IDEAS home Printed from https://ideas.repec.org/a/eee/jeborg/v166y2019icp288-308.html
   My bibliography  Save this article

Evolutionary dynamics in multitasking environments

Author

Listed:
  • Sawa, Ryoji
  • Zusai, Dai

Abstract

We formulate the best response dynamic in a multitasking environment; while agents engage in multiple games concurrently, an agent can switch her action in only one of the games upon receipt of a revision opportunity. The choice of the game in which to revise an action makes the multitasking dynamic behave differently from standard evolutionary dynamics. The timing of revisions in a game becomes endogenous, which causes the transition of the action distribution in each game to depend on those in other games. Despite such complexity, we verify the global stability of the Nash equilibrium set in potential and contractive games as well as the local stability of a regular evolutionary stable state. We also show that the equilibrium to which the multitasking dynamic converges may depend on the task choice rules.

Suggested Citation

  • Sawa, Ryoji & Zusai, Dai, 2019. "Evolutionary dynamics in multitasking environments," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 288-308.
    • Handle: RePEc:eee:jeborg:v:166:y:2019:i:c:p:288-308
    DOI: 10.1016/j.jebo.2019.06.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167268119302112
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jebo.2019.06.021?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. Brocas, Isabelle & Carrillo, Juan D., 2014. "Dual-process theories of decision-making: A selective survey," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 45-54.
    2. Bomze Immanuel M. & Weibull Jorgen W., 1995. "Does Neutral Stability Imply Lyapunov Stability?," Games and Economic Behavior, Elsevier, vol. 11(2), pages 173-192, November.
    3. Rydval, Ondrej & Ortmann, Andreas & Ostatnicky, Michal, 2009. "Three very simple games and what it takes to solve them," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 589-601, October.
    4. , & , H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
    5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    6. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    7. Bednar, Jenna & Chen, Yan & Liu, Tracy Xiao & Page, Scott, 2012. "Behavioral spillovers and cognitive load in multiple games: An experimental study," Games and Economic Behavior, Elsevier, vol. 74(1), pages 12-31.
    8. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    9. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2220-2259.
    10. Lindbeck, Assar & Snower, Dennis J, 2000. "Multitask Learning and the Reorganization of Work: From Tayloristic to Holistic Organization," Journal of Labor Economics, University of Chicago Press, vol. 18(3), pages 353-376, July.
    11. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    12. Alós-Ferrer, Carlos & Strack, Fritz, 2014. "From dual processes to multiple selves: Implications for economic behavior," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 1-11.
    13. Thomas Buser & Noemi Peter, 2012. "Multitasking," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 641-655, December.
    14. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    15. Boucekkine, Raouf & Crifo, Patricia, 2008. "Human Capital Accumulation And The Transition From Specialization To Multitasking," Macroeconomic Dynamics, Cambridge University Press, vol. 12(3), pages 320-344, June.
    16. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.
    17. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    18. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    19. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 49-72, January.
    20. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    21. In-Koo Cho & Anna Rubinchik, 2017. "Contemplation vs. intuition: a reinforcement learning perspective," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 141-167, November.
    22. , H., 2010. "Local stability under evolutionary game dynamics," Theoretical Economics, Econometric Society, vol. 5(1), January.
    23. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 73-75, January.
    24. B. Douglas Bernheim & Michael D. Whinston, 1990. "Multimarket Contact and Collusive Behavior," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 1-26, Spring.
    25. Dai Zusai, 2013. "Tempered Best Response Dynamics," DETU Working Papers 1301, Department of Economics, Temple University.
    26. Tadashi Sekiguchi, 2015. "Multimarket contact under demand fluctuations," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 1033-1048, November.
    27. Ross Cressman & Andrea Gaunersdorfer & Jean-François Wen, 2000. "Evolutionary And Dynamic Stability In Symmetric Evolutionary Games With Two Independent Decisions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 67-81.
    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. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org, revised Nov 2023.

    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. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.
    2. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Sawa, Ryoji & Zusai, Dai, 2014. "Evolutionary imitative dynamics with population-varying aspiration levels," Journal of Economic Theory, Elsevier, vol. 154(C), pages 562-577.
    4. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    5. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    6. Saeed Hadikhanloo & Rida Laraki & Panayotis Mertikopoulos & Sylvain Sorin, 2022. "Learning in nonatomic games, part Ⅰ: Finite action spaces and population games," Post-Print hal-03767995, HAL.
    7. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    8. Sylvain Sorin, 2023. "Continuous Time Learning Algorithms in Optimization and Game Theory," Dynamic Games and Applications, Springer, vol. 13(1), pages 3-24, March.
    9. Beauchêne, D., 2019. "Is ambiguity aversion bad for innovation?," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1154-1176.
    10. Dai Zusai, 2018. "Net gains in evolutionary dynamics: A unifying and intuitive approach to dynamic stability," Papers 1805.04898, arXiv.org, revised Oct 2023.
    11. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    12. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    13. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    14. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2019. "Best experienced payoff dynamics and cooperation in the Centipede game," Theoretical Economics, Econometric Society, vol. 14(4), November.
    15. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    16. Boyu Zhang & Josef Hofbauer, 2015. "Equilibrium selection via replicator dynamics in $$2 \times 2$$ 2 × 2 coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 433-448, May.
    17. Manxi Wu & Saurabh Amin & Asuman Ozdaglar, 2021. "Multi-agent Bayesian Learning with Best Response Dynamics: Convergence and Stability," Papers 2109.00719, arXiv.org.
    18. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2022. "Generalized perturbed best response dynamics with a continuum of strategies," Journal of Economic Theory, Elsevier, vol. 200(C).
    19. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner, 2021. "Cold play: Learning across bimatrix games," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 419-441.
    20. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July.

    More about this item

    Keywords

    Evolution; Multitasking; Bounded rationality; Best response dynamics; Evolutionary stable state; Stability of the Nash equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

    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:eee:jeborg:v:166:y:2019:i:c:p:288-308. 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: http://www.elsevier.com/locate/jebo .

    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.