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COMBIMA: truthful, budget maintaining, dynamic combinatorial market

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Abstract

Current interest in two-sided markets is motivated by examples of successful practical applications of market mechanisms in supply chain markets, online advertising exchanges, and pollution-rights markets. Many of these examples require markets where agents arrive dynamically and can trade multiple commodities. However, the known literature largely focuses on settings with single-commodity unit demand. We present, prove and evaluate a general solution that matches agents in a dynamic, two-sided combinatorial market. Multiple commodities, each with multiple units, are bought and sold in different bundles by agents that arrive over time. Our mechanism, COMBIMA, provides the first dynamic two-sided combinatorial market that allows truthful and individually-rational behavior for all agents, keeps the market budget balanced and approximates social welfare efficiency. We experimentally examine and compare the allocative efficiency of COMBIMA with respect to our proven theoretical bounds and with respect to all known (dynamic and non-dynamic) social-welfare maximizing two-sided markets under variety of distributions of bids, market demands and market size. COMBIMA performs well by all benchmarks and in many cases improves on previous mechanisms.

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Notes

  1. One exception in the literature is a recent work by Feldman et al. [14] that has a single commodity with multiple demand however their market is mediated.

  2. Bredin et al. [6] and Wurman et al. [30] did not provide an approximation guaranty.

  3. Except for the work by Bredin et al. [6] which assumed agents with bounded patience.

  4. If prices increase too quickly then early on the algorithm may encounter buyers with attractive bids who nevertheless cannot afford their desired bundle, i.e., cannot be allocated despite the fact that the allocation has not accumulated high enough SWF to guarantee the desirable approximation bound.

  5. The only previous work on dynamic markets that does not assume a similar assumption on the valuation range, is the work by Bredin et al. [6]. However [6]’s work assumes an alternative assumption: agents with bounded patience, otherwise no reasonable efficiency can be achieved.

  6. Note that the IR property is not affected by the later payments since if units of commodities in \(s_i\) are not sold in the market by its closing time, seller i is left to possess them. Also note that similarly to [6] we could have changed our algorithm to pay the arriving selling agents instantaneously and have the market “hold” the commodities until bought, however such approach will lead to market deficits during the market run as occurs in [6]’s market.

  7. matroid constraints—A matroid is a pair \(({\mathcal {Q}},{\mathcal {Z}})\) where \({\mathcal {Q}}\) is a finite set, \({\mathcal {Z}}\) is a family of subsets of \({\mathcal {Q}}\) and \({\mathcal {Z}}\) has the following properties: 1. \(\emptyset \in {\mathcal {Z}}\), 2. \(\forall Z' \subset Z \subseteq {\mathcal {Q}}\) if \(Z\in {\mathcal {Z}}\) then \(Z'\in {\mathcal {Z}}\), 3. if \(G,R \in {\mathcal {Z}}\) and \(|G|>|R|\) then \(\exists g\in G\) such that \(R \cup \{g\}\in {\mathcal {Z}}\).

  8. Subadditive—roughly speaking, the value of bundle A plus the value of bundle B is greater than the value of their union.

  9. Additive—roughly speaking, the value of bundle A is the sum of the values of the single commodity bundles composing it.

  10. Except for small markets with high theta value, in those, in order to achieve the desired theta , we allow number of sellers \(\,=\, \)number of buyers, while keeping number of each commodity units at \(5^7\).

  11. We say that a market is strong budget balanced (SBB) if the sum of the prices paid by the buying agents is equal to the sum of the prices paid to the selling agents

  12. [6] and [30] did not provide an approximation guaranty.

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Authors and Affiliations

  1. Department of Management and Economics, The Open University of Israel, 1 University Road, 43107, Raanana, Israel

    Rica Gonen

  2. Department of Mathematics and Computer Science, The Open University of Israel, 1 University Road, 43107, Raanana, Israel

    Ozi Egri

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  1. Rica Gonen
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  2. Ozi Egri
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Correspondence to Rica Gonen.

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A preliminary version of this work [16] was presented at AAMAS 2017.

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Gonen, R., Egri, O. COMBIMA: truthful, budget maintaining, dynamic combinatorial market. Auton Agent Multi-Agent Syst 34, 14 (2020). https://doi.org/10.1007/s10458-019-09437-7

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