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Implementation in stochastic dominance Nash equilibria

Author

Listed:
  • Eun Jeong Heo

    (Vanderbilt University)

  • Vikram Manjunath

    (Texas A&M University)

Abstract

We study solutions that choose lotteries for profiles of preferences defined over sure alternatives. We define Nash equilibria based on “stochastic dominance” comparisons and study the implementability of solutions in such equilibria. We show that a Maskin-style invariance condition is necessary and sufficient for implementability. Our results apply to an abstract Arrovian environment as well as a broad class of economic environments.

Suggested Citation

  • Eun Jeong Heo & Vikram Manjunath, 2017. "Implementation in stochastic dominance Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 5-30, January.
    • Handle: RePEc:spr:sochwe:v:48:y:2017:i:1:d:10.1007_s00355-015-0915-2
    DOI: 10.1007/s00355-015-0915-2
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    References listed on IDEAS

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    1. Stergios Athanassoglou & Jay Sethuraman, 2011. "House allocation with fractional endowments," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 481-513, August.
    2. Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
    3. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    4. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    5. Ehlers, Lars & Masso, Jordi, 2007. "Incomplete information and singleton cores in matching markets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 587-600, September.
    6. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
    7. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    8. Harris Milton & Townsend, Robert M, 1981. "Resource Allocation under Asymmetric Information," Econometrica, Econometric Society, vol. 49(1), pages 33-64, January.
    9. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
    10. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    11. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    12. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
    13. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    14. Pais, Joana, 2008. "Incentives in decentralized random matching markets," Games and Economic Behavior, Elsevier, vol. 64(2), pages 632-649, November.
    15. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    16. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    17. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    18. Partha Dasgupta & Peter Hammond & Eric Maskin, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 185-216.
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