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2x2 Delegation Games With Implementability In Weakly Undominated SPNE

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  • Junnosuke Shino

    (Bank of Japan)

Abstract

In this paper we study delegation environments based on Fershtman, Judd, and Kalai ([1987], hereafter FJK). By imposing a certain assumption on the notion of implementability, called implementability with mutually rational agents, they show that every efficient outcome can be fully implemented in subgame perfect Nash equilibrium (SPNE). For their analysis, we first argue that FJK's model can and should be interpreted as a problem in mechanism design. With this in mind, we first modify their model so that agents' participation decision is explicitly built in. Then, we argue that FJK uses a non-standard solution concepts in the mechanism design literature -- in order to attain full implementability, they strengthen notion of implementability, instead of using a refined equilibrium concept. In response, we follow the standard mechanism design approach -- employ a refined SPNE (weakly undominated SPNE, U-SPNE) as the equilibrium concept, while keeping the notion of the implementability unchanged. By applying U-SPNE, we show that in certain classes of 2x2 games -- including prisoners' dilemma, coordination games, and battle of sexes -- every efficient outcome is fully implementable in U-SPNE.

Suggested Citation

  • Junnosuke Shino, 2012. "2x2 Delegation Games With Implementability In Weakly Undominated SPNE," Departmental Working Papers 201202, Rutgers University, Department of Economics.
    • Handle: RePEc:rut:rutres:201202
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    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2012-02.pdf
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    References listed on IDEAS

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    1. Fershtman, Chaim & Judd, Kenneth L & Kalai, Ehud, 1991. "Observable Contracts: Strategic Delegation and Cooperation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 551-559, August.
    2. Yan Yu, 2005. "Public goods provision: Unit-by-unit cost-sharing rules and the core," Review of Economic Design, Springer;Society for Economic Design, vol. 9(4), pages 363-376, December.
    3. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    4. Persson, Torsten & Roland, Gerard & Tabellini, Guido, 1998. "Towards micropolitical foundations of public finance," European Economic Review, Elsevier, vol. 42(3-5), pages 685-694, May.
    5. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May.
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    Cited by:

    1. Junnosuke Shino, 2012. "Bertrand Delegation Games With Implementability In Weakly Undominated SPNE," Departmental Working Papers 201203, Rutgers University, Department of Economics.

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    More about this item

    Keywords

    Implementation; Delegation Game;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D04 - Microeconomics - - General - - - Microeconomic Policy: Formulation; Implementation; Evaluation
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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