Critical Discount Factor Values in Discounted Supergames

Kimmo Berg and Markus Kärki
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Kimmo Berg: Department of Mathematics and Systems Analysis, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto, Finland
Markus Kärki: Department of Mathematics and Systems Analysis, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto, Finland

Games, 2018, vol. 9, issue 3, 1-17

Abstract: 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.

Keywords: repeated game; folk theorem; discount factor; 2 × 2 games; payoff set; correlated equilibrium (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2018
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