Abstract
We consider budget feasible mechanisms for procurement auctions with additive valuation functions. For the divisible case, where agents can be allocated fractionally, there exists an optimal mechanism with approximation guarantee \(e/(e-1)\) under the small bidder assumption. We study the divisible case without the small bidder assumption, but assume that the true costs of the agents are bounded by the budget. This setting lends itself to modeling economic situations in which the goods represent time and the agents’ true costs are not necessarily small compared to the budget. Non-trivially, we give a mechanism with an approximation guarantee of 2.62, improving the result of 3 for the indivisible case. Additionally, we give a lower bound on the approximation guarantee of 1.25. We then study the problem in more competitive markets and assume that the agents’ value over cost efficiencies are bounded by some \(\theta \ge 1\). For \(\theta \le 2\), we give a mechanism with an approximation guarantee of 2 and a lower bound of 1.18. Finally, we extend these results to settings with different agent types with a linear capped valuation function for each type.
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Notes
- 1.
It is important to realize that the mechanism only has access to the declared costs \(\textbf{b}\), as the actual costs \(\textbf{c}\) are assumed to be private information of the agents.
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Acknowledgement
We thank Georgios Amanatidis for proposing to study budget feasible mechanisms for divisible agents when he was a postdoc at CWI. Part of this work was sponsored by the Open Technology Program of the Dutch Research Council (NWO), project number 18938.
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Klumper, S., Schäfer, G. (2022). Budget Feasible Mechanisms for Procurement Auctions with Divisible Agents. In: Kanellopoulos, P., Kyropoulou, M., Voudouris, A. (eds) Algorithmic Game Theory. SAGT 2022. Lecture Notes in Computer Science, vol 13584. Springer, Cham. https://doi.org/10.1007/978-3-031-15714-1_5
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