according to their current (dynamically changing) situation based upon private information and preferences. In this market, the coordination objects are modelled as autonomous, self interested ....

....as maximising their utilisation or, equivalently, minimising idle time. To reach this goal, cost functions can also be articulated for the resource agents. These cost functions represent the reserve prices (i.e. the price that will be charged for an empty slot) for the possible appointments [Wellman et al. 2001] . Through this, priorities between different resources can be established that allow penalisation of undesired appointment times (e.g. evening shift or overtime hours) Here, the basis for the resource agents cost functions comes from cost accounting. However, for inter agent utility comparison ....

M. Wellman, W. Walsh, P. Wurman, and J. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271-- 303, 2001.

....auction abstraction, XML based implementation and wider applicability. 1. Introduction Auction has been proposed to be used to build price determination system as the core of market based resource allocation in various open agent based applications, just as done in the literatures [Clearwater1996, Mullen1996, Bredin1998, Cliff1998, Wellman1998, etc]. However, openness and dynamism of open agent system implies that it is impossible to fix the market configuration for resource allocation in advance in such type of system. On one hand, openness implies the variety of agent participants which are on behalf of different owners. Therefore, it is ....

Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jeffrey K. MacKie-Mason. Auction protocols for decentralized scheduling. Technical report, University of Michigan, July 1998. http://citeseer.nj.nec.com/article/wellman98auction.html

....make and re evaluate their decisions as to which other agents they should interact with. These interactions might include the buying and selling of goods, negotiation over a set of tasks to perform, or cooperation to achieve a joint goal. A great deal of research, including auction theory [13], coalition formation [11] and team formation [12] has focused on how a group of agents can make these sorts of decisions. Two problems typically arise in these sorts of approaches: scaling to domains with large numbers of agents, and dealing with the fact that the composition of the agent ....

M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35(1/2):271--303, 2001.

....and canceling bids, and policies for hiding information from other users. They proposed a standardized format for describing the components of each speci c auction. Researchers have also investigated the application of auction algorithms to non nancial settings, such as scheduling problems [ Wellman et al. 2001 ] management of resources in wide area networks [ Chen et al. 2001 ] and co ordination of services performed by di erent companies [ Preist et al. 2001 ] The reader may nd a detailed survey of combinatorial auctions in the review article by de Vries and Vohra [2001] Although the ....

....agents for bidding in the Michigan AuctionBot; they used regression and learning techniques to predict the behavior of other bidders. Later, Hu et al. 2000] designed three types of agents and showed that their relative performance depended on the strategies of other auction participants. Hu and Wellman [2001] developed an agent that learned the behavior of its competitors and adjusted its strategy accordingly. Wurman [2001] considered a problem of building general purpose agents that simultaneously bid in multiple auctions. Parkes built a fast system for combinatorial auctions, but it worked only for ....

Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jerey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271-303, 2001.

....random strategy (in terms of bid) may dominate the queue if the service speed is too low. But when the service speed is very high, a regression strategy is dominant. Two prospective applications of this model are agent based social simulation and decentralized scheduling for resource allocation [10] for open multi agent systems. In the context of social simulation, we study the equilibrium of bidding bribing strategy used by customers in a queue. Customers (agents) could adopt illegitimate way (bribe) in the dirty competition for the service. Indeed, agents will act based upon normative ....

....upon normative rational behavior (in terms of von NeumannMorgenstern Expected Utility) in their decision makings [5, 11] However, if we regard the bribe as a legitimate action, the system becomes a closed bid auction for buying a position in a queue. This approach becomes decentralized scheduling [10], for resource allocation such as queuing for remote method object invocation, printing, and so on in a multi agent system. 2. THE SIMULATION 2.1 The M D 1 queue There is one queue with one server at the end of it. Customers come to the queue according to a Poisson process with a mean rate of m ....

Wellman, M.P., Walsh, W.E, Wurman,P.R., Mac-Kie,J.K. Auction protocols for decentralized scheduling. In Proceedings of the 18 th International conference in Distributed Computing Systems, 1998.

....will do just that. Thus, for example, congestion over some communication link in a network can be handled by auctioning the bandwidth of the link. This type of idea has indeed been applied in various forms both for low level resources like network bandwidth [15, 29, 27, 12] or computing resources [33, 35, 34, 13, 22, 24], and for many e commerce systems [2, 3, 1, 5, 4] Email: liad,noam cs.huji.ac.il. Supported by grants from the Israeli Academy of Sciences. Several researchers have considered the e ect of various computational considerations on the design of auctions: online behavior [14, 6] unbounded ....

W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), 1998.

..... 5.00. demonstration of the concept of autonomous agents working together without outside control. Moreover the simplicity and robustness of agent auction algorithms make them well suited to a variety of applications; e commerce naturally, but also more general resource allocation problems [9] [10]. However while an auction demonstrates distributed determination of prices, auctions are most often implemented using a central auctioneer and thus overall are not fully distributed systems. This central auctioneer distributes global information about current prices and deals made among traders. ....

Wellman, M., Walsh, E., Wurman, P., MacKie-Mason, J.: Auction Protocols for Decentralized Scheduling. Games and Economic Behavior 35:1-2 (2001) 271--303

....usercustomization, and self interest. A subfield of this general direction of research takes a game theoretic analysis of agents goals, and in particular uses notions from mechanism design [21] 22] 7] A related subfield of Distributed AI, sometimes termed market based computation [26] [8] 25] aims to leverage the notions of free markets in order to solve distributed problems. These subfields of DAI are related to our work. Communication Networks In recent years researchers in the field of network design adopted a game theoretic approach (See e.g. 11] In particular ....

W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998.

....and multiagent systems (MASs) Often agents need access to specific resources to pursue their objectives, but the needs of one agent may conflict with those of another. A number of market based approaches have been proposed as a means to deal with resource allocation and related problems in MASs [6, 20, 22]. Of particular interest are auction mechanisms, where each agent bids for a resource according to some protocol, and the allocation and price for the resource are determined by specific rules [14] Auctions have a number of desirable properties as a means for coordinating activities, including ....

.... protocol, and the allocation and price for the resource are determined by specific rules [14] Auctions have a number of desirable properties as a means for coordinating activities, including minimizing the communication between agents and, in some cases, guaranteeing Pareto efficient outcomes [14, 22]. In order to effectively make use of market mechanisms, an agent must be aware of the resources it needs, their value, and how best to obtain them. In sequential decision making under uncertainty, an agent will typically consider a number of potential courses of action and settle on one with ....

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M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. (manuscript), 1998.

....for surveys) The study of auctions has recently been facilitated by the famous FCC auction [3, 18, 21, 20] as well as by the huge popularity of them as an electronic commerce tool. As a result, in the recent years, there is an explosion in papers by AI researchers dealing with auctions (see [37, 5, 26, 1, 44, 12, 46, 32, 31, 30] for some, not necessarily completely representative, pointers) A central issue in the related line of research is that of winner determination, the selection of agents bids that will maximize the social surplus. Many of the algorithms that have been designed assume that agents bids reflect ....

M.P. Wellman, P.R. Wurman, W.E. Walsh, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

....studied cooperation and competition among software agents. Many of these papers use ideas from mechanism design to analyze strategies and responses of these agents in negotiations and resource allocations [14, 15, 18] Others use market based ideas to solve distributed computational problems [20, 21]. Researchers in networking have proposed game theoretic techniques to deal with congestion control in the Internet [5, 7, 13, 17] 2 Our paper is motivated by the algorithmic mechanism design paper of Nisan and Ronen [12] They investigate computational complexity and algorithmic issues in ....

....for communication, computation, and commerce, there is an increased need to design efficient protocols that motivate self interested agents 9 to cooperate. Example applications include resource allocation in computational grids [22] marketbased protocols for scheduling or task allocation [20, 21], and congestion control in the Internet [5, 7, 10, 17] One of the most celebrated results in the field of mechanism design is the Vickrey ClarkeGroves protocol, which uses a payment scheme to motivate selfish agents to bid truthfully. In this paper, we focused on the algorithmic aspect of ....

W. E. Walsh, M. P. Wellman, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proc. 18th International Conference on Distributed Computing Systems, 1998.

.... apply theoretical mechanisms to real systems (as pointed out in [12] Moreover, auction theorists usually make assumptions that are not applicable here, such as the existence of a currency different from the resources themselves, a distinction between producers and consumers, and global pricing [27]. Other investigators have looked at efficient clearing , or the best way to assign resources to bidders so as to maximize utility across the system. In this scenario, methods such as integer programming [4] can be used to solve the auction, but this assumes all resources and bids are known at ....

W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proc. ICDCS, May 1998.

....various types. This development occurred in many settings: in government privatizations and rights allocation (most famously, the FCC spectrum rights auctions) 17, 14] in the many Internet auction sites [1, 2] in the usage of techniques from auction theory for computational resource allocation [28, 9, 19]; in computerized Institute of Computer Science, Hebrew U. Jerusalem. This research was supported by grants from the Israeli ministry of Science and the Israeli academy of sciences. 1 agent systems [25, 22] and in current trends in business to business electronic commerce [21] With this new ....

....supporting this. Our first observation is that the linear program is intimately related to the question of whether prices can be attached to individual items in the auction. Such prices for individual items are certainly desirable and it is known that for some combinatorial auctions they exist [28, 29, 4] and in other cases they can not be defined in any reasonable manner [16, 13, 28, 29] When the bids are presented, as this paper assumes, in the OR language, we completely characterize the cases where individual item prices exist: ffl A combinatorial auction admits individual item prices if and ....

[Article contains additional citation context not shown here]

W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998.

No context found.

Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jeffrey K. MacKieMason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

No context found.

Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jeffrey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

....are patently important in the FCC spectrum allocation problem, yet separate markets were chosen over a combinatorial auction despite its high stakes and the authority of a single entity to set the mechanism. 2. SCHEDULING PROBLEM DEFINITION In the simple scheduling problem we consider [30], there are M units (called time slots) of a single schedulable resource, indexed 1, M . Each of N agents has a single job that can be accomplished using the resource. Agent j s job requires # j time slots to complete, and by accomplishing this job it obtains some value depending on the ....

....commodity. For this problem, Peters and Severinov [22] showed that straightforward bidding is a perfect Bayesian equilibrium. Up to a discretization error, the allocations from simultaneous ascending bid auctions are e#cient when agents follow straightforward bidding. We have shown elsewhere [30] that the final price vector will di#er from the minimum unique equilibrium price by at most ##, where # min(M,N ) The value of the allocation, defined to be the sum of the bidder surpluses, will di#er from the optimal by at most ##(1 #) A similar bound was established by Bertsekas [1] in a ....

[Article contains additional citation context not shown here]

M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

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W. E. Walsh, M. P. Wellman, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Proc 18th International Conference on Distributed Computing Systems (ICDCS), pages 612--621, 1998.

No context found.

Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jerey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271-303, 2001.

No context found.

Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jeffrey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

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Wellman, M.P., Walsh, W.E., Wurmann, P.R., MacKie-Mason, J.K.: Auction protocols for decentralized scheduling. In: 18th International Conference on Distributed Computing Systems, Amsterdam. (1999) Revised and extended version of "Some economics of market-based distributed scheduling".

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WELLMAN, M. P., WALSH, W. E., WURMAN, P. R., AND MACKIE-MASON, J. K. Auction protocols for decentralized scheduling. Games and Economic Behavior 35 (2001), 271--303.

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Wellman, M.; Walsh, W.; Wurman, P. and MacKie-Mason, J. (2001). Auction Protocols for Decentralized Scheduling, In: Games and Economic Behavior.

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M.P.Wellman,W.E.Walsh,P.R.Wurman,andJ.K.MacKieMason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

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Michael Wellman, William Walsh, Peter Wurman, and Je#rey MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271-- 303, 2001.

No context found.

Michael P Wellman, William E Walsh, Peter R Wurman, and Jeff K MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

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M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

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M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKieMason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001. 8

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MP Wellman, WE Walsh, PR Wurman, and JK MacKie-Mason. Auction Protocols for Decentralized Scheduling. Games and Economic Behavior 35:271-303, 2001.

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W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), 1998.

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W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The 44 Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998. 45

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W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998.

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M P Wellman, W E Walsh, P R Wurman, and J K MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 1999. To appear.

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M. P. Wellman, W. E. Walsh, P. R. Wurman, and J. K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

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W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998.

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Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jeffrey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001. http://ai.eecs.umich.edu/ people/wellman/pubs/geb01wwwmm.html.

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Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jerey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271-303, 2001.

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Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jerey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271-303, 2001.

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W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), 1998.

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Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jeffrey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001. http://ai.eecs.umich.edu/ people/wellman/pubs/geb01wwwmm.html.

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W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998. 36

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Michael P. Wellman, William E. Walsh, Peter R. Wurman, and Jeffrey K. MacKie-Mason. Auction protocols for decentralized scheduling. Games and Economic Behavior, 35:271--303, 2001.

No context found.

W.E. Walsh, M.P. Wellman, P.R. Wurman, and J.K. MacKie-Mason. Auction protocols for decentralized scheduling. In Proceedings of The 44 Eighteenth International Conference on Distributed Computing Systems (ICDCS-98), Amsterdam, The Netherlands, 1998. 45

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