Computational Economics

, Volume 41, Issue 1, pp 71–88 | Cite as

Computing Equilibria in Discounted 2 × 2 Supergames

  • Kimmo Berg
  • Mitri Kitti


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.


Repeated game 2 × 2 game Subgame perfect equilibrium Equilibrium path Payoff set Multigraph 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Aalto University School of Science, Systems Analysis LaboratoryAaltoFinland
  2. 2.Department of EconomicsUniversity of TurkuTurkuFinland

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