Combinatorial markets where bids can be submitted on bundles of items can be economically desirable coordination mechanisms in multiagent systems where the items exhibit complementarity and substitutability. There has been a surge of recent research on winner determination in combinatorial auctions. In this paper we study a wider range of combinatorial market designs: auctions, reverse auctions, and exchanges, with one or multiple units of each item, with and without free disposal. We first theoretically characterize the complexity. The most interesting results are that reverse auctions with free disposal can be approximated, and in all of the cases without free disposal, even finding a feasible solution is ÆÈ-complete. We then ran experiments on known benchmarks as well as ones which we introduced, to study the complexity of the market variants in practice. Cases with free disposal tended to be easier than ones without. On many distributions, reverse auctions with free disposal were easier than auctions with free disposal— as the approximability would suggest—but interestingly, on one of the most realistic distributions they were harder. Single-unit exchanges were easy, but multi-unit exchanges were extremely hard. 1

Combinatorial auctions where bidders can bid on bundles of items can lead to more economical allocations, but determining the winners is-complete and inapproximable. We present CABOB, a sophisticated search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid ordering heuristics, and a host of structural observations. Experiments against CPLEX 7.0 show that CABOB is usually faster, never drastically slower, and in many cases drastically faster. We also uncover interesting aspects of the problem itself. First, the problems with short bids that were hard for the first-generation of specialized algorithms are easy. Second, almost all of the CATS distributions are easy, and become easier with more bids. Third, we test a number of random restart strategies, and show that they do not help on this problem because the run-time distribution does not have a heavy tail (at least not for CABOB). 1

This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NP-hard, we present an efficient greedy 2-approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.

Generalized Vickrey mechanisms have received wide attention in the literature because they are efficient and strategyproof, i.e. truthful bidding is optimal whatever the bids of other agents. However it is well-known that it is impossible for an exchange, with multiple buyers and sellers, to be efficient and budget-balanced, even putting strategy-proofness to one side. A market-maker in an efficient exchange must make more payments than it collects. We enforce budget-balance as a hard constraint, and explore payment rules to distribute surplus after an exchange clears to minimize distance to Vickrey payments. Different rules lead to different levels of truthrevelation and efficiency. Experimental and theoretical analysis suggest a simple Threshold scheme, which gives surplus to agents with payments further than a certain threshold value from their Vickrey payments. The scheme appears able to exploit agent uncertainty about bids from other agents to reduce manipulation and boost allocative efficiency in comparison with other simple rules.

We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multi-unit allocation problem. The bidding language allows marginaldecreasing piecewise constant curves and quantity-based side constraints. We develop a fully polynomial-time approximation scheme for the multi-unit allocation problem, which computes a -approximation in worst-case time , given bids each with a constant number of pieces. We integrate this approximation scheme within a VickreyClarke -Groves mechanism and compute payments for an asymptotic cost of ! . The maximal possible gain from manipulation to a bidder in the combined scheme is bounded by 4294-16716 " is the total surplus in the efficient outcome.

technical challenges of wireless SensorNets. As the size and demand for these testbeds grow, resource management will become increasingly important to the effectiveness of these environments. In this paper, we argue that a microeconomic resource allocation scheme, specifically the combinatorial auction, is well suited to testbed resource management. To demonstrate this, we present the Mirage resource allocation system. In Mirage, testbed resources are allocated using a repeated combinatorial auction within a closed virtual currency environment. Users compete for testbed resources by submitting bids which specify resource combinations of interest in space/time (e.g., "any 32 MICA2 motes for 8 hours anytime in the next three days") along with a maximum value amount the user is willing to pay. A combinatorial auction is then periodically run to determine the winning bids based on supply and demand while maximizing aggregate utility delivered to users. We have implemented a fully functional and secure prototype of Mirage and have been operating it in daily use for approximately two months on Intel Research Berkeley's 148-mote SensorNet testbed.

Supply chain formation presents difficult coordination issues for distributed negotiation protocols. Agents must simultaneously negotiate production relationships at multiple levels, with important interdependencies among inputs and outputs at each level. Combinatorial auctions address this problem by global optimization over expressed offers to engage in compound exchanges. A one-shot combinatorial auction that optimizes the reported value of the bids results in optimal allocations with truthful bids. But autonomous self-interested agents have an incentive to bid strategically in an attempt to gain extra surplus. We investigate a particular combinatorial protocol consisting of a one-shot auction and a strategic bidding policy. We experimentally analyze the efficiency and producer surplus obtained in five networks, and compare this performance to that of a distributed, progressive auction protocol with non-strategic bidding. We find that producers can sometimes gain significantly by bi...

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Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we begin with general background in combinatorial game theory, which analyzes ideal play in perfect-information games. Then we survey results about the complexity of determining ideal play in these games, and the related problems of solving puzzles, in terms of both polynomial-time algorithms and computational intractability results. Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer. 1

Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is NP-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster—especially in cases with structure. CABOB’s search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem—the run-time distribution does not have a heavy tail.