Truthful Multi-unit Procurements with Budgets

Hau Chan; Jing Chen

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arXiv · 1409.7595

Truthful Multi-unit Procurements with Budgets

Hau Chan·Jing Chen

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Abstract

We study procurement games where each seller supplies multiple units of his item, with a cost per unit known only to him. The buyer can purchase any number of units from each seller, values different combinations of the items differently, and has a budget for his total payment. For a special class of procurement games, the {\em bounded knapsack} problem, we show that no universally truthful budget-feasible mechanism can approximate the optimal value of the buyer within $\ln n$, where $n$ is the total number of units of all items available. We then construct a polynomial-time mechanism that gives a $4(1+\ln n)$-approximation for procurement games with {\em concave additive valuations}, which include bounded knapsack as a special case. Our mechanism is thus optimal up to a constant factor. Moreover, for the bounded knapsack problem, given the well-known FPTAS, our results imply there is a provable gap between the optimization domain and the mechanism design domain. Finally, for procurement games with {\em sub-additive valuations}, we construct a universally truthful budget-feasible mechanism that gives an $O(\frac{\log^2 n}{\log \log n})$-approximation in polynomial time with a demand oracle.

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BibTeX RIS

Hau Chan, Jing Chen. 2014-09-26. Truthful Multi-unit Procurements with Budgets. https://arxiv.org/abs/1409.7595

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