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Nash implementation via mechanisms that allow for abstentions

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Abstract

In this paper, we consider Nash implementability in general settings under the assumption that one may abstain. We show that in the case of at least two individuals, any social choice rule is Nash implementable by mechanisms with abstentions if and only if it is Nash implementable. Moreover, we introduce the notions of minimal participation and participation in equilibrium. We then study the possibility of Nash implementability by mechanisms that satisfy minimal participation or participation.

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Notes

  1. If \(F\) satisfies monotonicity and no veto power, we can choose \(B=A\) and \({C}_{j}\left(a,\theta \right)={L}_{i}(a,\theta )\) in \({\Gamma }_{n}\).

References

  • Artemov, G. (2015). Time and Nash implementation. Games and Economic Behavior, 91, 229–236.

    Article  Google Scholar 

  • Benoît, J.-P., & Efe, A. O. (2008). Nash implementation without no-veto power. Games and Economic Behavior, 64, 51–67.

    Article  Google Scholar 

  • Bergemann, D., & Morris, S. (2008). Ex post implementation. Games and Economic Behavior, 63, 527–566.

    Article  Google Scholar 

  • Bochet, O. (2007). Nash implementation with lottery mechanisms. Social Choice and Welfare, 28, 111–125.

    Article  Google Scholar 

  • Cengelci, M. A., & Sanver, M. R. (2007). Is abstention an escape from Arrow’s theorem? Social Choice Welfare, 28, 439–442.

    Article  Google Scholar 

  • Dokow, E., & Holzman, R. (2010). Aggregation of binary evaluations with abstentions. Journal of Economic Theory, 145, 544–561.

    Article  Google Scholar 

  • Dutta, B., & Sen, A. (1991). Necessary and sufficient conditions for 2-person Nash implementation. Review of Economic Studies, 58, 121–129.

    Article  Google Scholar 

  • Dutta, B., Sen, A., & Vohra, R. (1994). Nash implementation through elementary mechanisms in economic environments. Economic Design, 1, 173–203.

    Article  Google Scholar 

  • Eliaz, K. (2002). Fault tolerant implementation. The Review of Economic Studies, 69, 589–610.

    Article  Google Scholar 

  • Jackson, M. O., & Palfrey, T. R. (2001). Voluntary implementation. Journal of Economic Theory, 98, 1–25.

    Article  Google Scholar 

  • Korpela, V. (2013). A simple sufficient condition for strong implementation. Journal of Economic Theory, 148, 2183–2193.

    Article  Google Scholar 

  • Lombardi, M. (2012). Nash implementation via simple stochastic mechanisms: strategy space reduction. Review of Economic Design, 16, 297–309.

    Article  Google Scholar 

  • Lombardi, M., & Yoshihara, N. (2013). A full characterization of Nash implementation with strategy space reduction. Economic Theory, 54, 131–151.

    Article  Google Scholar 

  • Maskin, E. (1999). Nash equilibrium and welfare optimality. Review of Economic Studies, 66, 23–38.

    Article  Google Scholar 

  • Maskin, E., & Moore, J. (1998). Implementation with renegotiation. Review of Economic Studies, 66, 39–56.

    Article  Google Scholar 

  • Mckelvey, R. (1989). Game forms for Nash implementation of general social choice correspondences. Social Choice and Welfare, 6, 139–156.

    Article  Google Scholar 

  • Mezzetti, C., & Renou, L. (2012). Implementation in mixed Nash equilibrium. Journal of Economic Theory, 147, 2357–2375.

    Article  Google Scholar 

  • Moore, J., & Repullo, R. (1990). Nash implementation: a full characterization. Econometrica, 58, 1083–1100.

    Article  Google Scholar 

  • Palfrey, T. R., & Srivastava, S. (1991). Nash implementation using undominated strategies. Econometrica, 59, 479–501.

    Article  Google Scholar 

  • Quesada, A. (2005). Abstention as an escape from Arrow’s theorem. Social Choice and Welfare, 25, 221–226.

    Article  Google Scholar 

  • Repullo, R. (1987). A simple proof of Maskin’s theorem on Nash implementation. Social Chioce and Welfare, 4, 39–41.

    Article  Google Scholar 

  • Saijo, T. (1988). Strategy space reduction in Maskin’s theorem: sufficient conditions for Nash implementation. Econometrica, 56, 693–700.

    Article  Google Scholar 

  • Saijo, T., Tatamitani, Y., & Yamato, T. (1996). Toward natural implementation. International Economic Review, 37, 949–980.

    Article  Google Scholar 

  • Sjostrom, T. (1994). Implementation by demand mechanisms. Economic Design, 1, 343–354.

    Article  Google Scholar 

  • Tatamitani, Y. (2001). Implementation by self-relevant mechanisms. Journal of Mathematical Economics, 35, 427–444.

    Article  Google Scholar 

  • Yi, J. (2011). Implementation via mechanisms with transfers. Mathematical Social Sciences, 61, 65–70.

    Article  Google Scholar 

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  1. School of Mathematic Sciences, South China Normal University, Guangzhou, 510631, China

    Jianxin Yi

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  1. Jianxin Yi
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Yi, J. Nash implementation via mechanisms that allow for abstentions. Theory Decis 91, 279–288 (2021). https://doi.org/10.1007/s11238-020-09790-0

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  • DOI: https://doi.org/10.1007/s11238-020-09790-0

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