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Two-Player Rationalizable Implementation

Author

Listed:
  • R Jain
  • V Korpela
  • M Lombardi
Abstract
The paper characterizes the class of two-player social choice functions implementable in rationalizable strategies. We offer two equivalent conditions, TwoPlayer Generalized Strict Maskin Monotonicity** and Partition Monotonicity. Similar to Bergemann et al. (2011) and Xiong (2022), Two-Player Generalized Strict Maskin Monotonicity** relies on the existence of a partition of the set of states. However, Partition Monotonicity provides a construction for the partition.

Suggested Citation

  • R Jain & V Korpela & M Lombardi, 2022. "Two-Player Rationalizable Implementation," Working Papers 202228, University of Liverpool, Department of Economics.
  • Handle: RePEc:liv:livedp:202228
    as

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    File URL: https://www.liverpool.ac.uk/media/livacuk/schoolofmanagement/docs/Two-Player,Rationalizable,Implementation.pdf
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    References listed on IDEAS

    as
    1. Laslier, Jean-François & Núñez, Matías & Remzi Sanver, M., 2021. "A solution to the two-person implementation problem," Journal of Economic Theory, Elsevier, vol. 194(C).
    2. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2021. "Rationalizable implementation in finite mechanisms," Games and Economic Behavior, Elsevier, vol. 129(C), pages 181-197.
    3. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    4. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," PSE-Ecole d'économie de Paris (Postprint) halshs-00754580, HAL.
    5. Ritesh Jain & Ville Korpela & Michele Lombardi, 2022. "Two-Player Rationalizable Implementation," CSEF Working Papers 660, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
    7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    8. 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.
    9. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    10. Ritesh Jain & Michele Lombardi, 2023. "On Interim Rationalizable Monotonicity," Working Papers 202315, University of Liverpool, Department of Economics.
    11. Geoffroy de Clippel & Kfir Eliaz & Brian Knight, 2014. "On the Selection of Arbitrators," American Economic Review, American Economic Association, vol. 104(11), pages 3434-3458, November.
    12. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    13. Xiong, Siyang, 2023. "Rationalizable implementation of social choice functions: complete characterization," Theoretical Economics, Econometric Society, vol. 18(1), January.
    14. Michele Lombardi & Naoki Yoshihara, 2013. "A full characterization of nash implementation with strategy space reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 131-151, September.
    15. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
    16. Takashi Kunimoto & Roberto Serrano, 2019. "Rationalizable Implementation of Correspondences," Management Science, INFORMS, vol. 44(4), pages 1326-1344, November.
    17. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    18. 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.
    19. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    20. R Jain & V Korpela & M Lombardi, 2021. "An Iterative Approach to Rationalizable Implementation," IEAS Working Paper : academic research 21-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    21. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    22. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    23. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1996. "Toward Natural Implementation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 949-980, November.
    24. 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.
    25. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    26. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    27. Hurwicz, Leonid & Schmeidler, David, 1978. "Construction of Outcome Functions Guaranteeing Existence and Pareto Optimality of Nash Equilibria," Econometrica, Econometric Society, vol. 46(6), pages 1447-1474, November.
    28. repec:hal:pseose:halshs-00754580 is not listed on IDEAS
    29. Mezzetti, Claudio & Renou, Ludovic, 2017. "Repeated Nash implementation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    30. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
    31. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    32. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    33. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. R Jain & V Korpela & M Lombardi, 2022. "Two-Player Rationalizable Implementation," Working Papers 202228, University of Liverpool, Department of Economics.
    2. Ritesh Jain & Michele Lombardi & Antonio Penta, 2024. "Strategically Robust Implementation," Working Papers 1461, Barcelona School of Economics.

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    More about this item

    Keywords

    Implementation; Two Players; Rationalizability; Complete Information;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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