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On the approximability of combinatorial exchange problems. (English) Zbl 1136.91347
Monien, Burkhard (ed.) et al., Algorithmic game theory. First international symposium, SAGT 2008, Paderborn, Germany, April 30–May 2, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-79308-3/pbk). Lecture Notes in Computer Science 4997, 83-94 (2008).
Summary: In a combinatorial exchange the goal is to find a feasible trade between potential buyers and sellers requesting and offering bundles of indivisible goods. We investigate the approximability of several optimization objectives in this setting and show that the problems of surplus and trade volume maximization are inapproximable even with free disposal and even if each agent’s bundle is of size at most 3. In light of the negative results for surplus maximization we consider the complementary goal of social cost minimization and present tight approximation results for this scenario. Considering the more general supply chain problem, in which each agent can be a seller and buyer simultaneously, we prove that social cost minimization remains inapproximable even with bundles of size 3, yet becomes polynomial time solvable for agents trading bundles of size 1 or 2. This yields a complete characterization of the approximability of supply chain and combinatorial exchange problems based on the size of traded bundles. We finally briefly address the problem of exchanges in strategic settings.
For the entire collection see [Zbl 1134.68008].
MSC:
91A46 Combinatorial games
90B05 Inventory, storage, reservoirs
91B26 Auctions, bargaining, bidding and selling, and other market models
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