High frequency repeated games with costly monitoring

Research output: Contribution to journalArticlepeer-review

Abstract

We study two-player discounted repeated games in which one player cannot monitor the other unless he pays a fixed amount. It is well known that in such a model the folk theorem holds when the monitoring cost is on the order of magnitude of the stage payoff. We analyze high frequency games in which the monitoring cost is small but still significantly higher than the stage payoff. We characterize the limit set of public perfect equilibrium payoffs as the monitoring cost tends to 0. It turns out that this set is typically a strict subset of the set of feasible and individually rational payoffs. In particular, there might be efficient and individually rational payoffs that cannot be sustained in equilibrium. We also make an interesting connection between games with costly monitoring and games played between long-lived and short-lived players. Finally, we show that the limit set of public perfect equilibrium payoffs coincides with the limit set of Nash equilibrium payoffs. This implies that our characterization applies also to sequential equilibria.

Original languageEnglish
Pages (from-to)87-113
Number of pages27
JournalTheoretical Economics
Volume13
Issue number1
DOIs
StatePublished - Jan 2018

Funding

FundersFunder number
Google Inter-university center for Electronic Markets and Auctions
Google
Israel Science Foundation323/13, 963/15, 212/09

    Keywords

    • High frequency repeated games
    • Nash equilibrium
    • characterization
    • costly monitoring
    • no folk theorem
    • public perfect equilibrium

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