Auctions with Heterogeneous Items and Budget Limits

We study individual rational, Pareto optimal, and incentive compatible mechanismsfor auctions with heterogeneous items and budget limits. For multi-dimensional valua-tions we show that there can be no deterministic mechanism with these properties fordivisible items. We use this to show that there can also be no randomized mechanismthat achieves this for either divisible or indivisible items. For single-dimensional val-uations we show that there can be no deterministic mechanism with these propertiesfor indivisible items, but that there is a randomized mechanism that achieves this foreither divisible or indivisible items. The impossibility results hold for public budgets,while the mechanism allows private budgets, which is in both cases the harder variantto show. While all positive results are polynomial-time algorithms, all negative resultshold independent of complexity considerations.