IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2109.05456.html
   My bibliography  Save this paper

Matching markets with middlemen under transferable utility

Author

Listed:
  • Ata Atay
  • Eric Bahel
  • Tam'as Solymosi

Abstract

This paper studies matching markets in the presence of middlemen. In our framework, a buyer-seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer-seller pairs. Direct trade between a buyer and a seller is costlier than a trade mediated by a middleman. For each such market, we examine an associated cooperative game with transferable utility. First, we show that an optimal matching for a matching market with middlemen can be obtained by considering the two-sided assignment market where each buyer-seller pair is allowed to use the mediation service of the middlemen free of charge and attain the maximum surplus. Second, we prove that the core of a matching market with middlemen is always non-empty. Third, we show the existence of a buyer-optimal core allocation and a seller-optimal core allocation. In general, the core does not exhibit a middleman-optimal matching. Finally, we establish the coincidence between the core and the set of competitive equilibrium payoff vectors.

Suggested Citation

  • Ata Atay & Eric Bahel & Tam'as Solymosi, 2021. "Matching markets with middlemen under transferable utility," Papers 2109.05456, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2109.05456
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2109.05456
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
    2. Atay, Ata & Solymosi, Tamás, 2018. "On bargaining sets of supplier-firm-buyer games," Economics Letters, Elsevier, vol. 167(C), pages 99-103.
    3. S. Miquel & M. Núñez, 2011. "The maximum and the addition of assignment games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 189-212, July.
    4. Oriol Tejada, 2010. "A note on competitive prices in multilateral assignment markets," Economics Bulletin, AccessEcon, vol. 30(1), pages 658-662.
    5. Ata Atay & Marina Núñez, 2019. "Multi-sided assignment games on m-partite graphs," Annals of Operations Research, Springer, vol. 279(1), pages 271-290, August.
    6. Stuart, Harborne Jr, 1997. "The supplier-firm-buyer game and its m-sided generalization," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 21-27, August.
    7. Bloch, Francis & Ryder, Harl, 2000. "Two-Sided Search, Marriages, and Matchmakers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 93-115, February.
    8. Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, vol. 3(4), pages 487-503, November.
    9. Katerina Sherstyuk, 1999. "Multisided matching games with complementarities," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 489-509.
    10. Alok Johri & John Leach, 2002. "Middlemen and the Allocation of Heterogeneous Goods," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 347-362, May.
    11. Yavas, Abdullah, 1994. "Middlemen in Bilateral Search Markets," Journal of Labor Economics, University of Chicago Press, vol. 12(3), pages 406-429, July.
    12. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    13. Oriol Tejada, 2013. "Analysis of the core of multisided Böhm-Bawerk assignment markets," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 189-205, April.
    14. Mo, Jie-Ping, 1988. "Entry and structures of interest groups in assignment games," Journal of Economic Theory, Elsevier, vol. 46(1), pages 66-96, October.
    15. Lloyd S. Shapley, 1962. "Complements and substitutes in the opttmal assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(1), pages 45-48, March.
    16. Saadia El Obadi & Silvia Miquel, 2019. "Assignment Games with a Central Player," Group Decision and Negotiation, Springer, vol. 28(6), pages 1129-1148, December.
    17. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 425-440, December.
    18. Ata Atay & Francesc Llerena & Marina Núñez, 2016. "Generalized three-sided assignment markets: core consistency and competitive prices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 572-593, October.
    19. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    20. Fingleton, John, 1997. "Competition among Middlemen When Buyers and Sellers Can Trade Directly," Journal of Industrial Economics, Wiley Blackwell, vol. 45(4), pages 405-427, December.
    21. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    22. John Fingleton, 1997. "Competition Among Middlemen When Buyers and Sellers Can Trade Directly," Journal of Industrial Economics, Wiley Blackwell, vol. 45(4), pages 405-427, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Atay, Ata & Solymosi, Tamás, 2018. "On bargaining sets of supplier-firm-buyer games," Economics Letters, Elsevier, vol. 167(C), pages 99-103.
    2. O. Tejada & M. Álvarez-Mozos, 2016. "Vertical syndication-proof competitive prices in multilateral assignment markets," Review of Economic Design, Springer;Society for Economic Design, vol. 20(4), pages 289-327, December.
    3. Martínez-de-Albéniz, F. Javier & Rafels, Carlos & Ybern, Neus, 2020. "Assortative multisided assignment games: The extreme core points," Games and Economic Behavior, Elsevier, vol. 120(C), pages 144-153.
    4. Pieter Gautier & Bo Hu & Makoto Watanabe, 2023. "Marketmaking Middlemen," RAND Journal of Economics, RAND Corporation, vol. 54(1), pages 83-103, March.
    5. Ata Atay & Francesc Llerena & Marina Núñez, 2016. "Generalized three-sided assignment markets: core consistency and competitive prices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 572-593, October.
    6. Ata Atay & Marina Núñez, 2019. "Multi-sided assignment games on m-partite graphs," Annals of Operations Research, Springer, vol. 279(1), pages 271-290, August.
    7. Streekstra, Leanne & Trudeau, Christian, 2020. "Stable source connection and assignment problems as multi-period shortest path problems," Discussion Papers on Economics 7/2020, University of Southern Denmark, Department of Economics.
    8. De Fraja, Gianni & Sákovics, József, 2012. "Exclusive nightclubs and lonely hearts columns: Non-monotone participation in optional intermediation," Journal of Economic Behavior & Organization, Elsevier, vol. 84(2), pages 618-632.
    9. Saadia El Obadi & Silvia Miquel, 2019. "Assignment Games with a Central Player," Group Decision and Negotiation, Springer, vol. 28(6), pages 1129-1148, December.
    10. Combe, Julien, 2022. "Matching with ownership," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    11. Oriol Tejada & Marina Núñez, 2012. "The nucleolus and the core-center of multi-sided Böhm-Bawerk assignment markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 199-220, April.
    12. Oriol Tejada, 2013. "Complements and Substitutes in Generalized Multisided Assignment Economies," CER-ETH Economics working paper series 13/180, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    13. Atay, Ata & Núñez, Marina, 2019. "A note on the relationship between the core and stable sets in three-sided markets," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 10-14.
    14. Oriol Tejada, 2013. "Analysis of the core of multisided Böhm-Bawerk assignment markets," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 189-205, April.
    15. Galeotti, Andrea & Moraga-González, José Luis, 2009. "Platform intermediation in a market for differentiated products," European Economic Review, Elsevier, vol. 53(4), pages 417-428, May.
    16. Trudeau, Christian, 2018. "From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution," Games and Economic Behavior, Elsevier, vol. 108(C), pages 225-238.
    17. Domenico Colucci & Vincenzo Valori, 2008. "Asset Price Dynamics When Behavioural Heterogeneity Varies," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 3-20, September.
    18. Tara Mitchell, 2014. "Is Knowledge Power? Competition and Information in Agricultural Markets," The Institute for International Integration Studies Discussion Paper Series iiisdp456, IIIS.
    19. Simon Loertscher, 2005. "Market making oligopoly," Diskussionsschriften dp0512, Universitaet Bern, Departement Volkswirtschaft.
    20. Blume, Lawrence E. & Easley, David & Kleinberg, Jon & Tardos, Éva, 2009. "Trading networks with price-setting agents," Games and Economic Behavior, Elsevier, vol. 67(1), pages 36-50, September.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2109.05456. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.