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CRRA utility and the sustainability of cooperation in infinitely-repeated games

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  • Collie, David R.

Abstract

In a symmetric infinitely-repeated game, where players have constant relative risk aversion (CRRA), or constant elasticity of intertemporal substitution, utility functions, it is shown that the critical discount factor required to sustain full cooperation is decreasing in the coefficient of relative risk aversion (increasing in the elasticity of intertemporal substitution). An application to cooperation in international environmental agreements (IEA) is presented and it is shown that the limit of the critical discount factor as the number of countries goes to infinity is equal to one (zero) if the coefficient of intertemporal inequality aversion is less (greater) than one.

Suggested Citation

  • Collie, David R., 2022. "CRRA utility and the sustainability of cooperation in infinitely-repeated games," Economics Letters, Elsevier, vol. 221(C).
    • Handle: RePEc:eee:ecolet:v:221:y:2022:i:c:s0165176522003718
    DOI: 10.1016/j.econlet.2022.110897
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    References listed on IDEAS

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    1. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 1-12.
    2. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    3. Dreber, Anna & Fudenberg, Drew & Rand, David G., 2014. "Who cooperates in repeated games: The role of altruism, inequity aversion, and demographics," Journal of Economic Behavior & Organization, Elsevier, vol. 98(C), pages 41-55.
    4. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    5. Sabater-Grande, Gerardo & Georgantzis, Nikolaos, 2002. "Accounting for risk aversion in repeated prisoners' dilemma games: an experimental test," Journal of Economic Behavior & Organization, Elsevier, vol. 48(1), pages 37-50, May.
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    More about this item

    Keywords

    Cooperation; Critical discount factor; Nash-reversion trigger strategies; CRRA utility function; International environmental agreement;
    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
    • Q58 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environmental Economics: Government Policy

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