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A dynamic recontracting process for multiple-type housing markets

  • Klaus, Bettina
  • Bochet, Olivier
  • Walzl, Markus

Abstract We consider multiple-type housing markets. To capture the dynamic aspect of trade in such markets, we study a dynamic recontracting process similar to the one introduced by Serrano and Volij (2008). First, we analyze the set of recurrent classes of this process as a (non-empty) solution concept. We show that each core allocation always constitutes a singleton recurrent class and provide examples of non-singleton recurrent classes consisting of blocking-cycles of individually rational allocations. For multiple-type housing markets stochastic stability never serves as a selection device among recurrent classes. Next, we propose a method to compute the limit invariant distribution of the dynamic recontracting process. Furthermore, we discuss how the limit invariant distribution is influenced by the relative coalitional stability and accessibility of the different stochastically stable allocations. We illustrate our findings with several examples. In particular, we demonstrate that some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.

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

Volume (Year): 47 (2011)
Issue (Month): 1 (January)
Pages: 84-98

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Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:84-98
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
  2. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
  3. Roberto Serrano & Oscar Volij, 2003. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economics Working Papers 0029, Institute for Advanced Study, School of Social Science.
  4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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  7. Klaus, Bettina & Bochet, Olivier & Walzl, Markus, 2011. "A dynamic recontracting process for multiple-type housing markets," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 84-98, January.
  8. Klaus,Bettina, 2005. "The Coordinate-Wise Core for Multiple-Type Housing Markets is Second-Best Incentive Compatible," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
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  13. Neuefeind, Wilhelm, 1974. "A stochastic bargaining process for n-person games," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 175-191, August.
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