Critical discount factor values in discounted supergames

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Critical discount factor values in discounted supergames. / Berg, Kimmo; Kärki, Markus.

In: Games, Vol. 9, No. 3, 47, 10.07.2018, p. 1-17.

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Berg, Kimmo ; Kärki, Markus. / Critical discount factor values in discounted supergames. In: Games. 2018 ; Vol. 9, No. 3. pp. 1-17.

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@article{0d9a72af2fc046a195d5d8860ff44fa4,
title = "Critical discount factor values in discounted supergames",
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 = "2×2 games, Correlated equilibrium, Discount factor, Folk theorem, Payoff set, Repeated game",
author = "Kimmo Berg and Markus K{\"a}rki",
year = "2018",
month = "7",
day = "10",
doi = "10.3390/g9030047",
language = "English",
volume = "9",
pages = "1--17",
journal = "Games (MDPI)",
issn = "2073-4336",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "3",

}

RIS - Download

TY - JOUR

T1 - Critical discount factor values in discounted supergames

AU - Berg, Kimmo

AU - Kärki, Markus

PY - 2018/7/10

Y1 - 2018/7/10

N2 - 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.

AB - 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.

KW - 2×2 games

KW - Correlated equilibrium

KW - Discount factor

KW - Folk theorem

KW - Payoff set

KW - Repeated game

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U2 - 10.3390/g9030047

DO - 10.3390/g9030047

M3 - Article

VL - 9

SP - 1

EP - 17

JO - Games (MDPI)

JF - Games (MDPI)

SN - 2073-4336

IS - 3

M1 - 47

ER -

ID: 26723715