History's Role in Coordinating Decentralized Allocation Decisions:
Laboratory Evidence on Repeated Binary Allocation Games
Donald M. Meyer, John B. Van Huyck, Raymond C. Battalio, and Thomas R. Saving
May 1991
[ Introduction | Conclusion | References | John's Web ]
Abstract: What causes individual suppliers to allocate goods in such a way that the aggregate allocation satisfies the law of one price? A satisfactory answer to this question must confront two related problems: Equal net prices at all locations provide no information to suppliers about the quantity to deliver to a specific location and strategic uncertainty makes an observed violation of the law of one price an unreliable indicator of a profit opportunity. This paper develops a simple analytical framework to formalize these two problems, reviews some solutions found in the literature, and reports laboratory evidence on how people solve them. In addressing these issues, we focus on the role historical prices play in coordinating decentralized allocation decisions.
Acknowledgments: We would like to thank the National Science Foundation (SES-8911032) for financial support.
© 1991 by the authors. All rights reserved.
A central result in price theory is the law of one price, which states that in a competitive economy the price net of transportation costs for a homogenous good sold at different locations will be equal. A corollary to the law of one price is that the risk adjusted rates of return for investment in alternative industries must be equal. Ignoring for a moment what Varian (1978;p.188) calls the "elaborate mythology" of the Walrasian auctioneer, what causes individual suppliers to allocate goods or capital in such a way that the aggregate allocation satisfies the law of one price? The usual answer to this question is that a violation of the law of one price not only provides information that efficiency requires a reallocation of goods or capital, but also provides suppliers with a pecuniary incentive to reallocate goods or capital in the prescribed manner.
There are two related problems with the conventional answer. First, if prices or rates of return across markets are equal, there is no pecuniary incentive to conform to the equilibrium allocation of goods and capital. The equilibrium prices or rates of return, in and of themselves, provide neither the information not the incentive needed to implement the equilibrium allocation. Second, if prices or rates of return across markets are not equal, strategic uncertainty makes an observed violation of the law of one price an unreliable indicator of a profit opportunity, because the profitability of responding to an observed violation depends on how other suppliers respond. For example, economists are notorious for their unwillingness to invest in a business venture where current participants are earning supra-normal returns, because, by the time the investment is made, entry by others will have wiped out the opportunity for supra-normal returns. Suppliers must coordinate their response to an observed violation of the law of one price if their responses are to be mutually profitable.
In sum, when the law of one price is satisfied suppliers confront an information/incentive problem, and when the law of one price is violated they confront a coordination problem. This paper develops a simple analytical framework to formalize these problems, reviews some solutions found in the literature, and reports laboratory evidence on how people actually solve them. In addressing these issues, we focus on the role historical prices play in coordinating decentralized allocation decisions.
[ Top | Introduction | Conclusion | References | John's Web ]
This paper has reported laboratory evidence on repeated binary allocation games. The experiments provide support for the view that disequilibrium dynamics are an important source of fluctuations in market prices and quantities. For example, historical violations of the law of one price were positively serially correlated in the baseline experiments, E(15). Apparently, naive subjects are aware that an historical violation of the law of one price does not reliably signal the existence of a profit opportunity, because the profitability of responding to the information depends on how other suppliers respond. Hence, naive subjects allowed violations to persist. Nevertheless, the symmetric equilibrium accurately predicted the average quantity supplied, the average price, and the average market efficiency in the baseline experiments, E(15).
Experiments using 60 repetitions of the binary allocation game, E(60), failed to convergence to a pure strategy equilibrium. Naive subjects were not able to learn to coordinate on useful precedents. While naive subjects learn to respond to systematic violations of the law of one price, this behavior produces non-stationary, rather than equilibrium, time series for market aggregates. We suspect that this non-stationary disequilibrium dynamics may be difficult to organize in a theory and note that again the symmetric equilibrium accurately predicted the average quantity supplied, the average price, and the average market efficiency in E(60). Experiments using a linear, rather than iso-elastic, market demand function also failed to converge to a pure strategy equilibrium in 60 periods.
In sharp contrast to naive subjects, experienced subjects used historical precedents to coordinate on pure strategy equilibrium outcomes. One interpretation of the contrast between long runs with naive subjects and short runs with experienced subjects is that precedent is a fragile coordination mechanism in these binary allocation games. If subjects do not expect to solve the allocation problem using precedents initially, it appears to be difficult for the group to learn to coordinate on historical precedents in these binary allocation games.
[ Top | Introduction | Conclusion | References | John's Web ]
Crawford, Vincent, and Hans Haller, "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica 58, 1990, 571-95.
Debreu, Gerard, Theory of Value: An Axiomatic Analysis of Economic Equilibrium, (New Haven: Yale University Press, 1959).
Diamond, Peter, A Search-Equilibrium Approach to the Micro Foundations of Macroeconomics, (Cambridge: The MIT Press, 1984).
Ezekiel, Mordecai, "The Cobweb Theorem", Quarterly Journal of Economics, 52, February 1938; p. 255-80.
Fisher, Franklin, Disequilibrium Foundations of Equilibrium Economics, (Cambridge: Cambridge University Press, 1983).
Lewis, David, Convention: a philosophical study, (Cambridge: Harvard University Press, 1969).
Marshall, Alfred, Principles of Economics: an introductory volume, eighth edition, (London: McMillan, 1966).
Muth, John F., "Rational Expectations and the Theory of Price Movements," Econometrica, vol. 29, no.6, 1961.
Ochs, Jack, "The Coordination Problem in Decentralized Markets: An Experiment," Quarterly Journal of Economics, May 1990.
O'Driscoll, Jr., Gerald P., Economics as a Coordination Problem: The Contributions of Friedrich A. Hayek, (Kansas City: Sheed Andrews and McMeel, 1977).
Phelps, Edmund S., et.al., Microeconomic Foundations of Employment and Inflation Theory, (New York: Norton & Company, 1970).
Saari, Donald G., "Iterative Price Mechanisms", Econometrica, 53(5), September 1985.
Shubik, Martin, A Game-Theoretic Approach to Political Economy, (Cambridge: The MIT Press, 1984).
Van Huyck, John B., Gillette, Ann B., and Battalio, Raymond C., "Credible Assignments in Non-Cooperative Games," Games and Economic Behavior, forthcoming.
Varian, Hal R., Microeconomic Analysis, (New York: W.W. Norton & Company, 1978).
[ Top | Introduction | Conclusion | References | John's Web ]