Money as Minimal Complexity

Pradeep Dubey, Siddhartha Sahi and Martin Shubik
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Siddhartha Sahi: Dept. of Mathematics, Rutgers University

No 1990, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We consider mechanisms that provide traders 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 mechanism M_G that satisfies some natural conditions of "fairness" and "convenience." Let \cal{M}(m) denote the class of mechanisms M_G obtained by varying G on the commodity set {1,...,m}. We define the complexity of a mechanism M in \cal{M}(m) to be a pair of integers \tau(M), \pi(M) which represent the "time" required to exchange i for j and the "information" needed to determine the exchange ratio (each in the worst case scenario, across all i not equal to i \ne j). This induces a quasiorder \preceq on \cal{M}(m) by the rule M \preceq M' if tau(M) \le \tau(M') and \pi(M) \le \pi(M'). We show that, for m > 3, there are precisely three \preceq-minimal mechanisms M_G in \cal{M}(m), 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. Our main result is that, for any weights \lambda, \mu > 0; the star mechanism is the unique minimizer of \lambda\tau(M) + \mu\pi(M) on \cal{M}(m) for large enough m.

Keywords: Exchange mechanism; Minimal complexity; Prices; money (search for similar items in EconPapers)
JEL-codes: C70 C72 C79 D44 D63 D82 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2015-02
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Money as minimal complexity (2018)
Working Paper: Money as Minimal Complexity (2015)
Working Paper: Money as Minimal Complexity (2015)
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