Abstract
We study the design of multilateral markets, where agents with several different roles engage in trade. We first observe that the modular approach proposed by Dütting et al. [5] for bilateral markets can also be applied in multilateral markets. This gives a general method to design Deferred Acceptance mechanisms in such settings; these mechanisms, defined by Milgrom and Segal [10], are known to satisfy some highly desired properties.
We then show applications of this framework in the context of supply chains. We show how existing mechanisms can be implemented as multilateral Deferred Acceptance mechanisms, and thus exhibit nice practical properties (as group strategy-proofness and equivalence to clock auctions). We use the general framework to design a novel mechanism that improves upon previous mechanisms in terms of social welfare. Our mechanism manages to avoid “trade reduction” in some scenarios, while maintaining the incentive and budget-balance properties.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
- 2.
- 3.
Our work is inspired by [8] in several ways. First, we sacrifice efficiency in order to satisfy incentive constraints and budget balance and our mechanism loses at most the least valuable procurement set. In addition, McAfee’s mechanism computed a price as a function of the “best” losing bids, and if this price cleared the market, no trade reduction would take place. Our mechanism acts in the same spirit and sometimes implements the efficient allocation, but it is not a generalization of McAfee’s mechanism. In fact, our mechanism always omits one trade when applied to the degenerate supply chain of a single two-sided market with unit-demand buyers; the benefits of our mechanism stem in more complex markets.
- 4.
Threshold payments will be formally defined in the next section. Informally, these are the highest bids for a winning agent such that he remains a winner.
- 5.
In a two-sided market with producers and consumers of a homogeneous good, \(N_1\) might be the set of producers and \(N_2\) might be the set of consumers. In that case producers’ types will be thought of as production costs, so a producer with a cost \(c_i\) will have utility of \(-c_i+p_i\) if \(i\in {A}\), and \(p_i\) otherwise. Consumers’ types will be thought of as their value from possessing one item of the traded good.
- 6.
As mentioned in Sect. 2, [10] define DA auctions with finite bid spaces. In order to use their results, we do the same. This also requires a more delicate definition of truthfulness and we follow the definition of strategy-proofness in [10] which uses the standard dominant-strategy truthfulness, only with taking care of the finite bid space. We refer the readers to [10] for the exact definition.
- 7.
In order to keep notation simple, the scoring functions are denoted with superscript t yet they are allowed to depend on the entire history of active agents \((A_1,...,A_t)\) and not just on the t-period information. In the remainder of the paper, all objects denoted with superscript t are allowed to be history dependent.
- 8.
In the full paper, we relax the assumption of unique manufacturing technology and design an MDA mechanism for scenarios where a certain good can be produced from different types of inputs.
- 9.
A topological ordering of a directed a-cyclical graph is an ordering of the nodes such that for every edge (j, k), the node j comes before k in that ordering.
- 10.
The assumption that \(q_{j,k}\) for \(j<k\) is an integer, rather than a real number, is without loss of generality since any amount of items can be regarded as one unit. For example, if item j is flour and all items \(k>j\) are produced using amounts of flour in multiples of 0.5 kg, set one unit of item j to be 0.5 kg of flour.
- 11.
Q is a unitriangular matrix with negative integers on the entries above the main diagonal. Since \(d\in {\mathbb {N}^K}\), it can be shown that \(\tilde{\mu }=Q^{-1}\cdot {d}\) is a vector of non-negative integers and thus appropriately represents numbers of agents.
- 12.
Consumers’ bid spaces are defined as subsets of \([-\bar{v},0]\) so we can treat all agents, producers and consumers, in a similar manner such that higher bidding agents are less attractive. Thus, the mechanism will determine negative monetary transfers for consumers and positive transfers for producers. The maximal (minimal) possible bid of a producer (consumer) is set to be higher (lower) than his highest possible cost (lowest possible value) to insure that participation is strictly preferable to non-participation (see [10]).
- 13.
For any \(k=1,..,K\) such that \(|N_k\setminus {A_t}|<\tilde{\mu }_k\), set \(c^t_{k,(|N_k\setminus {A_t}|+1)}=c^t_{k,(|N_k\setminus {A_t}|+2)}=...=c^t_{k,(\tilde{\mu }_k)}=\max {B_k}\) and if no consumer was rejected prior to period t, set \(v^t_{max}=0\). Specifically, for \(t=1\) set \( NC^1(\emptyset )=\sum _{k=1}^K \tilde{\mu }_k\max {B_k} \).
- 14.
Note that this procedure is not equivalent to the following mechanism: run VCG if it is budget balanced, otherwise run a trade reduction. This mechanism is not truthful, as the VCG payment of an agent can be determined by agents of other classes (who therefore can manipulate the outcome). The Modified Trade Reduction mechanism uses bounds on the payments that are determined only by the agents of each class, and therefore it is strategy-proof.
References
Babaioff, M., Nisan, N.: Concurrent auctions across the supply chain. J. Artif. Intell. Res. 21, 595–629 (2004)
Babaioff, M., Walsh, W.E.: Incentive-compatible, budget-balanced, yet highly efficient auctions for supply chain formation. Decision Sup. Sys. 39(1), 123–149 (2005)
Cripps, M.W., Swinkels, J.M.: Efficiency of large double auctions. Econometrica 74(1), 47–92 (2006)
Dütting, P., Gkatzelis, V., Roughgarden, T.: The performance of deferred-acceptance auctions. In: Proceedings of the Fifteenth ACM Conference on Economics and Computation, pp. 187–204. ACM (2014)
Dütting, P., Roughgarden, T., Talgam-Cohen, I.: Modularity and greed in double auctions. In: Proceedings of the Fifteenth ACM Conference on Economics and Computation, pp. 241–258. ACM (2014)
Lehmann, D., Oćallaghan, L.I., Shoham, Y.: Truth revelation in approximately efficient combinatorial auctions. J. ACM (JACM) 49(5), 577–602 (2002)
Lubin, B., Parkes, D.C.: Approximate strategyproofness. Curr. Sci. 103(9), 1021–1032 (2012)
McAfee, R.P.: A dominant strategy double auction. J. Econ. Theor. 56(2), 434–450 (1992)
Mehta, A., Roughgarden, T., Sundararajan, M.: Beyond moulin mechanisms. In: 8th ACM Conference on Electronic Commerce, EC 2007, pp. 1–10 (2007)
Milgrom, P., Segal, I.: Deferred-acceptance auctions and radio spectrum reallocation. In: Proceedings of the Fifteenth ACM Conference on Economics and Computation, pp. 185–186. ACM (2014)
Moulin, H.: Incremental cost sharing: characterization by coalition strategy-proofness. Soc. Choice Welfare 16(2), 279–320 (1999)
Myerson, R.B., Satterthwaite, M.A.: Efficient mechanisms for bilateral trading. J. Econ. Theor. 29(2), 265–281 (1983)
Rustichini, A., Satterthwaite, M.A., Williams, S.R.: Convergence to efficiency in a simple market with incomplete information. Econometrica 62(5), 1041–63 (1994)
Satterthwaite, M.A., Williams, S.R.: The optimality of a simple market mechanism. Econometrica 70(5), 1841–1863 (2002)
Singer, Y.: Budget feasible mechanisms. In: The 51st Annual Symposium on Foundations of Computer Science, FOCS 2010, pp. 765–774 (2010)
Vorobeychik, Y., Kiekintveld, C., Wellman, M.P.: Empirical mechanism design: methods, with application to a supply-chain scenario. In: ACM Conference on Electronic Commerce, pp. 306–315 (2006)
Walsh, W., Wellman, M., Ygge, F.: Combinatorial auctions for supply chain formation. In: Proceedings of the ACM Conference on Electronic Commerce, pp. 260–269 (2000)
Acknowledgments
We thank Moshe Babaioff for helpful discussions. Liad Blumrosen was supported by the Israel Science Foundation (grant No. 230/10).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blumrosen, L., Zohar, O. (2015). Multilateral Deferred-Acceptance Mechanisms. In: Markakis, E., Schäfer, G. (eds) Web and Internet Economics. WINE 2015. Lecture Notes in Computer Science(), vol 9470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48995-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-662-48995-6_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48994-9
Online ISBN: 978-3-662-48995-6
eBook Packages: Computer ScienceComputer Science (R0)