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Construction of Stationary Markov Equilibria in a Strategic Market Game

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Abstract

This paper studies stationary noncooperative equilibria in an economy with fiat money, one nondurable commodity, countably many time periods, no credit or futures market, and a measure space of agents -- who may differ in their preferences and in the distributions of their (random) endowments. These agents are immortal, and hold fiat money as a means of hedging against the random fluctuations in their endowments of the commodity. In the aggregate, these fluctuations offset each other, and equilibrium prices are constant. We carry out an equilibrium analysis that focuses on distribution of wealth, on consumption, and on price formation. A careful analysis of the one-agent, infinite-horizon optimization problem, and of the invariant measure for the associated optimally controlled Markov chain, leads by aggregation to a stationary noncooperative or competitive equilibrium. This consists of a price for the commodity and of a distribution of wealth across agents which, under appropriate simple strategies for the agents, stay fixed from period to period and preserve the basic quantities of the model. We hope that, in future work, we shall be able to address additional features of the model treated here, such as borrowing and lending at appropriate (endogenously determined) interest rates, the endogenous production of the commodity, overlapping generations of agents, and bankruptcy and treatment of creditors.

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File URL: http://cowles.econ.yale.edu/P/cd/d10a/d1033.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1033.

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Length: 44 pages
Date of creation: Oct 1992
Date of revision:
Publication status: Published in Mathematics of Operations Research (November 1994), 19(4): 975-1006
Handle: RePEc:cwl:cwldpp:1033

Note: CFP 884.
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  1. Deaton, A., 1989. "Saving And Liquidity Constraints," Papers 153, Princeton, Woodrow Wilson School - Public and International Affairs.
  2. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
  3. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  4. Mendelssohn, Roy & Sobel, Matthew J., 1980. "Capital accumulation and the optimization of renewable resource models," Journal of Economic Theory, Elsevier, vol. 23(2), pages 243-260, October.
  5. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
  6. Martin Shubik & Ward Whitt, 1973. "Fiat Money in an Economy with One Nondurable Good and No Credit (A Noncooperative Sequential Game)," Cowles Foundation Discussion Papers 355, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. John H. Miller & Martin Shubik, 1992. "Some Dynamics of a Strategic Market Game with a Large Number of Agents," Cowles Foundation Discussion Papers 1037, Cowles Foundation for Research in Economics, Yale University.
  2. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1995. "A Strategic Market Game with Secured Lending," Cowles Foundation Discussion Papers 1099, Cowles Foundation for Research in Economics, Yale University.
  3. Miao, Jianjun, 2006. "Competitive equilibria of economies with a continuum of consumers and aggregate shocks," Journal of Economic Theory, Elsevier, vol. 128(1), pages 274-298, May.
  4. Andrzej Nowak & Eilon Solan & Sylvain Sorin, 2013. "Preface: Special Issue on Stochastic Games," Dynamic Games and Applications, Springer, vol. 3(2), pages 125-127, June.
  5. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
  6. Cheng-Zhong Qin & Martin Shubik, 2009. "Selecting a Unique Competitive Equilibrium with Default Penalties," Cowles Foundation Discussion Papers 1712, Cowles Foundation for Research in Economics, Yale University.
  7. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 2008. "Financial Control of a Competitive Economy without Randomness," Cowles Foundation Discussion Papers 1681, Cowles Foundation for Research in Economics, Yale University.
  8. John Geanakoplos & Ioannis Karatzas & Martin Shubik & William D. Sudderth, 2009. "Inflationary Equilibrium in a Stochastic Economy with Independent Agents," Cowles Foundation Discussion Papers 1708, Cowles Foundation for Research in Economics, Yale University.
  9. Martin Shubik, 2011. "The Present and Future of Game Theory," Cowles Foundation Discussion Papers 1808, Cowles Foundation for Research in Economics, Yale University.
  10. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 2000. "Information and the Existence of Stationary Markovian Equilibrium," Cowles Foundation Discussion Papers 1261, Cowles Foundation for Research in Economics, Yale University.
  11. I. Karatzas & M. Shubik & W. Sudderth, 2000. "A Stochastic Overlapping Generations Economy with Inheritance," Working Papers 00-04-023, Santa Fe Institute.
  12. Martin Shubik & Nicolaas J. Vriend, 1999. "A Behavioral Approach to a Strategic Market Game," Research in Economics 99-01-003e, Santa Fe Institute.
  13. Martin Shubik, 1993. "The Theory of Money and Financial Institutions," Cowles Foundation Discussion Papers 1056, Cowles Foundation for Research in Economics, Yale University.
  14. Pradeep Dubey & John Geanakoplos, 2000. "Inside and Outside Money, Gains to Trade, and IS-LM," Cowles Foundation Discussion Papers 1257, Cowles Foundation for Research in Economics, Yale University.
  15. Barbara Bennie, 2009. "Strategic market games with cyclic endowments," Annals of Finance, Springer, vol. 5(2), pages 209-230, March.
  16. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," CORE Discussion Papers 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Piotr Więcek, 2009. "Pure equilibria in a simple dynamic model of strategic market game," Computational Statistics, Springer, vol. 69(1), pages 59-79, March.

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