When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?

Olivier Gossner; Johannes Hörner

doi:10.1016/j.jet.2009.07.002

When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?

When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff? — Journal of Economic Theory 145(1), 63–84 (2010)

Authors

Olivier Gossner

Johannes Hörner

Abstract

We study the relationship between a player’s lowest equilibrium payoff in a repeated game with imperfect monitoring and this player’s min max payoff in the corresponding one-shot game. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under an identifiability assumption, we further show that, if the monitoring structure of an infinitely repeated game “nearly” satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.

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Journal of Economic Theory 145(1), 63–84 (2010)

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Citation

BibTeX citation:

@article{gossner2010,
  author = {Gossner, Olivier and Hörner, Johannes},
  title = {When Is the Lowest Equilibrium Payoff in a Repeated Game
    Equal to the Minmax Payoff?},
  journal = {Journal of Economic Theory},
  volume = {145},
  number = {1},
  pages = {63–84},
  date = {2010},
  url = {https://gossner.me/papers/when-is-the-individually-rational-payoff-in-a-repeated-game-equal-to-the-minmax.html},
  doi = {10.1016/j.jet.2009.07.002},
  langid = {en},
  abstract = {We study the relationship between a player’s lowest
    equilibrium payoff in a repeated game with imperfect monitoring and
    this player’s min max payoff in the corresponding one-shot game. We
    characterize the signal structures under which these two payoffs
    coincide for any payoff matrix. Under an identifiability assumption,
    we further show that, if the monitoring structure of an infinitely
    repeated game “nearly” satisfies this condition, then these two
    payoffs are approximately equal, independently of the discount
    factor. This provides conditions under which existing folk theorems
    exactly characterize the limiting payoff set.}
}

For attribution, please cite this work as:

Gossner, Olivier, and Johannes Hörner. 2010. “When Is the Lowest Equilibrium Payoff in a Repeated Game Equal to the Minmax Payoff?” Journal of Economic Theory 145 (1): 63–84. https://doi.org/10.1016/j.jet.2009.07.002.