Repeated games with general discounting

Ichiro Obara, Jaeok Park

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we introduce a general class of time discounting, which may exhibit present bias or future bias, to repeated games with perfect monitoring. A strategy profile is called an agent subgame perfect equilibrium if there is no profitable one-shot deviation by any player at any history. We study strongly symmetric agent subgame perfect equilibria for repeated games with a symmetric stage game. We find that the worst punishment equilibrium takes different forms for different types of bias. When players are future-biased or have quasi-hyperbolic discounting, the worst punishment payoff can be achieved by a version of stick-and-carrot strategies. When players are present-biased, the worst punishment path may fluctuate over time forever. We also find that the stage-game minmax payoff does not serve as a tight lower bound for the limit equilibrium payoff set. The worst punishment payoff can be below the minmax payoff with future bias and above the minmax payoff with present bias, even when players are very patient. Lastly, we compare the effect of making players interact more frequently and the effect of making them more patient for a given intertemporal bias structure defined on continuous time.
Original languageEnglish
Pages (from-to)348-375
Number of pages28
JournalJournal of Economic Theory
Volume172
DOIs
Publication statusPublished - 2017 Nov

Fingerprint

Punishment
Repeated games
Discounting
Subgame perfect equilibrium
Present bias
Quasi-hyperbolic discounting
Lower bounds
Continuous time
Monitoring
Deviation

Cite this

Obara, Ichiro ; Park, Jaeok. / Repeated games with general discounting. In: Journal of Economic Theory. 2017 ; Vol. 172. pp. 348-375.
@article{f035db8f27384cbb8166c61fdae4affc,
title = "Repeated games with general discounting",
abstract = "In this paper, we introduce a general class of time discounting, which may exhibit present bias or future bias, to repeated games with perfect monitoring. A strategy profile is called an agent subgame perfect equilibrium if there is no profitable one-shot deviation by any player at any history. We study strongly symmetric agent subgame perfect equilibria for repeated games with a symmetric stage game. We find that the worst punishment equilibrium takes different forms for different types of bias. When players are future-biased or have quasi-hyperbolic discounting, the worst punishment payoff can be achieved by a version of stick-and-carrot strategies. When players are present-biased, the worst punishment path may fluctuate over time forever. We also find that the stage-game minmax payoff does not serve as a tight lower bound for the limit equilibrium payoff set. The worst punishment payoff can be below the minmax payoff with future bias and above the minmax payoff with present bias, even when players are very patient. Lastly, we compare the effect of making players interact more frequently and the effect of making them more patient for a given intertemporal bias structure defined on continuous time.",
author = "Ichiro Obara and Jaeok Park",
year = "2017",
month = "11",
doi = "10.1016/j.jet.2017.09.008",
language = "English",
volume = "172",
pages = "348--375",
journal = "Journal of Economic Theory",
issn = "0022-0531",
publisher = "Academic Press Inc.",

}

Repeated games with general discounting. / Obara, Ichiro; Park, Jaeok.

In: Journal of Economic Theory, Vol. 172, 11.2017, p. 348-375.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Repeated games with general discounting

AU - Obara, Ichiro

AU - Park, Jaeok

PY - 2017/11

Y1 - 2017/11

N2 - In this paper, we introduce a general class of time discounting, which may exhibit present bias or future bias, to repeated games with perfect monitoring. A strategy profile is called an agent subgame perfect equilibrium if there is no profitable one-shot deviation by any player at any history. We study strongly symmetric agent subgame perfect equilibria for repeated games with a symmetric stage game. We find that the worst punishment equilibrium takes different forms for different types of bias. When players are future-biased or have quasi-hyperbolic discounting, the worst punishment payoff can be achieved by a version of stick-and-carrot strategies. When players are present-biased, the worst punishment path may fluctuate over time forever. We also find that the stage-game minmax payoff does not serve as a tight lower bound for the limit equilibrium payoff set. The worst punishment payoff can be below the minmax payoff with future bias and above the minmax payoff with present bias, even when players are very patient. Lastly, we compare the effect of making players interact more frequently and the effect of making them more patient for a given intertemporal bias structure defined on continuous time.

AB - In this paper, we introduce a general class of time discounting, which may exhibit present bias or future bias, to repeated games with perfect monitoring. A strategy profile is called an agent subgame perfect equilibrium if there is no profitable one-shot deviation by any player at any history. We study strongly symmetric agent subgame perfect equilibria for repeated games with a symmetric stage game. We find that the worst punishment equilibrium takes different forms for different types of bias. When players are future-biased or have quasi-hyperbolic discounting, the worst punishment payoff can be achieved by a version of stick-and-carrot strategies. When players are present-biased, the worst punishment path may fluctuate over time forever. We also find that the stage-game minmax payoff does not serve as a tight lower bound for the limit equilibrium payoff set. The worst punishment payoff can be below the minmax payoff with future bias and above the minmax payoff with present bias, even when players are very patient. Lastly, we compare the effect of making players interact more frequently and the effect of making them more patient for a given intertemporal bias structure defined on continuous time.

U2 - 10.1016/j.jet.2017.09.008

DO - 10.1016/j.jet.2017.09.008

M3 - Article

VL - 172

SP - 348

EP - 375

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

ER -