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Matching models with a conservation law: The existence and global structure of the set of stationary equilibria

  • Kamiya, Kazuya
  • Talman, Dolf

We study random matching models where there is a set of infinitely lived agents, and in each period agents are pairwise matched to each other and play a stage game. We investigate the basic structure of equilibria in such models: the existence of equilibria and the global structure of the set of equilibria. Specifically, we focus on models with a conservation law, which typically holds in economies having some assets, such as money. In such models, under certain regularity conditions the set of equilibria is one-dimensional and each connected component of it is a piecewise smooth one-dimensional manifold being homeomorphic to either the unit circle or the unit interval. Moreover, in an endpoint of an interval all agents have the same amount of assets.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 5-6 (May)
Pages: 397-413

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Handle: RePEc:eee:mateco:v:45:y:2009:i:5-6:p:397-413
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  1. Herings, P.J.J. & Talman, A.J.J. & Zang, Z., 1994. "The computation of a continuum of constrained equilibria," Discussion Paper 1994-38, Tilburg University, Center for Economic Research.
  2. P. A. Diamond, 1982. "Money in Search Equilibrium," Working papers 297, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Ruilin Zhou, 1996. "Individual and aggregate real balances in a random matching model," Staff Report 222, Federal Reserve Bank of Minneapolis.
  4. Kazuya Kamiya & Takashi Shimizu, 2007. "On The Role Of Tax Subsidy Scheme In Money Search Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(2), pages 575-606, 05.
  5. Zhu, Tao, 2005. "Existence of a monetary steady state in a matching model: divisible money," Journal of Economic Theory, Elsevier, vol. 123(2), pages 135-160, August.
  6. Edward J. Green & Ruilin Zhou, 1996. "A Rudimentary Random-Matching Model with Divisible Money and Prices," GE, Growth, Math methods 9606001, EconWPA, revised 25 Jul 1996.
  7. Kazuya Kamiya & Takashi Shimizu, 2007. "Existence of Equilibria in Matching Models of Money: A New Technique," Economic Theory, Springer, vol. 32(3), pages 447-460, September.
  8. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-54, August.
  9. Laan, Gerard van der, 1982. "Simplicial approximation of unemployment equilibria," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 83-97, January.
  10. Kamiya, Kazuya & Shimizu, Takashi, 2006. "Real indeterminacy of stationary equilibria in matching models with divisible money," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 594-617, August.
  11. Diamond, Peter A, 1982. "Wage Determination and Efficiency in Search Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 217-27, April.
  12. Rosenthal, R W, 1979. "Sequences of Games with Varying Opponents," Econometrica, Econometric Society, vol. 47(6), pages 1353-66, November.
  13. Kamiya, K. & Sato, T., 2002. "Equilibrium Price Dispersion in a Matching Model with Divisible Money," Discussion Paper 2002-118, Tilburg University, Center for Economic Research.
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