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Minimally Complex Exchange Mechanisms: Emergence of Prices, Markets, and Money

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Abstract

We consider abstract exchange mechanisms wherein individuals submit "diversified" offers in m commodities, which are then redistributed to them. Our first result is that if the mechanism satisfies certain natural conditions embodying "fairness" and "convenience" then it admits unique prices, in the sense of consistent exchange-rates across commodity pairs ij that equalize the valuation of offers and returns for each individual. We next define certain integers tau_{ij}, pi_{ij}, and k_{i} which represent the "time" required to exchange i for j, the "difficulty" in determining the exchange ratio, and the "dimension" of the offer space in i; we refer to these as time-, price- and message-complexity of the mechanism. Our second result is that there are only a finite number of minimally complex mechanisms, which moreover correspond to certain directed graphs G in a precise sense. The edges of G can be regarded as markets for commodity pairs, and prices play a stronger role in that the return to a trader depends only on his own offer and the prices. Finally we consider "strongly" minimal mechanisms, with smallest "worst case" complexities tau = max tau_{ij} and pi = max pi_{ij}. Our third main result is that for m > 3 commodities that there are precisely three such mechanisms, which correspond to the star, cycle, and complete graphs, and have complexities (pi,tau) = (4,2), (2,m - 1), (m^{2} - m, 1) respectively. Unlike the other two mechanisms, the star mechanism has a distinguished commodity -- the money -- that serves as the sole medium of exchange. As m approaches infinity it is the only mechanism with bounded (pi,tau).

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1945.

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Length: 43 pages
Date of creation: Apr 2014
Date of revision:
Handle: RePEc:cwl:cwldpp:1945

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Keywords: Exchange mechanism; Minimal complexity; Prices; Markets; Money;

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References

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  1. Hahn, F H, 1971. "Equilibrium with Transaction Costs," Econometrica, Econometric Society, vol. 39(3), pages 417-39, May.
  2. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
  3. Dubey, Pradeep & Geanakoplos, John, 2003. "From Nash to Walras via Shapley-Shubik," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 391-400, July.
  4. Howitt, Peter & Clower, Robert, 2000. "The emergence of economic organization," Journal of Economic Behavior & Organization, Elsevier, vol. 41(1), pages 55-84, January.
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  7. Foley, Duncan K., 1970. "Economic equilibrium with costly marketing," Journal of Economic Theory, Elsevier, vol. 2(3), pages 276-291, September.
  8. Li, Yiting & Wright, Randall, 1998. "Government Transaction Policy, Media of Exchange, and Prices," Journal of Economic Theory, Elsevier, vol. 81(2), pages 290-313, August.
  9. Dubey, Pradeep, 1982. "Price-Quantity Strategic Market Games," Econometrica, Econometric Society, vol. 50(1), pages 111-26, January.
  10. Heller, Walter Perrin, 1974. "The holding of money balances in general equilibrium," Journal of Economic Theory, Elsevier, vol. 7(1), pages 93-108, January.
  11. Joseph M. Ostroy & Ross M. Starr, 1973. "Money and the Decentralization of Exchange," Cowles Foundation Discussion Papers 349, Cowles Foundation for Research in Economics, Yale University.
  12. Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
  13. Banerjee, Abhijit V & Maskin, Eric S, 1996. "A Walrasian Theory of Money and Barter," The Quarterly Journal of Economics, MIT Press, vol. 111(4), pages 955-1005, November.
  14. Joseph M. Ostroy, 1972. "The Informational Efficiency of Monetary Exchange," UCLA Economics Working Papers 021, UCLA Department of Economics.
  15. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-54, August.
  16. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-68, October.
  17. Kiyotaki, Nobuhiro & Wright, Randall, 1993. "A Search-Theoretic Approach to Monetary Economics," American Economic Review, American Economic Association, vol. 83(1), pages 63-77, March.
  18. Dubey, Pradeep & Sahi, Siddhartha, 2003. "Price-mediated trade with quantity signals: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 377-389, July.
  19. Menger, Carl, 1892. "On the Origins of Money," History of Economic Thought Articles, McMaster University Archive for the History of Economic Thought, vol. 2, pages 239-255.
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