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Money as Minimal Complexity

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  • Pradeep Dubey
  • Siddhartha Sahi
  • Martin Shubik

Abstract

We consider mechanisms that provide the opportunity to exchange commodity i for commodity j, for certain ordered pairs ij. Given any connected graph G of opportunities, we show that there is a unique “G-mechanism” that satisfies some natural conditions of “fairness” and “convenience”. Next we define time and price complexity for any G-mechanism as (respectively) the time required to exchange i for j, and the information needed to determine the exchange ratio (each for the worst pair ij). If the number of commodities exceeds three, there are precisely three minimally complex G-mechanisms, where G corresponds to the star, cycle and complete graphs. The star mechanism has a distinguished commodity — the money — that serves as the sole medium of exchange and mediates trade between decentralized markets for the other commodities. Furthermore, for any weighted sum of complexities, the star mechanism is the unique minimizer of the sum for large enough m.
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Suggested Citation

  • Pradeep Dubey & Siddhartha Sahi & Martin Shubik, 2015. "Money as Minimal Complexity," Department of Economics Working Papers 15-01, Stony Brook University, Department of Economics.
  • Handle: RePEc:nys:sunysb:15-01
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    References listed on IDEAS

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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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