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A Dynamic Recontracting Process for Multiple-Type Housing Markets

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  • Bettina Klaus
  • Olivier Bochet
  • Markus Walzl

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 inuenced by the relative coalitional stability and accessibility of the different stochastically stable allocations. We illustrate our finndings 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.

Suggested Citation

  • Bettina Klaus & Olivier Bochet & Markus Walzl, 2010. "A Dynamic Recontracting Process for Multiple-Type Housing Markets," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 10.02, Université de Lausanne, Faculté des HEC, DEEP.
  • Handle: RePEc:lau:crdeep:10.02
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    References listed on IDEAS

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    1. Klaus, Bettina, 2008. "The coordinate-wise core for multiple-type housing markets is second-best incentive compatible," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 919-924, September.
    2. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
    5. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    6. Kawasaki, Ryo, 2010. "Farsighted stability of the competitive allocations in an exchange economy with indivisible goods," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 46-52, January.
    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. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
    9. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    10. 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.
    11. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    12. Agastya, Murali, 2004. "Stochastic stability in a double auction," Games and Economic Behavior, Elsevier, vol. 48(2), pages 203-222, August.
    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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    Cited by:

    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. 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.

    More about this item

    Keywords

    core; indivisible goods; limit invariant distribution; stochastic stability;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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