Repeated games with probabilistic horizon
Repeated games with probabilistic horizon are defined as those games where players have a common probability structure over the length of the game's repetition, T. In particular, for each t, they assign a probability pt to the event that "the game ends in period t". In this framework we analyze Generalized Prisoners' Dilemma games in both finite stage and differentiable stage games. Our construction shows that it is possible to reach cooperative equilibria under some conditions on the distribution of the discrete random variable T even if the expected length of the game is finite. More precisely, we completely characterize the existence of sub-game perfect cooperative equilibria in finite stage games by the (first order) convergence speed: the behavior in the limit of the ratio between the ending probabilities of two consecutive periods. Cooperation in differentiable stage games is determined by the second order convergence speed, which gives a finer analysis of the probability convergence process when the first convergence speed is zero.Leptokurtic distributions are defined as those distributions for which the (first order) convergence speed is zero and they preclude cooperation in finite stage games with probabilistic horizon. However, this negative result is obtained in differential stage games only for a subset of these distributions.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jones, Michael A., 1998. "Cones of cooperation, Perron-Frobenius Theory and the indefinitely repeated Prisoners' Dilemma," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 187-206, September.
- Michael A. Jones, 1999. "The effect of punishment duration of trigger strategies and quasifinite continuation probabilities for Prisoners' Dilemmas," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 533-546.
- Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
- Bernheim B. Douglas & Dasgupta Aniruddha, 1995. "Repeated Games with Asymptotically Finite Horizons," Journal of Economic Theory, Elsevier, vol. 67(1), pages 129-152, October.
When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:50:y:2005:i:1:p:39-60. 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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.