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Smooth Monotone Contribution Games

Author

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  • Steven A. Matthews

    () (Department of Economics, University of Pennsylvania)

Abstract

A monotone game is a multistage game in which no player can lower her action in any period below its previous level. A motivation for the monotone games of this paper is dynamic voluntary contribution to a public project. Each player's utility is a strictly concave function of the public good, and quasilinear in the private good. The main result is a description of the limit points of (subgame perfect) equilibrium paths as the period length shrinks. The limiting set of such profiles is equal to the undercore of the underlying static game - the set of profiles that cannot be blocked by a coalition using a smaller profile. A corollary is that the limiting set of achievable profiles does not depend on whether the players can move simultaneously or only in a round-robin fashion. The familiar core is the efficient subset of the undercore; hence, some but not all profiles that are efficient and individually rational can be nearly achieved when the period length is small. As the period length shrinks, any core profile can be achieved in a “twinkling of the eye†- neither real-time gradualism nor inefficiency are necessary.

Suggested Citation

  • Steven A. Matthews, 2006. "Smooth Monotone Contribution Games," PIER Working Paper Archive 06-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:06-018
    as

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    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/working-papers/06-018.pdf
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    References listed on IDEAS

    as
    1. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 327-358.
    2. Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 339-356.
    3. Pitchford, Rohan & Snyder, Christopher M., 2004. "A solution to the hold-up problem involving gradual investment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 88-103, January.
    4. Compte, Olivier & Jehiel, Philippe, 2003. "Voluntary contributions to a joint project with asymmetric agents," Journal of Economic Theory, Elsevier, vol. 112(2), pages 334-342, October.
    5. Anat R. Admati & Motty Perry, 1991. "Joint Projects without Commitment," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 259-276.
    6. Ochs, Jack & Park, In-Uck, 2010. "Overcoming the coordination problem: Dynamic formation of networks," Journal of Economic Theory, Elsevier, vol. 145(2), pages 689-720, March.
    7. Zissimos, Ben, 2007. "The GATT and gradualism," Journal of International Economics, Elsevier, vol. 71(2), pages 410-433, April.
    8. Mark Bagnoli & Barton L. Lipman, 1989. "Provision of Public Goods: Fully Implementing the Core through Private Contributions," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 583-601.
    9. Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
    10. Choi, Syngjoo & Gale, Douglas & Kariv, Shachar, 2008. "Sequential equilibrium in monotone games: A theory-based analysis of experimental data," Journal of Economic Theory, Elsevier, vol. 143(1), pages 302-330, November.
    11. Gale, Douglas, 1995. "Dynamic Coordination Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 1-18, January.
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    More about this item

    Keywords

    dynamic games; monotone games; core; public goods; voluntary contribution; gradualism;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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