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Markovian Core, Indivisibility, and Successive Pareto-Improvements

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  • Satoru Fujishige
  • Zaifu Yang

Abstract

We study a general barter market in which every agent is initially endowed with several inherently indivisible items and wishes to exchange with other agents. There is no medium of exchange like money. Agents have general preferences over bundles of items and may acquire several items. It is well-known that the core of such an economy is typically empty. We propose a new but more general notion of core called a Markovian core. A Markovian core allocation is individually rational, but Pareto-efficient and stable against any possible coalition deviation by comparison with their current assignments instead of their initial endowments. We show that the market has always a nonempty strict Markovian core through a decentralized Pareto-improvement process.

Suggested Citation

  • Satoru Fujishige & Zaifu Yang, 2019. "Markovian Core, Indivisibility, and Successive Pareto-Improvements," Discussion Papers 19/11, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:19/11
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    References listed on IDEAS

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    1. Chen, Bo & Fujishige, Satoru & Yang, Zaifu, 2016. "Random decentralized market processes for stable job matchings with competitive salaries," Journal of Economic Theory, Elsevier, vol. 165(C), pages 25-36.
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    5. Inoue, Tomoki, 2008. "Indivisible commodities and the nonemptiness of the weak core," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 96-111, January.
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    More about this item

    Keywords

    Decentralized market; barter market; indivisibility; efficiency; stability; Markovian core.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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