Abstract
We study individual rational, Pareto optimal, and incentive compatible mechanisms for auctions with heterogeneous items and budget limits. For multi-dimensional valuations we show that there can be no deterministic mechanism with these properties for divisible items. We use this to show that there can also be no randomized mechanism that achieves this for either divisible or indivisible items. For single-dimensional valuations we show that there can be no deterministic mechanism with these properties for indivisible items, but that there is a randomized mechanism that achieves this for either divisible or indivisible items. The impossibility results hold for public budgets, while the mechanism allows private budgets, which is in both cases the harder variant to show. While all positive results are polynomial-time algorithms, all negative results hold independent of complexity considerations.
This work was funded by the Vienna Science and Technology Fund (WWTF) through project ICT10-002, by the University of Vienna through IK I049-N, and by a Google Research Award.
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Dütting, P., Henzinger, M., Starnberger, M. (2012). Auctions with Heterogeneous Items and Budget Limits. In: Goldberg, P.W. (eds) Internet and Network Economics. WINE 2012. Lecture Notes in Computer Science, vol 7695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35311-6_4
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DOI: https://doi.org/10.1007/978-3-642-35311-6_4
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