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Nash blocks

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  • Peter Wikman

    (Esplanade de l’Université)

Abstract

A product set of pure strategies is a Nash block if it contains all best replies to the Nash equilibria of the game in which the players are restricted to the strategies in the block. This defines an intermediate block property, between curb (Basu and Weibull, Econ Lett 36(2):141–146, https://doi.org/10.1016/0165-1765(91)90179-O , http://www.sciencedirect.com/science/article/pii/016517659190179O , 1991) and coarse tenability (Myerson and Weibull (2015) Econometrica 83(3):943–976, https://doi.org/10.3982/ECTA11048 ). While the new concept is defined without reference to the consideration-set framework that defines tenability, the framework can be used to characterize Nash blocks in terms of potential conventions when large populations of individuals recurrently interact. Although weaker than curb, Nash blocks nevertheless maintain several robustness properties of curb sets. For example, every Nash block contains an essential component and is robust against payoff perturbations.

Suggested Citation

  • Peter Wikman, 2022. "Nash blocks," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 29-51, March.
    • Handle: RePEc:spr:jogath:v:51:y:2022:i:1:d:10.1007_s00182-021-00784-y
    DOI: 10.1007/s00182-021-00784-y
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    References listed on IDEAS

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    1. Faruk Gül & David Pearce & Ennio Stacchetti, 1993. "A Bound on the Proportion of Pure Strategy Equilibria in Generic Games," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 548-552, August.
    2. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    3. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    4. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Balkenborg, Dieter G. & Hofbauer, Josef & Kuzmics, Christoph, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
    7. Blume Andreas, 1994. "Equilibrium Refinements in Sender-Receiver Games," Journal of Economic Theory, Elsevier, vol. 64(1), pages 66-77, October.
    8. MERTENS, Jean-François, 1989. "Stable equilibria - a reformulation. Part I. Definition and basic properties," LIDAM Reprints CORE 866, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Blume, Andreas, 1998. "Communication, Risk, and Efficiency in Games," Games and Economic Behavior, Elsevier, vol. 22(2), pages 171-202, February.
    10. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, Oxford University Press, vol. 102(2), pages 179-221.
    11. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 207-236.
    12. Roger Myerson & Jörgen Weibull, 2015. "Tenable Strategy Blocks and Settled Equilibria," Econometrica, Econometric Society, vol. 83(3), pages 943-976, May.
    13. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    14. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    15. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    16. Voorneveld, Mark, 2005. "Persistent retracts and preparation," Games and Economic Behavior, Elsevier, vol. 51(1), pages 228-232, April.
    17. Jean-François Mertens, 1991. "Stable Equilibria—A Reformulation. Part II. Discussion of the Definition, and Further Results," Mathematics of Operations Research, INFORMS, vol. 16(4), pages 694-753, November.
    18. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
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