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Fast Convergence in the Double Oral Auction

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Web and Internet Economics (WINE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9470))

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Abstract

A classical trading experiment consists of a set of unit demand buyers and unit supply sellers with identical items. Each agent’s value or opportunity cost for the item is their private information and preferences are quasi-linear. Trade between agents employs a double oral auction (DOA) in which both buyers and sellers call out bids or offers which an auctioneer recognizes. Transactions resulting from accepted bids and offers are recorded. This continues until there are no more acceptable bids or offers. Remarkably, the experiment consistently terminates in a Walrasian price. The main result of this paper is a mechanism in the spirit of the DOA that converges to a Walrasian equilibrium in a polynomial number of steps, thus providing a theoretical basis for the above-described empirical phenomenon. It is well-known that computation of a Walrasian equilibrium for this market corresponds to solving a maximum weight bipartite matching problem. The uncoordinated but rational responses of agents thus solve in a distributed fashion a maximum weight bipartite matching problem that is encoded by their private valuations. We show, furthermore, that every Walrasian equilibrium is reachable by some sequence of responses. This is in contrast to the well known auction algorithms for this problem which only allow one side to make offers and thus essentially choose an equilibrium that maximizes the surplus for the side making offers. Our results extend to the setting where not every agent pair is allowed to trade with each other.

The full version of this paper can be found in [1]. Supported in part by National Science Foundation grants CCF-1116961, CCF-1552909, and IIS-1447470.

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Notes

  1. 1.

    In Chamberlin’s experiment, buyers and sellers had to seek each other out to determine prices. This search cost meant that each agent was not necessarily aware of all prices on the other side of the market.

  2. 2.

    This is common for eliminating no trade equilibria.

  3. 3.

    This is part of many experimental implementations of the DOA.

  4. 4.

    An action at time time t will take effect at the time \(t+1\), and \(P^t\) is the price function before any action is made at time t.

References

  1. Assadi, S., Khanna, S., Li, Y., Vohra, R.: Fast convergence in the double oral auction. CoRR abs/1510.00086 (2015)

    Google Scholar 

  2. Bertsekas, D.: A distributed algorithm for the assignment problem. Laboratory for Information and Decision Systems, Working Paper, M.I.T., Cambridge (1979)

    Google Scholar 

  3. Bertsekas, D.P.: Linear Network Optimization: Algorithms and Codes. MIT Press, Cambridge (1991)

    Google Scholar 

  4. Bertsekas, D.P., Castaon, D.A.: A forward/reverse auction algorithm for asymmetric assignment problems. Comput. Optim. Appl. 1(3), 277–297 (1992). doi:10.1007/BF00249638

    Article  MathSciNet  Google Scholar 

  5. Chamberlin, E.H.: An experimental imperfect market. J. Polit. Econ. 56(2), 95–108 (1948)

    Article  Google Scholar 

  6. Crawford, V.P., Knoer, E.M.: Job matching with heterogeneous firms and workers. Econometrica J. Econometric Soc. 49, 437–450 (1981)

    Article  Google Scholar 

  7. Demange, G., Gale, D., Sotomayor, M.: Multi-item auctions. J. Polit. Econ. 94, 863–872 (1986)

    Article  Google Scholar 

  8. Friedman, D.P., Rust, J.: The Double Auction Market: Institutions, Theories, and Evidence. Westview Press, Boulder (1993)

    Google Scholar 

  9. Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 69, 9–15 (1962)

    Article  MathSciNet  Google Scholar 

  10. Kanoria, Y., Bayati, M., Borgs, C., Chayes, J., Montanari, A.: Fast convergence of natural bargaining dynamics in exchange networks. In: SODA (2011). http://dl.acm.org/citation.cfm?id=2133036.2133154

  11. Knuth, D.: Mariages stables et leurs relations avec d&autres problèmes combinatoires: Collection de la Chaire Aisenstadt, Presses de l’Université de Montréal (1976). http://books.google.com/books?id=eAmFAAAAIAAJ

  12. Kuhn, H.W.: The Hungarian method for the assignment problem. In: Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L. (eds.) 50 Years of Integer Programming 1958–2008 - From the Early Years to the State-of-the-Art, pp. 29–47. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Nax, H.H., Pradelski, B.S.R., Young, H.P.: Decentralized dynamics to optimal and stable states in the assignment game. In: CDC (2013)

    Google Scholar 

  14. Pradelski, B.S.: Decentralized dynamics and fast convergence in the assignment game: extended abstract. In: EC. ACM, New York (2015)

    Google Scholar 

  15. Roth, A.E., Vate, J.H.V.: Random paths to stability in two-sided matching. Econometrica J. Econometric Soc. 58, 1475–1480 (1990)

    Article  MathSciNet  Google Scholar 

  16. Shapley, L., Shubik, M.: The assignment game I: the core. Int. J. Game Theory 1(1), 111–130 (1971). doi:10.1007/BF01753437

    Article  MathSciNet  Google Scholar 

  17. Smith, V.L.: An experimental study of competitive market behavior. J. Polit. Econ. 70(2), 111–137 (1962)

    Article  Google Scholar 

  18. Smith, V.L.: Papers in Experimental Economics. Cambridge University Press, New York (1991)

    Book  Google Scholar 

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Correspondence to Yang Li .

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Assadi, S., Khanna, S., Li, Y., Vohra, R. (2015). Fast Convergence in the Double Oral Auction. 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_5

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  • DOI: https://doi.org/10.1007/978-3-662-48995-6_5

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