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Global Dynamics in Repeated Games with Additively Separable Payoffs

Author

Listed:
  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • Taiji Furusawa

    (Graduate School of Economics, Hitotsubashi University, Tokyo, Japan)

Abstract

This paper studies the global dynamics of a class of infinitely repeated two-player games in which the action space of each player is an interval, and the one-shot payoff of each player is additively separable in their actions. We define an immediately reactive equilibrium (IRE) as a pure-strategy subgame perfect equilibrium such that each player's action is a stationary function of the opponent's last action. We completely characterize IREs and their dynamics in terms of certain indifference curves. Our results are used to show that in a prisoners' dilemma game with observable mixed strategies, gradual cooperation occurs when the players are sufficiently patient, and that in a certain duopoly game, kinked demand curves emerge naturally.

Suggested Citation

  • Takashi Kamihigashi & Taiji Furusawa, 2010. "Global Dynamics in Repeated Games with Additively Separable Payoffs," Discussion Paper Series DP2010-04, Research Institute for Economics & Business Administration, Kobe University, revised Jun 2010.
    • Handle: RePEc:kob:dpaper:dp2010-04
    as

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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2010-04.pdf
    File Function: Revised version, 2010
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    References listed on IDEAS

    as
    1. Haller, Hans & Lagunoff, Roger, 2010. "Markov Perfect equilibria in repeated asynchronous choice games," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1103-1114, November.
    2. Taiji Furusawa, 2001. "Threats and Concessions in Tariff Settings," Boston University - Department of Economics - The Institute for Economic Development Working Papers Series dp-123, Boston University - Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Taiji Furusawa & Takashi Kamihigashi, 2012. "Threats Or Promises? A Built-In Mechanism Of Gradual Reciprocal Trade Liberalization," The Japanese Economic Review, Japanese Economic Association, vol. 63(2), pages 259-279, June.
    2. Takashi Kamihigashi, 2014. "Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 251-273, June.
    3. Artem Baklanov, 2021. "Reactive Strategies: An Inch of Memory, a Mile of Equilibria," Games, MDPI, vol. 12(2), pages 1-28, May.

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    More about this item

    Keywords

    Immediately reactive equilibria; Additively separable payoffs; Kinked demand; Gradual cooperation; Prisoners' dilemma;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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