IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v17y2015i03ns0219198915500061.html
   My bibliography  Save this article

On the Strategic Equivalence of Linear Dynamic and Repeated Games

Author

Listed:
  • Joachim Hubmer

    (Department of Economics, Yale University, 28 Hillhouse Avenue, New Haven, CT 06520, USA)

Abstract

Dynamic (or stochastic) games are, in general, considerably more complicated to analyze than repeated games. This paper shows that for every deterministic dynamic game that islinear in the state, there exists astrategically equivalentrepresentation as a repeated game. A dynamic game is said to be linear in the state if it holds for both the state transition function as well as for the one-period payoff function that (i) they are additively separable in action profiles and states and (ii) the state variables enter linearly. Strategic equivalence refers to the observation that the two sets of subgame perfect equilibria coincide, up to a natural projection of dynamic game strategy profiles on the much smaller set of repeated game histories. Furthermore, it is shown that the strategic equivalence result still holds for certain stochastic elements in the transition function if one allows for additional signals in the repeated game or in the presence of a public correlating device.

Suggested Citation

  • Joachim Hubmer, 2015. "On the Strategic Equivalence of Linear Dynamic and Repeated Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 1-11.
    • Handle: RePEc:wsi:igtrxx:v:17:y:2015:i:03:n:s0219198915500061
    DOI: 10.1142/S0219198915500061
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198915500061
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198915500061?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. 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)

    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. Daron Acemoglu & Matthew O. Jackson, 2017. "Social Norms and the Enforcement of Laws," Journal of the European Economic Association, European Economic Association, vol. 15(2), pages 245-295.
    2. Ernesto Dal Bó & Pedro Dal Bó & Rafael Di Tella, 2007. "Reputation When Threats and Transfers Are Available," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(3), pages 577-598, September.
    3. Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    4. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    5. Matsushima Hitoshi, 2020. "Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 20(1), pages 1-11, January.
    6. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2012. "Communication and Learning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 419-450.
    7. Do, Jihwan & Miklós-Thal, Jeanine, 2023. "Partial secrecy in vertical contracting," International Journal of Industrial Organization, Elsevier, vol. 90(C).
    8. Contou-Carrère, Pauline & Tomala, Tristan, 2011. "Finitely repeated games with semi-standard monitoring," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 14-21, January.
    9. Jayakumar Subramanian & Amit Sinha & Aditya Mahajan, 2023. "Robustness and Sample Complexity of Model-Based MARL for General-Sum Markov Games," Dynamic Games and Applications, Springer, vol. 13(1), pages 56-88, March.
    10. Hart, Sergiu & Rinott, Yosef, 2020. "Posterior probabilities: Dominance and optimism," Economics Letters, Elsevier, vol. 194(C).
    11. W. Bentley MacLeod, 2006. "Reputations, Relationships and the Enforcement of Incomplete Contracts," CESifo Working Paper Series 1730, CESifo.
    12. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    13. Daron Acemoglu & Matthew O. Jackson, 2015. "History, Expectations, and Leadership in the Evolution of Social Norms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(2), pages 423-456.
    14. Chatterjee, Satyajit & Corbae, Dean & Ríos-Rull, José-Víctor, 2008. "A finite-life private-information theory of unsecured consumer debt," Journal of Economic Theory, Elsevier, vol. 142(1), pages 149-177, September.
    15. Attanasi, Giuseppe & Battigalli, Pierpaolo & Manzoni, Elena & Nagel, Rosemarie, 2019. "Belief-dependent preferences and reputation: Experimental analysis of a repeated trust game," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 341-360.
    16. Sofia Moroni, 2018. "Games with Private Timing," Working Paper 6400, Department of Economics, University of Pittsburgh.
    17. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    18. Fausti, Scott W. & Qasmi, Bashir A. & Diersen, Matthew A & Adamson, Bill, 2014. "Grid Valuation of Beef Carcass Quality: Market Power and Market Trends," Economics Staff Papers 171423, South Dakota State University, Department of Economics.
    19. John Tyson Chatagnier, 2015. "Conflict bargaining as a signal to third parties," Journal of Theoretical Politics, , vol. 27(2), pages 237-268, April.
    20. Matros, Alexander & Smirnov, Vladimir, 2016. "Duplicative search," Games and Economic Behavior, Elsevier, vol. 99(C), pages 1-22.

    More about this item

    Keywords

    Dynamic games; stochastic games; repeated games; C73;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    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:wsi:igtrxx:v:17:y:2015:i:03:n:s0219198915500061. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.