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A strategic market game with secured lending

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  • Karatzas, Ioannis
  • Shubik, Martin
  • Sudderth, William D.

Abstract

We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money market, and a continuum of agents. These use fiat money in order to offset random fluctuations in their endowments of the commodity, are not allowed to borrow more than they can pay back (secured lending), and maximize expected discounted utility from consumption of the commodity. Their aggregate optimal actions determine dynamically prices and/or interest rates for borrowing and lending, in each period of play. In equilibrium, random fluctuations in endowment- and wealth-levels offset each other, and prices and interest rates remain constant. As in our related recent work, KSS (1994), we study in detail the individual agents' dynamic optimization problems, and the invariance measures for the associated, optimally controlled Markov chains. By appropriate aggregation, these individual problems lead to the construction of stationary Markov competitive equilibrium for the economy as a whole. Several examples are studied in detail, fairly general existence theorems are established, and open questions are indicated for further research.
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  • 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.
  • Handle: RePEc:eee:mateco:v:28:y:1997:i:2:p:207-247
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    References listed on IDEAS

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    1. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    2. Levine, David K & Pesendorfer, Wolfgang, 1995. "When Are Agents Negligible?," American Economic Review, American Economic Association, vol. 85(5), pages 1160-1170, December.
    3. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    4. 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.
    5. Dubey, Pradeep, 1982. "Price-Quantity Strategic Market Games," Econometrica, Econometric Society, vol. 50(1), pages 111-126, January.
    6. Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
    7. Dubey, Pradeep & Mas-Colell, Andreau & Shubik, Martin, 1980. "Efficiency properties of strategies market games: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 22(2), pages 339-362, April.
    8. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1992. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Cowles Foundation Discussion Papers 1033, Cowles Foundation for Research in Economics, Yale University.
    9. 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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    1. repec:spr:compst:v:69:y:2009:i:1:p:59-79 is not listed on IDEAS
    2. Oderanti, Festus Oluseyi & De Wilde, Philippe, 2010. "Dynamics of business games with management of fuzzy rules for decision making," International Journal of Production Economics, Elsevier, vol. 128(1), pages 96-109, November.
    3. 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).
    4. Wozny Lukasz & Growiec Jakub, 2012. "Intergenerational Interactions in Human Capital Accumulation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-47, June.
    5. Martin Shubik & Nicolaas J. Vriend, 1999. "A Behavioral Approach to a Strategic Market Game," Research in Economics 99-01-003e, Santa Fe Institute.
    6. Piotr Więcek, 2009. "Pure equilibria in a simple dynamic model of strategic market game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 59-79, March.
    7. Geanakoplos, John & Karatzas, Ioannis & Shubik, Martin & Sudderth, William D., 2014. "Inflationary equilibrium in a stochastic economy with independent agents," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 1-11.
    8. 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.
    9. 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.
    10. Geanakoplos, J. & Karatzas, I. & Shubik, M. & Sudderth, W., 2000. "A strategic market game with active bankruptcy," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 359-396, November.
    11. 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.
    12. I. Karatzas & M. Shubik & W. Sudderth, 2000. "A Stochastic Overlapping Generations Economy with Inheritance," Working Papers 00-04-023, Santa Fe Institute.

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