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Evolutionary dynamics and equitable core selection in assignment games

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  • Heinrich H. Nax
  • Bary S.R. Pradelski

Abstract

We study evolutionary dynamics in assignment games where many agents interact anonymously at virtually no cost. The process is decentralized, very little information is available and trade takes place at many different prices simultaneously. We propose a completely uncoupled learning process that selects a subset of the core of the game with a natural equity interpretation. This happens even though agents have no knowledge of other agents' strategies, payoffs, or the structure of the game, and there is no central authority with such knowledge either. In our model, agents randomly encounter other agents, make bids and offers for potential partnerships and match if the partnerships are profitable. Equity is favored by our dynamics beause it is more stable, not because of any ex ante fairness criterion.

Suggested Citation

  • Heinrich H. Nax & Bary S.R. Pradelski, 2012. "Evolutionary dynamics and equitable core selection in assignment games," Economics Series Working Papers 607, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:607
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    File URL: http://www.economics.ox.ac.uk/materials/papers/12040/revised-paper607.pdf
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    References listed on IDEAS

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    1. Rozen, Kareen, 2008. "Conflict Leads to Cooperation in Nash Bargaining," Working Papers 39, Yale University, Department of Economics.
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    4. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
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    6. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    7. Murali Agastya, 1997. "Adaptive Play in Multiplayer Bargaining Situations," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 411-426.
    8. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    9. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
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    11. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
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    Cited by:

    1. Newton, Jonathan & Sawa, Ryoji, 2015. "A one-shot deviation principle for stability in matching problems," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1-27.

    More about this item

    Keywords

    assignment games; cooperative games; core; equity; evolutionary game theory; learning; matching markets; stochastic stability;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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