2015/12/08 by Pradeep Dubey, Siddhartha Sahi, Dubey, Pradeep +3
Decision Sciences · Economics, Econometrics and Finance · #91B64 #Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #Economic Theory and Institutions #Economic theories and models #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.1512.02317
openalex publication_date 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 MG that satisfies some natural conditions of "fairness" and "convenience". Let \mathfrakM(m) denote the class of mechanisms MG obtained by varying G on the commodity set \1,…,m\ . We define the complexity of a mechanism M in \mathfrakM(m) to be a certain pair of integers τ(M),π(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≠ j). This induces a quasiorder \preceq on \mathfrakM(m) by the rule M\preceq M′ifτ(M)≤τ(M′)andπ(M)≤π(M′). We show that, for m>3, there are precisely three \preceq-minimal mechanisms MG in \mathfrakM(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 λ,μ>0, the star mechanism is the unique minimizer of λτ(M)+μπ(M) on \mathfrakM(m) for large enough m.