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Tenable strategy blocks and settled equilibria

Author

Listed:
  • Roger Myerson

    (Unknown)

  • Jörgen W. Weibull

    (IAST - Institute for Advanced Study in Toulouse)

Abstract

When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set-valued concepts, coarsely and finely tenable blocks, that formalize this notion for finite normal-form games. We then identify settled equilibria, which are Nash equilibria with support in minimal tenable blocks. For a generic class of normal-form games, our coarse and fine concepts are equivalent, and yet they differ from standard solution concepts on open sets of games. We demonstrate the nature and power of the solutions by way of examples. Settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games. With fine tenability, we obtain invariance under the insertion of a subgame with a unique totally mixed payoff-equivalent equilibrium, a property that other related concepts have not satisfied.

Suggested Citation

  • Roger Myerson & Jörgen W. Weibull, 2015. "Tenable strategy blocks and settled equilibria," Post-Print hal-04302684, HAL.
  • Handle: RePEc:hal:journl:hal-04302684
    DOI: 10.3982/ECTA11048
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    Cited by:

    1. Block, Juan I. & Fudenberg, Drew & Levine, David K., 2019. "Learning dynamics with social comparisons and limited memory," Theoretical Economics, Econometric Society, vol. 14(1), January.
    2. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    3. Ingela Alger & Jean-François Laslier, 2022. "Homo moralis goes to the voting booth: Coordination and information aggregation," Journal of Theoretical Politics, , vol. 34(2), pages 280-312, April.
    4. Lindbeck, Assar & Weibull, Jörgen, 2020. "Delegation of investment decisions, and optimal remuneration of agents," European Economic Review, Elsevier, vol. 129(C).
    5. Govindan, Srihari & Laraki, Rida & Pahl, Lucas, 2023. "On sustainable equilibria," Journal of Economic Theory, Elsevier, vol. 213(C).
    6. Alger, Ingela & Weibull, Jörgen W., 2016. "Morality: evolutionary foundations and policy implications," TSE Working Papers 16-702, Toulouse School of Economics (TSE).
    7. Lina Andersson, 2020. "Cooperation between Emotional Players," Games, MDPI, vol. 11(4), pages 1-16, October.
    8. Ingela Alger & Jörgen W. Weibull, 2017. "Strategic Behavior of Moralists and Altruists," Games, MDPI, vol. 8(3), pages 1-21, September.
    9. Juan I Block & Drew Fudenberg & David K Levine, 2017. "Learning Dynamics Based on Social Comparisons," Levine's Working Paper Archive 786969000000001375, David K. Levine.
    10. Milgrom, Paul & Mollner, Joshua, 2021. "Extended proper equilibrium," Journal of Economic Theory, Elsevier, vol. 194(C).
    11. P. Jean-Jacques Herings & Andrey Meshalkin & Arkadi Predtetchinski, 2020. "Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment," Dynamic Games and Applications, Springer, vol. 10(2), pages 478-492, June.
    12. Yiyin Cao & Yin Chen & Chuangyin Dang, 2024. "A Differentiable Path-Following Method with a Compact Formulation to Compute Proper Equilibria," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 377-396, March.
    13. Hans Carlsson & Philipp Christoph Wichardt, 2019. "Strict Incentives and Strategic Uncertainty," CESifo Working Paper Series 7715, CESifo.
    14. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    15. Peter Wikman, 2022. "Nash blocks," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 29-51, March.
    16. Virginia Cecchini Manara & Lorenzo Sacconi, 2019. "Institutions, Frames, and Social Contract Reasoning," Econometica Working Papers wp71, Econometica.
    17. Carlos Alós-Ferrer & Klaus Ritzberger, 2020. "Reduced normal forms are not extensive forms," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 281-288, October.

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