IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/36031.html
   My bibliography  Save this paper

A simple axiomatics of dynamic play in repeated games

Author

Listed:
  • Mathevet, Laurent

Abstract

This paper proposes an axiomatic approach to study two-player infinitely repeated games. A solution is a correspondence that maps the set of stage games into the set of infinite sequences of action profiles. We suggest that a solution should satisfy two simple axioms: individual rationality and collective intelligence. The paper has three main results. First, we provide a classification of all repeated games into families, based on the strength of the requirement imposed by the axiom of collective intelligence. Second, we characterize our solution as well as the solution payoffs in all repeated games. We illustrate our characterizations on several games for which we compare our solution payoffs to the equilibrium payoff set of Abreu and Rubinstein (1988). At last, we develop two models of players' behavior that satisfy our axioms. The first model is a refinement of subgame-perfection, known as renegotiation proofness, and the second is an aspiration-based learning model.

Suggested Citation

  • Mathevet, Laurent, 2012. "A simple axiomatics of dynamic play in repeated games," MPRA Paper 36031, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:36031
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/36031/1/MPRA_paper_36031.pdf
    File Function: original version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    2. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Axiomatic approach; repeated games; classification of games; learning; renegotiation;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • 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

    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:pra:mprapa:36031. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.