Computing Equilibria in Discounted 2 × 2 Supergames
This article examines the subgame perfect pure strategy equilibrium paths and payoff sets of discounted supergames with perfect monitoring. The main contribution is to provide methods for computing and tools for analyzing the equilibrium paths and payoffs in repeated games. We introduce the concept of a first-action feasible path, which simplifies the computation of equilibria. These paths can be composed into a directed multigraph, which is a useful representation for the equilibrium paths. We examine how the payoffs, discount factors and the properties of the multigraph affect the possible payoffs, their Hausdorff dimension, and the complexity of the equilibrium paths. The computational methods are applied to the 12 symmetric strictly ordinal 2 × 2 games. We find that these games can be classified into three groups based on the complexity of the equilibrium paths. Copyright Springer Science+Business Media, LLC. 2013
Volume (Year): 41 (2013)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/economics/economic+theory/journal/10614/PS2|
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.:
- Cronshaw, Mark B, 1997. "Algorithms for Finding Repeated Game Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 10(2), pages 139-168, May.
- Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
- Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
- Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, 07.
- Salonen, Hannu & Vartiainen, Hannu, 2008.
"Valuating payoff streams under unequal discount factors,"
Elsevier, vol. 99(3), pages 595-598, June.
- Hannu Salonen & Hannu Vartiainen, 2007. "Valuating Payoff Streams under Unequal Discount Factors," Discussion Papers 16, Aboa Centre for Economics.
- Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
- Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
- Mailath, George J. & Obara, Ichiro & Sekiguchi, Tadashi, 2002. "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 40(1), pages 99-122, July.
- George J. Mailath & Ichiro Obara & Tadashi Sekiguchi, "undated". "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Penn CARESS Working Papers 83719e84b6825736ffcfdfacb, Penn Economics Department.
- Mitri Kitti, 2011. "Conditionally Stationary Equilibria in Discounted Dynamic Games," Dynamic Games and Applications, Springer, vol. 1(4), pages 514-533, December.
- Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
- Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
- Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
- Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:41:y:2013:i:1:p:71-88. 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: (Sonal Shukla)or (Rebekah McClure)
If references are entirely missing, you can add them using this form.