Computing Equilibria in Discounted 2 × 2 Supergames

Kimmo Berg*, Mitri Kitti

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)


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. © 2011 Springer Science+Business Media, LLC.

Original languageEnglish
Pages (from-to)71-88
Number of pages18
Issue number1
Publication statusPublished - 2013
MoE publication typeA1 Journal article-refereed


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


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