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A Strategic Market Game with Active Bankruptcy

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Author Info

  • J. Geanakoplos
  • I. Karatzas
  • M. Shubik
  • W. Sudderth

Abstract

We construct stationary Markov equilibria for an economy with fiat money, one nondurable 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, and 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 in ation. General results are provided for the existence of such stationary equilibria, and several explicitly solvable examples are treated in detail. Submitted to Journal of Mathematical Economics.

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Bibliographic Info

Paper provided by Santa Fe Institute in its series Working Papers with number 99-04-025.

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Date of creation: Apr 1999
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Handle: RePEc:wop:safiwp:99-04-025

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Keywords: Stochastic games; bankruptcy; strategic market games; parallel dynamic programs; theory of money;

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References

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  1. 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.
  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. 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.
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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. 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.
  3. Kannai, Yakar & Rosenm├╝ller, Joachim, 2010. "Strategic behavior in financial markets," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 148-162, March.
  4. 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.
  5. I. Karatzas & M. Shubik & W. Sudderth, 2000. "A Stochastic Overlapping Generations Economy with Inheritance," Working Papers 00-04-023, Santa Fe Institute.
  6. 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.
  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. 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.
  9. Kannai,Y. & Rosenmueller,J., 2003. "Strategic behavior on financial markets," Working Papers 351, Bielefeld University, Center for Mathematical Economics.
  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. 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.

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