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Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension

Author

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  • Yannick Viossat

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

Abstract

A game is elementary if it has strict correlated equilibrium distributions with full support. A game is full if its correlated equilibrium polytope has full dimension. Any elementary game is full. We show that a full game is elementary if and only if all the correlated equilibrium incentive constraints are nonvacuous. Characterizations of full games are provided and examples are given. Finally, we give a method to build full, nonelementary games.

Suggested Citation

  • Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242991
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242991
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    References listed on IDEAS

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    1. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    2. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    3. Yannick Viossat, 2003. "Properties of Dual Reduction," Working Papers hal-00242992, HAL.
    4. Robert W. Rosenthal, 1973. "Correlated Equilibria in Some Classes of Two-Person Games," Discussion Papers 45, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    6. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
    7. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    8. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
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