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A Strategic Market Game with Active Bankruptcy

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Abstract

We construct stationary Markov equilibria for an economy with fiat money, one non-durable commodity, countably-many time periods, and a continuum of agents. The total production of commodity remains constant, but individual agents' endowments fluctuate in a random fashion, from period to period. In order to hedge against these random fluctuations, agents find it useful to hold fiat money which they can borrow or deposit at appropriate rates of interest; such activity may take place either at a central bank (which fixes interest rates judiciously) or through a money-market (in which interest rates are determined endogenously). We carry out an equilibrium analysis, based on a careful study of Dynamic Programming equations and on properties of the Invariant Measures for associated optimally-controlled Markov chains. This analysis yields the stationary distribution of wealth across agents, as well as the stationary price (for the commodity) and interest rates (for the borrowing and lending of fiat money). A distinctive feature of our analysis is the incorporation of bankruptcy, both as a real possibility in an individual agent's optimization problem, as well as a determinant of interest rates through appropriate balance equations. These allow a central bank (respectively, a money-market) to announce (respectively, to determine endogenously) interest rates in a way that conserves the total money-supply and controls inflation. General results are provided for the existence of such stationary equilibria, and several explicitly solvable examples are treated in detail.

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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 1183.

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Length: 42 pages
Date of creation: Jun 1998
Date of revision:
Publication status: Published in Journal of Mathematical Economics (2000), 34(3): 359-396
Handle: RePEc:cwl:cwldpp:1183

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References

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  1. Hohn Miller & Martin Shubik, 1994. "Some dynamics of a strategic market game with a large number of agents," Journal of Economics, Springer, vol. 60(1), pages 1-28, February.
  2. Karatzas, Ioannis & Shubik, Martin & Sudderth, William D., 1997. "A strategic market game with secured lending," Journal of Mathematical Economics, Elsevier, vol. 28(2), pages 207-247, September.
  3. John Geanakoplos & Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1998. "A Strategic Market Game with Active Bankruptcy," Cowles Foundation Discussion Papers 1183, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
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Cited by:
  1. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1997. "A Stochastic Infinite-Horizon Economy with Secured Lending, or Unsecured Lending and Bankruptcy," Cowles Foundation Discussion Papers 1156, Cowles Foundation for Research in Economics, Yale University.
  2. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 2000. "A Stochastic Overlapping Generations Economy with Inheritance," Cowles Foundation Discussion Papers 1262, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. Kannai, Yakar & Rosenm├╝ller, Joachim, 2010. "Strategic behavior in financial markets," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 148-162, March.
  5. John Geanakoplos & Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1998. "A Strategic Market Game with Active Bankruptcy," Cowles Foundation Discussion Papers 1183, Cowles Foundation for Research in Economics, Yale University.
  6. Juergen Huber & Martin Shubik & Shyam Sunder, 2011. "Financing of Public Goods through Taxation in a General Equilibrium Economy: Theory and Experimental Evidence," Cowles Foundation Discussion Papers 1830, Cowles Foundation for Research in Economics, Yale University.
  7. Kannai,Y. & Rosenmueller,J., 2003. "Strategic behavior on financial markets," Working Papers 351, Bielefeld University, Center for Mathematical Economics.
  8. 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.
  9. Juergen Huber & Martin Shubik & Shyam Sunder, 2011. "Financing of Public Goods through Taxation in a General Equilibrium Economy: Experimental Evidence," Cowles Foundation Discussion Papers 1830R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2013.
  10. Takeoka, Norio, 2003. "On the consistency of stationary Markov equilibria with an exogenous distribution," Journal of Economic Theory, Elsevier, vol. 113(2), pages 316-324, December.
  11. 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.

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