IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v274y2016icp393-402.html
   My bibliography  Save this article

The payoff matrix of repeated asymmetric 2×2 gamesAuthor-Name: Elshobaky, Entisarat M

Author

Listed:
  • El-Seidy, Essam
  • Taha, Mohammad A.

Abstract

Many researches in game theory have been devoted to study the symmetric contest between the contestants. This is due to the computational advantage in this type of game. In contrast, asymmetric games are more complicated in mathematical computations than the symmetric one. This article is particularly interested in the model of asymmetric games. In this model, we cannot interchange the identities of the players without interchanging the payoff of the strategies. This model differs from the symmetric model, where each player has two different choices from the two choices of the other one. We consider that the round of the game is infinitely repeated (infinitely repeated and asymmetric 2×2 game). The payoff matrix corresponding to all possible strategies of the game is obtained. Furthermore, we will apply the resulting matrix in two examples. During this, we will draw the attention towards the behavior of some of the strategies and the evolutionary stability.

Suggested Citation

  • El-Seidy, Essam & Taha, Mohammad A., 2016. "The payoff matrix of repeated asymmetric 2×2 gamesAuthor-Name: Elshobaky, Entisarat M," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 393-402.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:393-402
    DOI: 10.1016/j.amc.2015.11.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315014654
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.11.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
    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. Zhang, Yifan & Shu, Gang & Li, Ya, 2017. "Strategy-updating depending on local environment enhances cooperation in prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 224-232.
    2. Taha, Mohammad A. & Ghoneim, Ayman, 2020. "Zero-determinant strategies in repeated asymmetric games," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    3. Taha, Mohammad A. & Ghoneim, Ayman, 2021. "Zero-determinant strategies in infinitely repeated three-player prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

    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. van Damme, E.E.C., 1995. "Game theory : The next stage," Other publications TiSEM 7779b0f9-bef5-45c7-ae6b-7, Tilburg University, School of Economics and Management.
    2. Federico Di Pace & Matthias Hertweck, 2019. "Labor Market Frictions, Monetary Policy, and Durable Goods," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 32, pages 274-304, April.
    3. Bhaskar V., 1996. "On the neutral stability of mixed strategies in asymmetric contests," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 56-57, February.
    4. Bergantiños, Gustavo & Vidal-Puga, Juan, 2010. "Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms," European Journal of Operational Research, Elsevier, vol. 201(3), pages 811-820, March.
    5. Guth, Werner & Ritzberger, Klaus & van Damme, Eric, 2004. "On the Nash bargaining solution with noise," European Economic Review, Elsevier, vol. 48(3), pages 697-713, June.
    6. Scharpf, Fritz W. & Mohr, Matthias, 1994. "Efficient self-coordination in policy networks: A simulation study," MPIfG Discussion Paper 94/1, Max Planck Institute for the Study of Societies.
    7. Fandel, Günter & Giese, Anke & Mohn, Brigitte, 2012. "Measuring synergy effects of a Public Social Private Partnership (PSPP) project," International Journal of Production Economics, Elsevier, vol. 140(2), pages 815-824.
    8. Schumacher, Heiner, 2013. "Imitating cooperation and the formation of long-term relationships," Journal of Economic Theory, Elsevier, vol. 148(1), pages 409-417.
    9. António Brandão & Joana Pinho & Hélder Vasconcelos, 2014. "Asymmetric Collusion with Growing Demand," Journal of Industry, Competition and Trade, Springer, vol. 14(4), pages 429-472, December.
    10. Dinar, Ariel, 1989. "Application of the Nash Bargaining Model to a Problem of Efficient Resources Use and Cost-Benefit Allocation," 1989 Annual Meeting, July 30-August 2, Baton Rouge, Louisiana 270685, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Bergstrom, Theodore C & Stark, Oded, 1993. "How Altruism Can Prevail in an Evolutionary Environment," American Economic Review, American Economic Association, vol. 83(2), pages 149-155, May.
    12. Volodymyr Babich & Simone Marinesi & Gerry Tsoukalas, 2021. "Does Crowdfunding Benefit Entrepreneurs and Venture Capital Investors?," Manufacturing & Service Operations Management, INFORMS, vol. 23(2), pages 508-524, March.
    13. Zhigang Cao, 2011. "Remarks on Bargaining and Cooperation in Strategic Form Games," Discussion Paper Series dp565, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    14. Ley, Eduardo, 2006. "Statistical inference as a bargaining game," Economics Letters, Elsevier, vol. 93(1), pages 142-149, October.
    15. Anna Castañer & Jesús Marín-Solano & Carmen Ribas, 2021. "A time consistent dynamic bargaining procedure in differential games with hterogeneous discounting," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 555-584, June.
    16. Graham Pyatt, 1986. "Inertia in Labor Markets," Eastern Economic Journal, Eastern Economic Association, vol. 12(3), pages 243-250, Jul-Sep.
    17. Laurence J. Kotlikoff & John B. Shoven & Avia Spivak, 1987. "Annuity Markets, Savings, and the Capital Stock," NBER Chapters, in: Issues in Pension Economics, pages 211-236, National Bureau of Economic Research, Inc.
    18. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.
    19. Maria Montero & Alex Possajennikov, 2021. "An Adaptive Model of Demand Adjustment in Weighted Majority Games," Games, MDPI, vol. 13(1), pages 1-17, December.
    20. Bhaskar, V., 1993. "Neutral Stability in Assymetric Evolutionary Games," Papers 9358, Tilburg - Center for Economic Research.

    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:eee:apmaco:v:274:y:2016:i:c:p:393-402. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.