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Uncertainty, instrument choice, and the uniqueness of Nash equilibrium: microeconomic and macroeconomic examples

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  • Dale W. Henderson
  • Ning S. Zhu

Abstract

This paper contains two examples of static, symmetric, positive-sum games with two strategic players and a play by nature: (1) a microeconomic game between duopolists with joint costs facing uncertain demands for differentiated goods and (2) a macroeconomic game between two countries' with inflation-bias preferences confronting uncertain demands for moneys. In both examples, each player can choose either of two variables as an instrument, and reaction functions are linear in the chosen instruments. With no uncertainty, there are four (Nash) equilibria, one for each possible instrument pair, because each player is indifferent between instruments given the instrument choice and instrument value of the other player. With uncertainty in the form of an additive disturbance, there are fewer equilibria because each player is not indifferent between instruments. These results are in accordance with the logic of Poole (1970) and Weitzman (1974) as explained by Klemperer and Meyer (1986) using examples of differentiated duopoly games with independent costs. In their main example with linear reaction functions, there is always a unique equilibrium. In contrast, in each of our examples with uncertainty, there is a unique equilibrium for some parameter values, but there are two equilibria for others. It is somewhat surprising that in both the Klmperer and Meyer example and our examples with unique equilibria, for some parameter values with the smallest amount of uncertainty the symmetric instrument pair chosen in the unique equilibrium is the one that yields the lower payoff with no uncertainty.

Suggested Citation

  • Dale W. Henderson & Ning S. Zhu, 1995. "Uncertainty, instrument choice, and the uniqueness of Nash equilibrium: microeconomic and macroeconomic examples," International Finance Discussion Papers 526, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgif:526
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    References listed on IDEAS

    as
    1. Martin L. Weitzman, 1974. "Prices vs. Quantities," Review of Economic Studies, Oxford University Press, vol. 41(4), pages 477-491.
    2. Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
    3. Canzoneri, Matthew B. & Henderson, Dale W., 1988. "Is sovereign policymaking bad?," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 28(1), pages 93-140, January.
    4. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    5. William Poole, 1969. "Optimal choice of monetary policy instruments in a simple stochastic macro model," Special Studies Papers 2, Board of Governors of the Federal Reserve System (U.S.).
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    7. Turnovsky, Stephen J & d'Orey, Vasco, 1986. "Monetary Policies in Interdependent Economies with Stochastic Disturbances: A Strategic Approach," Economic Journal, Royal Economic Society, vol. 96(383), pages 696-721, September.
    8. Matthew B. Canzoneri & Dale W. Henderson, 1991. "Monetary Policy in Interdependent Economies: A Game-Theoretic Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262031787, January.
    9. Giavazzi, Francesco & Giovannini, Alberto, 1989. "Monetary Policy Interactions under Managed Exchange Rates," Economica, London School of Economics and Political Science, vol. 56(222), pages 199-213, May.
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    11. Dale Henderson & Ning Zhu, 1990. "Uncertainty and the choice of instruments in a two-country monetary-policy game," Open Economies Review, Springer, vol. 1(1), pages 39-65, February.
    12. Leonard Cheng, 1985. "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 146-152, Spring.
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