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Dynamic Recontracting processes with Multiple Indivisible Goods

Author

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  • Bochet Olivier
  • Klaus Bettina
  • Walzl Markus

    (METEOR)

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 (2005). 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. The limit invariant distribution exploits the interplay of coalitional stability and accessibility that determines a probability distribution over final allocations. We provide various examples to demonstrate how the limit invariant distribution discriminates among stochastically stable allocations: surprisingly, some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.

Suggested Citation

  • Bochet Olivier & Klaus Bettina & Walzl Markus, 2007. "Dynamic Recontracting processes with Multiple Indivisible Goods," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2007018
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    References listed on IDEAS

    as
    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. BOCHET, Olivier & KLAUS, Bettina & WALZL, Markus, 2007. "Dynamic recontracting processes with multiple indivisible goods," CORE Discussion Papers 2007061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
    5. Ken Binmore & Larry Samuelson & Petyon Young, 2003. "Equilibrium Selection in Bargaining Models," Levine's Bibliography 506439000000000466, UCLA Department of Economics.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    8. 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.
    9. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    10. Agastya, Murali, 2004. "Stochastic stability in a double auction," Games and Economic Behavior, Elsevier, vol. 48(2), pages 203-222, August.
    11. Neuefeind, Wilhelm, 1974. "A stochastic bargaining process for n-person games," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 175-191, August.
    12. 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.
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    Cited by:

    1. BOCHET, Olivier & KLAUS, Bettina & WALZL, Markus, 2007. "Dynamic recontracting processes with multiple indivisible goods," CORE Discussion Papers 2007061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.

    More about this item

    Keywords

    microeconomics ;

    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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