Critical discount factor values in discounted supergames

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2018-07-10

Department

Department of Mathematics and Systems Analysis

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Mcode

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Language

en

Pages

1-17

Series

Games, Volume 9, issue 3

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.

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Keywords

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

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DOI

10.3390/g9030047

Citation

Berg, K & Kärki, M 2018, ' Critical discount factor values in discounted supergames ', Games, vol. 9, no. 3, 47, pp. 1-17 . https://doi.org/10.3390/g9030047

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https://urn.fi/URN:NBN:fi:aalto-201808014072

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[article-cris] Perustieteiden korkeakoulu / SCI