Implicit Markets in Economics via Pairwise Matching

I explore a class of probabilistic pairwise matching social settings without formal prices. I nevertheless find that they may be interpreted as implicit markets, equilibrated by probabilities. The seminar focuses on two primary examples: I first explore a perfect foresight equilibrium of a directed search model of journal rejection rates when papers have uncertain quality. I then turn to a applications of implicit markets instead based on anonymous random matching. Here, I discuss passing games, such as an equilibrium model of prevalence rates with contagious diseases, and “cat and mouse” resource theft games as a foundation for a model of crime rates. I conclude with a model of counterfeit money, which merges these two games. The Economics of Counterfeiting∗ Elena Quercioli† Economics Department Central Michigan Lones Smith‡ Economics Department Wisconsin April 7, 2014 Abstract This paper develops a new tractable strategic theory of counterfeiting as a multimarket large game played by good and bad guys. There is free entry of bad guys, who choose whether to counterfeit, and what quality to produce. Opposing them is a continuum of good guys who select a costly verification effort. A counterfeiting equilibrium consists of a “cat and mouse” game between effort and quality, and a collateral “hotpotato” passing game among good guys. With log-concave verification costs, counterfeiters producer better quality at higher notes, but verifiers try sufficiently harder that the verification rate still rises. We prove that the passed and counterfeiting rates vanish for low and high notes. We develop and use a graphical framework for deducing comparative statics. Our theory applies to fixed-value counterfeits, like checks, money orders, or money. Focusing on counterfeit money, we assemble a unique data set from the U.S. Secret Service. We identify some new time series and cross-sectional patterns, and explain them: (1) the ratio of all counterfeit money (seized or passed) to passed money rises in the note, but less than proportionately; (2) the passed-circulation ratio rises in the note, and is very small at $1 notes; (3) the vast majority of counterfeit money used to be seized before circulation, but this is no longer true; and (4) the ratio of the internal Federal Reserve Banks passed rate to the economy-wide average falls in the note until the $100 note. Our theory explains how to estimate from data the counterfeiting rate, the street price of counterfeit notes, and the incredibly small costs expended verifying each note.This paper develops a new tractable strategic theory of counterfeiting as a multimarket large game played by good and bad guys. There is free entry of bad guys, who choose whether to counterfeit, and what quality to produce. Opposing them is a continuum of good guys who select a costly verification effort. A counterfeiting equilibrium consists of a “cat and mouse” game between effort and quality, and a collateral “hotpotato” passing game among good guys. With log-concave verification costs, counterfeiters producer better quality at higher notes, but verifiers try sufficiently harder that the verification rate still rises. We prove that the passed and counterfeiting rates vanish for low and high notes. We develop and use a graphical framework for deducing comparative statics. Our theory applies to fixed-value counterfeits, like checks, money orders, or money. Focusing on counterfeit money, we assemble a unique data set from the U.S. Secret Service. We identify some new time series and cross-sectional patterns, and explain them: (1) the ratio of all counterfeit money (seized or passed) to passed money rises in the note, but less than proportionately; (2) the passed-circulation ratio rises in the note, and is very small at $1 notes; (3) the vast majority of counterfeit money used to be seized before circulation, but this is no longer true; and (4) the ratio of the internal Federal Reserve Banks passed rate to the economy-wide average falls in the note until the $100 note. Our theory explains how to estimate from data the counterfeiting rate, the street price of counterfeit notes, and the incredibly small costs expended verifying each note. ∗This is a radical revision of a 2009 submission to this journal. The paper began in 2005 as “Counterfeit $$$”, as a model just of the hot potato game; the cat and mouse game was developed while Lones visited the Cowles Foundation in 2006. We have profited from the insights and/or data of Charles Bruce (Director, National Check Fraud Center), Pierre Duguay (Deputy Governor, Bank of Canada), Antti Heinonen (European Central Bank, Counterfeit Deterrence Chairman), Ruth Judson (Federal Reserve), John Mackenzie (counterfeit specialist, Bank of Canada), Stephen Morris, and Lorelei Pagano (former Special Agent, Secret Service) — as well as comments at I.G.I.E.R. (Bocconi), the 2006 Bonn Matching Conference, the 2006 SED in Vancouver, the Workshop on Money at the Federal Reserve Bank of Cleveland, Tulane, Michigan, the Bank of Canada, the 2007 NBER-NSF GE conference at Northwestern, the 2008 Midwest Theory Conference in Columbus, the 2011 Yale Summer Theory Conference, Maryland, Pittsburgh, Stanford, and Georgetown.