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Implementation in undominated strategies by bounded mechanisms: Some results on compromise alternatives

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  • Mukherjee, Saptarshi

Abstract

We consider an impossibility result in Börgers (1991), which says in a restricted environment with two players or three alternatives it is impossible to implement a social choice correspondence that is efficient, enforces compromises at a profile and is implementable in undominated strategies by a bounded mechanism. We extend and refine this result in many ways- we generalize the impossibility result for any number of players and alternatives when the compromises are enforced at a near-unanimous preference profile. We further show that the impossibility result in Börgers (1991) holds good if we replace efficiency of SCCs by neutrality. Also the impossibility result holds good for two agents and any number of alternatives when the SCC is unanimous and minimal. Interestingly, we get a possibility result when we relax the assumption of minimality.

Suggested Citation

  • Mukherjee, Saptarshi, 2018. "Implementation in undominated strategies by bounded mechanisms: Some results on compromise alternatives," Research in Economics, Elsevier, vol. 72(3), pages 384-391.
    • Handle: RePEc:eee:reecon:v:72:y:2018:i:3:p:384-391
    DOI: 10.1016/j.rie.2018.07.002
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    References listed on IDEAS

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    1. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
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    5. Mukherjee, Saptarshi & Muto, Nozomu & Ramaekers, Eve & Sen, Arunava, 2019. "Implementation in undominated strategies by bounded mechanisms: The Pareto correspondence and a generalization," Journal of Economic Theory, Elsevier, vol. 180(C), pages 229-243.
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    7. Mukherjee, Saptarshi & Muto, Nozomu & Ramaekers, Eve, 2017. "Implementation in undominated strategies with partially honest agents," Games and Economic Behavior, Elsevier, vol. 104(C), pages 613-631.
    8. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
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