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

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  • Kamiya, Kazuya
  • Talman, Dolf

Abstract

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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Bibliographic Info

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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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Matching model Money Stationary Markov perfect equilibria Non-linear complementarity problem;

References

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  1. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 97(4), pages 927-54, August.
  2. Rosenthal, R W, 1979. "Sequences of Games with Varying Opponents," Econometrica, Econometric Society, Econometric Society, vol. 47(6), pages 1353-66, November.
  3. Zhu, Tao, 2003. "Existence of a monetary steady state in a matching model: indivisible money," Journal of Economic Theory, Elsevier, vol. 112(2), pages 307-324, October.
  4. 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.
  5. Zhou, Ruilin, 1999. "Individual and Aggregate Real Balances in a Random-Matching Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 1009-38, November.
  6. P. A. Diamond, 1982. "Money in Search Equilibrium," Working papers 297, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Diamond, Peter A, 1982. "Wage Determination and Efficiency in Search Equilibrium," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 49(2), pages 217-27, April.
  8. Laan, Gerard van der, 1982. "Simplicial approximation of unemployment equilibria," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 83-97, January.
  9. Kazuya Kamiya & Takashi Sato, 2004. "Equilibrium Price Dispersion in a Matching Model with Divisible Money," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 413-430, 05.
  10. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(2), pages 575-606, 05.
  11. Green, Edward J. & Zhou, Ruilin, 1998. "A Rudimentary Random-Matching Model with Divisible Money and Prices," Journal of Economic Theory, Elsevier, vol. 81(2), pages 252-271, August.
  12. Kazuya Kamiya & Takashi Shimizu, 2007. "Existence of Equilibria in Matching Models of Money: A New Technique," Economic Theory, Springer, Springer, vol. 32(3), pages 447-460, September.
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Cited by:
  1. Sylvain Béal & Eric Rémila & Philippe Solal, 2012. "Axioms of Invariance for TU-games," Working Papers 2012-01, CRESE.

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