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Quality Cycles and the Strategic Manipulation of Value

Qatar Campus, H. John Heinz III School of Public Policy and Management, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213
Research Group for Operations Research and Nonlinear Dynamical Systems, Vienna University of Technology, Argentinierstrasse 8, A-1040 Vienna, Austria
Research Group for Operations Research and Nonlinear Dynamical Systems, Vienna University of Technology, Argentinierstrasse 8, A-1040 Vienna, Austria
Research Group for Operations Research and Nonlinear Dynamical Systems, Vienna University of Technology, Argentinierstrasse 8, A-1040 Vienna, Austria
caulkins{at}cmu.edu
gustav.feichtinger+e105{at}tuwien.ac.at
josef.leopold.haunschmied+e105{at}tuwien.ac.at
gernot.tragler+e105{at}tuwien.ac.at

We present a two-state, one-control model of a seller's decision about how good a "deal" to give customers when price and quantity are observable, but the customer does not observe quality until after committing to the transaction, so the quality of the bargain affects future demand only indirectly by influencing the reputation of the seller. This situation describes well the markets for many illicit drugs. Analysis reveals two optimal strategies: converging to a unique steady state with a positive sales volume or exploiting the initial customer base by selling cut-rate products until the seller's reputation is so bad that sales go to zero. Numerical analysis with parameters based on the U.S. cocaine market shows that there is a so-called Dechert-Nishimura-Skiba (DNS) curve in the state space, where the seller is indifferent between these two strategies. Convergence to the steady state with positive sales is oscillatory. Because different sellers may be at different phases of the oscillation at any given time, this oscillation implies that a population of homogenous sellers can generate dispersion in market prices—a phenomenon characteristic of drug markets that has been difficult to explain.

Subject classifications: dynamic programming/optimal control: multiple equilibria, Dechert-Nishimura-Skiba thresholds; marketing: pricing, competition strategy; judicial/legal: drug markets, prices.
History: Received September 2002; revision received February 2005; accepted August 2005.