IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/2039r.html
   My bibliography  Save this paper

Expected Worth for 2 � 2 Matrix Games with Variable Grid Sizes

Author

Listed:

Abstract

We offer a detailed examination of a broad class of 2 x 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.

Suggested Citation

  • Michael R. Powers & Martin Shubik & Wen Wang, 2016. "Expected Worth for 2 � 2 Matrix Games with Variable Grid Sizes," Cowles Foundation Discussion Papers 2039R, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2039r
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d20/d2039-r.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Martin Shubik, 2012. "What Is a Solution to a Matrix Game," Cowles Foundation Discussion Papers 1866R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2013.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    3. Michael R. Powers & Martin Shubik & Wen Wang, 2016. "Expected Worth for 2 � 2 Matrix Games with Variable Grid Sizes," Cowles Foundation Discussion Papers 2039, Cowles Foundation for Research in Economics, Yale University.
    4. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(3), pages 277-286.
    5. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-764, May.
    6. Martin Shubik & Gerrit Wolf & Byron Poon, 1974. "Perception of Payoff Structure and Opponent's Behavior in Related Matrix Games," Journal of Conflict Resolution, Peace Science Society (International), vol. 18(4), pages 646-655, December.
    7. anonymous, 1976. "The economy in 1975," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Feb, pages 71-81.
    8. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michael R. Powers & Martin Shubik & Wen Wang, 2016. "Expected Worth for 2 � 2 Matrix Games with Variable Grid Sizes," Cowles Foundation Discussion Papers 2039, Cowles Foundation for Research in Economics, Yale University.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Antonio Cabrales & Rosemarie Nagel & Roc Armenter, 2007. "Equilibrium selection through incomplete information in coordination games: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 221-234, September.
    2. Giovanna Devetag & Andreas Ortmann, 2007. "When and why? A critical survey on coordination failure in the laboratory," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 331-344, September.
    3. Capraro, Valerio & Rodriguez-Lara, Ismael & Ruiz-Martos, Maria J., 2020. "Preferences for efficiency, rather than preferences for morality, drive cooperation in the one-shot Stag-Hunt game," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 86(C).
    4. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    5. Siegfried K. Berninghaus & Lora Todorova & Bodo Vogt, 2011. "A Simple Questionnaire Can Change Everything - Are Strategy Choices in Coordination Games Stable?," Jena Economics Research Papers 2011-057, Friedrich-Schiller-University Jena.
    6. Boone, Jan & Müller, Wieland & Suetens, Sigrid, 2009. "Naked exclusion: Towards a behavioral approach to exclusive dealing," CEPR Discussion Papers 7303, C.E.P.R. Discussion Papers.
    7. Vyrastekova, J., 2002. "Efficiency versus Risk Dominance in an Evolutionary Model with Cheap Talk," Discussion Paper 2002-6, Tilburg University, Center for Economic Research.
    8. Pietro Guarnieri & Tommaso Luzzati & Stefano Marchetti, 2019. "An experiment on coordination in a modified stag hunt game," Discussion Papers 2019/246, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    9. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.
    10. Arno Riedl & Ingrid M. T. Rohde & Martin Strobel, 2016. "Efficient Coordination in Weakest-Link Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(2), pages 737-767.
    11. Fabian Dvorak & Sebastian Fehrler, 2024. "Negotiating Cooperation under Uncertainty: Communication in Noisy, Indefinitely Repeated Interactions," American Economic Journal: Microeconomics, American Economic Association, vol. 16(3), pages 232-258, August.
    12. Nax, Heinrich Harald & Newton, Jonathan, 2022. "Deep and shallow thinking in the long run," Theoretical Economics, Econometric Society, vol. 17(4), November.
    13. Dal Bó, Pedro & Fréchette, Guillaume R. & Kim, Jeongbin, 2021. "The determinants of efficient behavior in coordination games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 352-368.
    14. Berninghaus, Siegfried K. & Todorova, Lora & Vogt, Bodo, 2011. "A simple questionnaire can change everything: Are strategy choices in coordination games stable?," Working Paper Series in Economics 37, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    15. Gerlagh, Reyer & van der Heijden, Eline, 2015. "Going Green : Framing Effects in a Dynamic Coordination Game," Other publications TiSEM c3b6b46c-0fb0-4098-8251-d, Tilburg University, School of Economics and Management.
    16. Juan Carlos González-Avella & Haydée Lugo & Maxi San Miguel, 2019. "Coordination in a skeptical two-group population," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 203-214, March.
    17. Leland, Jonathan W. & Schneider, Mark, 2018. "A theory of focal points in 2 × 2 games," Journal of Economic Psychology, Elsevier, vol. 65(C), pages 75-89.
    18. Jan Boone & Wieland Müller & Sigrid Suetens, 2014. "Naked Exclusion in the Lab: The Case of Sequential Contracting," Journal of Industrial Economics, Wiley Blackwell, vol. 62(1), pages 137-166, March.
    19. Poulsen, Anders & Poulsen, Odile, 2010. "Prisoner's Dilemma payoffs and the evolution of co-operative preferences," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 39(2), pages 158-162, April.
    20. Roger Lee Mendoza, 2018. "The Hare Question in Assurance Games: Practical Problems and Insights From Robotic Surgery," The American Economist, Sage Publications, vol. 63(1), pages 18-30, March.

    More about this item

    Keywords

    2 � 2 matrix games; efficiency; coordination; worth of coordination;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:2039r. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.