Critical discount factor values in discounted supergames

Kimmo Berg*, Markus Kärki

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
109 Downloads (Pure)


This paper examines the subgame-perfect equilibria in symmetric 2 × 2 supergames. We solve the smallest discount factor value for which the players obtain all the feasible and individually rational payoffs as equilibrium payoffs. We show that the critical discount factor values are not that high in many games and they generally depend on how large the payoff set is compared to the set of feasible payoffs. We analyze how the stage-game payoffs affect the required level of patience and organize the games into groups based on similar behavior. We study how the different strategies affect the set of equilibria by comparing pure, mixed and correlated strategies. This helps us understand better how discounting affects the set of equilibria and we can identify the games where extreme patience is required and the type of payoffs that are difficult to obtain. We also observe discontinuities in the critical values, which means that small changes in the stage-game payoffs may affect dramatically the equilibrium payoffs.

Original languageEnglish
Article number47
Pages (from-to)1-17
Issue number3
Publication statusPublished - 10 Jul 2018
MoE publication typeA1 Journal article-refereed


  • 2×2 games
  • Correlated equilibrium
  • Discount factor
  • Folk theorem
  • Payoff set
  • Repeated game


Dive into the research topics of 'Critical discount factor values in discounted supergames'. Together they form a unique fingerprint.

Cite this