On the Approximability of Combinatorial Exchange Problems

Babaioff, Moshe; Briest, Patrick; Krysta, Piotr

doi:10.1007/978-3-540-79309-0_9

Cited by 7 publications

(5 citation statements)

References 16 publications

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“…Our focus in this paper was not computational complexity, but it turns out that all of our mechanisms run in polynomial time, except the mechanism for combinatorial exchanges (see [12,4] for computational issues in combinatorial exchanges). Developing a polynomial time mechanism for the latter setting seems hard as in particular it implies a solution to the notorious problem of developing truthful polynomial time algorithm for combinatorial auctions with subadditive (and submodular) bidders (see, e.g., [7], [9], and [8]).…”

Section: Discussionmentioning

confidence: 99%

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Reallocation mechanisms

Blumrosen

Dobzinski

2014

Proceedings of the Fifteenth ACM Conference on Economics and Computation

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We consider exchange economies, where the initial endowment of each agent consists of some set of resources. The private information of the agents is their value for every possible subset of all the resources. The goal is to redistribute resources among agents to maximize efficiency, where monetary transfers are allowed. As agents may simultaneously play the role of buyers and sellers, the standard method for implementing efficient outcomes -VCG mechanisms -may not be budget balanced. In fact, it is known (Myerson and Satterthwaite, 1983) that even in the simplest bilateral-trade setting no mechanism can simultaneously achieve full efficiency, individual rationality and budget balance in (Bayes Nash) equilibrium.In this paper, we develop incentive-compatible, individually-rational and budget balanced mechanisms for several classic settings. All our mechanisms (except one) provide a constant approximation to the optimal efficiency in these settings, even in ones where the preferences of the agents are complex multi-parameter functions. Some of our mechanisms achieve approximation guarantee in expectation, given prior distributions on the preferences of the agents, and other approximation results hold for every realization of the preferences.We start with analyzing the simple one-buyer one-seller bilateral trade setting, where some design challenges start revealing. We present a mechanism that achieves in expectation at least half of the expected value of the efficient allocation. We then show how this mechanism can be used to achieve the same approximation ratio for the more general Partnership Dissolving setting, where several agents initially hold fractions of a divisible item.Both bilateral trade and partnership dissolving are single-parameter domains. Our main technical results are two mechanisms for more complex multi-parameter domains. The first domain is combinatorial exchange, where a set of m indivisible heterogeneous items is initially distributed among the agents. Agents have combinatorial sub-additive preferences. We show that there exists a truthful, individually rational, weakly budget balanced mechanism that provides an 8Hm-approximation to the optimal welfare (where Hm is the m'th harmonic number). Our second multi-parameter domain is the classic exchange model of Arrow and Debreu, where agents have concave valuation functions for a single divisible good. We devise a truthful, prior-free, individually rational, weakly budget balanced mechanism that provides a constant approximation to the optimal social welfare (as long as no single agent holds a huge chunk of the good).

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Section: Discussionmentioning

confidence: 99%

“…Theorem: There exists a truthful, individually rational, weakly budget balanced, randomized mechanism that provides an 8H t -approximation to the optimal welfare if all valuations are subadditive 4 . The only distributional knowledge that the mechanism uses is the median value of the distribution of the endowment of each player.…”

Section: Combinatorial Exchangesmentioning

confidence: 99%

Reallocation mechanisms

Blumrosen

Dobzinski

2014

Proceedings of the Fifteenth ACM Conference on Economics and Computation

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“…This property ensures that the exchange does not run at a loss. Also Babaioff et al [15] have shown that the problems of surplus maximization or volume maximization (EFF) in Shantanu [16], [19] have shown that in a combinatorial exchange with multiple buyers and sellers, even with discriminatory pricing, competitive equilibrium may not exist. Therefore we can only achieve competitive equilibrium under special conditions.…”

Section: Introductionmentioning

confidence: 98%

An iterative auction mechanism for combinatorial exchanges

Biswas

Narahari

2010

2010 IEEE International Conference on Automation Science and Engineering

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Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest to solve among all economic mechanisms. In this paper, we develop computationally efficient iterative auction mechanisms for solving combinatorial exchanges. Our mechanisms satisfy Individual-rationality (IR) and budgetnonnegativity (BN) properties. We also show that our method is bounded and convergent. Our numerical experiments show that our algorithm produces good quality solutions and is computationally efficient.

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“…This property ensures that the exchange does not run at a loss. Also Babaioff et al [13] have shown that the problems of surplus maximization or volume maximization (EFF) in combinatorial exchanges are inapproximable even with free disposal.…”

Section: Introductionmentioning

confidence: 99%

Approximately Efficient Iterative Mechanisms for Combinatorial Exchanges

Biswas

Narahari

2009

2009 IEEE Conference on Commerce and Enterprise Computing

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Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest to solve among all economic mechanisms. In this paper, we develop computationally efficient iterative auction mechanisms for solving combinatorial exchanges. Our mechanisms satisfy Individualrationality (IR) and budget-nonnegativity (BN) properties. We also show that the exchange problem can be reduced to combinatorial auction problem when either the buyers or the sellers are single minded. Our numerical experiments show that our algorithm produces good quality solutions and is computationally efficient.

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On the Approximability of Combinatorial Exchange Problems

Cited by 7 publications

References 16 publications

Reallocation mechanisms

Reallocation mechanisms

An iterative auction mechanism for combinatorial exchanges

Approximately Efficient Iterative Mechanisms for Combinatorial Exchanges

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