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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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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Pradeep Dubey & Siddhartha Sahi & Martin Shubik, 2015. "Money as Minimal Complexity," Department of Economics Working Papers 15-01, Stony Brook University, Department of Economics.

    More about this item

    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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