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Minimally complex exchange mechanisms: Emergence of prices, markets, and money

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  • Pradeep Dubey
  • Siddhartha Sahi
  • Martin Shubik

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 integers 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; and 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.

Suggested Citation

  • Pradeep Dubey & Siddhartha Sahi & Martin Shubik, 2014. "Minimally complex exchange mechanisms: Emergence of prices, markets, and money," Department of Economics Working Papers 14-01, Stony Brook University, Department of Economics.
    • Handle: RePEc:nys:sunysb:14-01
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    Cited by:

    1. Jacques Melitz, 2019. "Some Doubts about the Economic Analysis of the Flow of Silver to China in 1550–1820," Open Economies Review, Springer, vol. 30(1), pages 105-131, February.
    2. Martin Shubik, 2016. "Three Essays on the Theory of Money and Financial Institutions Essay 3: The Economy with Innovation, Externalities and Context," Cowles Foundation Discussion Papers 2067, Cowles Foundation for Research in Economics, Yale University.
    3. Dubey, Pradeep & Sahi, Siddhartha & Shubik, Martin, 2018. "Money as minimal complexity," Games and Economic Behavior, Elsevier, vol. 108(C), pages 432-451.
    4. Martin Shubik, 2018. "The Paradox of Competition: Power, Markets, and Money - Who Gets What, When, How"," Cowles Foundation Discussion Papers 2118R, Cowles Foundation for Research in Economics, Yale University.
    5. Martin Shubik, 2018. "Who Gets What, When, How? Power, Organization, Markets, Money and the Allocation of Resources," Cowles Foundation Discussion Papers 3018, Cowles Foundation for Research in Economics, Yale University.
    6. Martin Shubik, 2018. "Who Gets What, When, How" Power, Organization, Markets, Money and the Allocation of Resources," Cowles Foundation Discussion Papers 2118, Cowles Foundation for Research in Economics, Yale University.

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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