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An Experimental Analysis of a Combinatorial Market Mechanism for Bandwidth Trading

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An Experimental Analysis of a Combinatorial Market Mechanism for Bandwidth Trading Charis Kaskiris School of Information University of California Berkeley, California
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An Experimental Analysis of a Combinatorial Market Mechanism for Bandwidth Trading Charis Kaskiris School of Information University of California Berkeley, California Yusuf Bütün EECS University of California Berkeley, California Rahul Jain EECS University of California Berkeley, CA Abstract We conduct a human experimental and computational simulation investigation of the efficiency properties of a combinatorial double-sided sealed-bid uniform price auction mechanism for allocation of bandwidth over combinations of links to form routes. Two different market structures are used: the benchmark case with valuations over every route combination and the alternative case with buyer valuations only on specific combinations and restricted supply of links. Experimental results show that the mechanism achieves an average of 78% and 87% efficiency in the benchmark and alternative cases respectively. Implementing a naive-bidding strategy in an iterative version of the benchmark case improves efficiency, with bigger improvements as the number of participants increases. I. INTRODUCTION Advances in information technology and cost reduction in network connectivity have created the opportunity for electronic market transactions between businesses and consumers to interact with and between each other. This has let to the creation of electronic markets to provide more efficient, cheaper and timely services. The main mechanisms for information submission, rules of assigning allocation, and pricing based on participant submitted information are described through auctions. [1]. In the last decade there has also been a shift from static to dynamic Internet applications which require dedicated quality of service (QoS) guarantees which requires that Internet Service Providers (ISPs) provision their network in a more efficient manner. Given the current bilateral negotiation format of securing interconnection contracts, ISPs hedge the risk of under- provisioning by over-provisioning which leads to low network utilization and low return on investment. The promise of liquid bandwidth trading markets has been heralded as a solution towards dynamic fluid bandwidth allocation. We study the interaction between internet service providers who lease bandwidth from owners of individual links to form desired routes through a combinatorial auction mechanism. These bandwidth markets have been a rather polarized issue since their inception in the late nineties, predominately by the involvement of Enron. These dynamic markets were setup to deal with the inefficient bilateral negotiations used in industry. Market dynamics, technical difficulties, and the collapse of Enron have brought these markets to an end [3]. Ferreira, Mindel and McKnight [6] identified two main factors that hamper the implementation of dynamic and fluid spot markets for bandwidth trading: the excessive time needed to disseminate new routing information caused by the bilateral nature of contracting for routes, and the balance-loading issues once the carriers get interconnected. The inefficiency of bilateral contracting is due to the exposure effect [12] caused by the inability of forming attractive routes from individually leased links. This is a general problem with markets with complementarities. Combinatorial auctions have been proposed to alleviate the exposure effect [14] and theoretically explored as mechanisms for bandwidth allocation [7] [11] [8]. The latter proposes a double-sided combinatorial sealed-bid uniform price mechanism for bandwidth trading whose properties we experimentally and computationally explore in this paper. The rest of the paper is organized as follows. In section II we present a brief discussion of bandwidth trading, combinatorial auctions, and experimental economic methods in evaluating these auctions. In section III we present the c-sebida combinatorial auction algorithm and then present an experimental investigation in section IV. We further explore simulation-based methods for assessing the overall efficiency of the mechanism in section V. We then conclude. II. BANDWIDTH MARKETS, COMBINATORIAL AUCTIONS, AND ECONOMIC EXPERIMENTS In the late 1990s backbone ISPs such as AT&T, Sprint, Level 3, WorldCom, and Qwest have invested heavily in expanding their fibre capacity and national interconnection coverage. These investments were made in anticipation of exponential growth rate in bandwidth demand. Bandwidth reflects transmission capacity over network links. A route consisting of links represents a backbone network connection between two metropolitan areas, eg. New York and London. By 2002, the abundance of bandwidth let to a dramatic drop in prices which prompted the idea that bandwidth could be traded as a commodity. Bandwidth s particular characteristics make its trading different from other commodities like electricity. Bandwidth is a transmission medium and hence it is nonstorable and non-transportable, which introduces rigidities in the supply conditions which are best handled by flexible market mechanisms. Bandwidth markets were pioneered by Enron during the late 1990s, which provided pooling points for switching and interconnecting. Williams Communications and RateExchange followed suit with their own bandwidth trading markets. Distress in the telecommunication sector and supply-demand imbalance, coupled with technical feasibility problems and the collapse of Enron, let to the demise of bandwidth trading exchanges 1. The development of efficient path switching techniques, such as Multi Protocol Label Switching (MPLS) which force network packets to follow particular routes which are explicitly chosen at or before the packet enters the network, provide a technical solution to route selection with QoS guarantees. Efficient utilization of MPLS would require economic mechanisms that deal effectively with the inherent complementarity between links to form preselected routes. Combinatorial auctions are mechanisms which can accommodate such preferences and we further explore them. A. Combinatorial Auctions In many market environments and auction settings bidders have complex preferences over combinations of items they want. This is particularly the case when items are complements, that is, when the utility of all items is higher than the sum of the utilities of each item. Single item auction formats do not provide a mechanism for bidders to express the complementary properties of such bundles of items. Simultaneous auctions provide a mechanism for expressing these preferences, however, not in an efficient manner. Combinatorial auctions provide a language and mechanism for accommodating such preferences. Combinatorial auctions are a general class of auctions dealing with economic environments with complements. Different auction formats can be compared with regards to the revenue they generate, the analysis of equilibrium bidding strategies, and efficiency. Given the nascent nature of combinatorial auctions few results exist for combinatorial auctions. We briefly described some of the combinatorial auction formats. These include single-round sealed-bid first price, Vickrey- Clarke-Groves (VCG) mechanisms, uniform price, and iterative combinatorial auctions. We describe the theoretically appealing VCG and iterative auction formats. The most widely used form of combinatorial auction format is the Vickrey-Clarke-Groves mechanism, which has the desirable property of being implementable in dominant strategies. However these mechanisms are impractical, because they are not budget balancing. The amount of information revelation is impossible to be provided, given consequences of revealing one s true valuations beyond the scope of the particular auction. VCG mechanisms serve the purpose of providing a theoretical threshold for comparisons. The major motivation for iterative processes is to help bidders express their preferences by providing provisional pricing and allocation information. This information allows bidders to focus on their own valuations and what is feasible for them given the other bidders bidding 1 BandX, Bandwidth Market and Invisible Hand Networks are currently bandwidth trading exchanges which are currently in operation. behavior. This learning flexibility however may also create incentives for collusive behavior. B. Combinatorial Auction Experiments In designing combinatorial auctions, a set of design questions need to be considered. How does the format of the auction withstand the threshold effect ; does iterative bidding allow for strategy building through learning; what is the appropriate level of information feedback to the bidders; what is the computational cost of the algorithms proposed. The realization that economic modeling could be used in the design of reallife mechanisms and potentially in the design of market-based control systems in engineering and computer science created the need for investigating the validity of assumptions made in theoretical contexts and their empirical applicability. Dealing with complex economic environments, where complementarities exist, has proven a formidable task for auction theorists. The theoretical properties of different auction formats such as the simultaneous ascending bid auctions and combinatorial auctions were poorly understood. Designers of such systems turned to experimental economics to investigate the properties of such mechanisms. Experimental economics is the application of the laboratory method to test the validity of various economic theories and to test bed new market mechanisms. Using cash-motivated subjects, economic experiments create real-world incentives to help us better understand why markets and other exchange systems work the way they do [4]. These economic environments have been described as combined value auctions and were experimentally investigated in the context of airline slot allocation [15], payloads for NASA s Space Station [2], tracking routes, pollution license trading, and spectrum auctions [10]. Further applications are discussed in [5] [16]. What has been observed in the field and during experiments is that in complex economic environments iterative auctions which permit the participants to observe the competition and learn when and how to bid, produce better results than sealed bid auctions. There are two current frameworks used for iterative procedures. The first one is the use of continuous auctions [2] during which bidders may see a set of provisional winning bids as well as a set of bids to be combined from a standby list. The standby list consists of non-winning bids and these bids are there to signal willingness to combine bids to outbid larger-package bids. The second one is the use of multiple rounds using sealed-bid formats [14] which solves repeated integer programming problems. In general auction systems that provide feedback and allow bidders to revise their bids seem to produce more efficient outcomes. III. COMBINATORIAL SELLER BID DOUBLE AUCTION MECHANISM The Combinatorial Sellers Bid Double Auction Mechanism (c-sebida) was proposed by Jain and Varaiya [8]. They investigated bandwidth markets in which service providers lease bandwidth from each other in order to build routes. The players in the market are strategic, i.e. they maximize their 2 own utility. Bandwidth is assumed to be traded in indivisible amounts (e.g. multiples of 100 Mbps). Buyers can bid on multiple links to build routes, whereas sellers bid only per link. This bid expression language allows the mechanism to be combinatorial. In the setting of c-sebida, buyers can submit bundle bids, which are all or none type bids, i.e. if he does not obtain a resource on its bundle, he does not get other resources. Due to this property, the mechanism eliminates the exposure problem, which was explained before. The auctioneer acts as a mediator and does not place a bid. He just receives all buy and sell bids, solves a mixed-integer model to determine the winners and announces the winners and prices of each link. The mixed-integer model maximizes the total surplus given the bids submitted. According to the mechanism, the prices on each link are determined as the highest price asked by a matched seller. Due to this nature, the mechanism is a seller s bid auction. At the end each link has a uniform price. A. The Formulation The mechanism based on [8] is formally described as follows. Let there be L items l 1,, l L, m buyers and n sellers. Buyer i has a valuation v i per unit for a bundle of items R i {l 1,, l L}. He submits a buy bid of b i per unit and demands up to δ i units of the bundle R i. The buyers are assumed to have quasi-linear utility functions of the form u b i(x; ω, R i) = v i(x) + ω where ω is money and v i(x) = ( x v i, for x δ i, δ i v i, for x δ i. Seller j has cost of c j per unit. He offers at most σ j units of l j at a unit price of a j. Since sellers offer only one link we can write L j = {l j}. Like buyers, sellers are assumed to have quasi-linear utility functions of the form u s j(x; ω, L j) = c j(x) + ω where ω is money and ( x c j, for x σ j, c j(x) =, for x σ j. The decision variables of the mathematical model are x i, y j, where 0 x i δ i is the number of units of bundle R i allocated to buyer i and 0 y j σ j is the number of units of item l j sold by seller j. The mathematical model is formulated as a Mixed Integer Program (MIP) as shown below: max x,y s.t. P i bixi P j ajyj (1) P j yj1(l Lj) P i xi1(l Ri) 0, l, x i [0 : δ i], i, y j [0, σ j], j Integer For each item, c-sebida prices are determined by the highest ask-price among matched sellers. Formally, ˆp l = max{a j : y j 0, l L j}. (2) B. The Theoretical Results Jain and Varaiya [8] demonstrate that bidding truthfully is a dominant strategy for each user except for the matched seller with the highest bid on each item. Their work also show that, Nash equilibrium allocation is always efficient. In the complete information case the mechanism is always efficient, budgetbalanced, ex-post individual rational and almost dominant strategy incentive compatible. In the incomplete information case, it is budget-balanced, ex-post individual rational, asymptotically efficient and Bayesian incentive compatible. In this case the mechanism is efficient when the number of players go to infinity. Truth-telling is a dominant strategy for all the players but the seller with the highest ask bid for each link (hence almost dominant strategy incentive compatible). Please note that this player s bid determines the price for each link. Thus, he might increase his bid to increase the price of the link, however by doing so he faces the risk of not selling it. According to the mechanism, matched buyers pay the sum of the prices of items in their bundle; and matched sellers receive a payment equal to the number of units sold times the price for the item. IV. EXPERIMENTAL SETUP Our experimental design reflected our interest in exploring the efficiency of the algorithm under two different demand and supply environments. The purpose is to test the efficiency of the mechanism and the behavior it induces under different conditions. We describe the economic environment, the valuation structure, the experimental procedure, and efficiency results below. A. The Economic Environment In each auction, 8 subjects participate in the market for 3 links (A,B, and C) each of which has a capacity of 3 trunks. Each bundle of links represents a possible route of interest. There are 2 types of participants in each auction, namely sellers and buyers. Subjects had a 50% chance of being a buyer or a seller. Each round had an equal number of sellers and buyers. In this experiment we compared the efficiency of the mechanism across two different demand and supply conditions. In the benchmark condition (experiment 1), each seller has 3 trunks of each link. Each buyer has a full set of valuations over all combinations of up to 3 trunks and bundles. In the alternate condition (experiment 2), the supply condition is such that there are a total of 12 units of particular link and 6 for each of the remaining. The demand condition is such that the 12 unit link has no value for buyers unless combined with another link in a bundle. Given the demand condition the best allocation is in bundles of two items rather than bundles of three items. Two experimental sessions of four rounds each were conducted. During the first session, subjects participated in four rounds of using the Combinatorial Seller s Bid Double Auctions using the benchmark setup. During the second session subjects participated in four rounds using the same auction format but with the alternative setup valuations. 3 TABLE I EXAMPLE OF SELLER VALUATIONS Trunks link A link B link C TABLE II EXAMPLE OF BUYER VALUATIONS Trunks A B C AB BC AC ABC B. Valuation Structure We followed a valuation structure similar to the one used in [13], where users were given valuations over combinations of links and trunks. Subjects were provided with valuation charts over different combinations of goods at different quantities. Sellers: Each seller owns a combination of links and trunks on those links. Each seller has a cost of operation of each item-trunk pair, is drawn from a uniform discrete distribution between 5 and 15. The cost of each additional trunk within the same link is uniform. Operation costs are only incurred when a link-trunk combination is sold by a seller. There is no cost and no benefit associated with unsold link-trunk combinations. Table I presents an example of a seller who is endowed three trunks on each one of the links available. In the setup we used for experiments, there were four sellers, each owning three trunks on one type of link. Sellers can submit multiple bids (asks) with the restriction that bids cannot be combinatorial. Seller bids specify the maximum units they are willing to sell of their endowment and also the per-unit price they ask for. Buyers: Buyers begin each round without owning any links and trunks. They are however provided with chart of private valuations over the all possible subsets and trunks that they may obtain. In the benchmark setup valuations for each subset of items are generated in the following way: Valuation for each item is generated from a discrete uniform distribution between 10 and 20. For example, item A maybe valued at 12. Valuation for each subset of two items is generated by adding the valuation for the two items. Then a number from a uniform distribution between 0 and 5 is added. For example, item A is valued at 12, item B is valued at 14, and the bundle AB is valued at 29. Valuation for having all three items is generated by the maximum additive valuation between combinations of two items and the valuation of the remaining object. Then a number from a uniform distribution between 0 and 2 is added. Each additional trunk for each combination is valued at -1 of the previous single item trunk; -2 of the previous double item combination; -3 of the previous all item combination. This structure was implemented for diminishing marginal utility of each additional unit of a bundle. Table II demonstrates an example of a valuation chart of a buyer based on the procedure described above. C. Experimental Procedure The experiment consisted of hour sessions which were conducted at the end of July 2004 at the xlab facilities at the University of California, Berkeley. Subjects were recruited from among graduate students in electrical engineering, information management and systems, and economics using e- mail postings. Participants were either required to be familiar with basic networking and/or auction understanding, which was stated in the original solicitation. There were two experiments of four rounds each. The subjects were instructed on how to bid using the web-based interface and also explained on how the system calculates prices and performs matching. Test
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