Communication and cooperation in repeated games

Abstract

We study the role of communication in repeated games with private monitoring. We first show that without communication, the set of Nash equilibrium payoffs in such games is a subset of the set of ε-coarse correlated equilibrium payoffs (ε-CCE) of the underlying one-shot game. The value of ε depends on the discount factor and the quality of monitoring. We then identify conditions under which there are equilibria with "cheap talk" that result in nearly efficient payoffs outside the set ε-CCE. Thus, in our model, communication is necessary for cooperation.

Collusion and Information Exchange

“…Hereafter, we will briefly explain what a coarse correlated equilibrium is, and then how ε is determined. Precise arguments can be found in sections 2 and 4 of Awaya and Krishna ().…”

“…What happens in a more general case? Awaya and Krishna () construct an equilibrium that works with a general repeated game. When is sufficiently big, the profit of each firm is arbitrarily close to the monopolist profit .…”

“…For a fixed δ , ε is increasing in η and Formal definition of monitoring quality involves total variation distance, and the interested reader can find this in section 2 of Awaya and Krishna (). The formula for log‐normal distribution is presented in section 3 of Awaya and Krishna ().…”

“…In Awaya and Krishna (), we show that exchange of aggregate sales data, which are deemed to be legal, can also be anti‐competitive. I also describe an upper bound of the set of equilibrium payoffs of a general repeated game, developed by Awaya and Krishna (), which plays a key role in understanding the effect of information exchange on firms’ profits.…”

Monitoring versus Discounting in Repeated Games

“…] for all h t ∈ H t . By the law of total variance (e.g., Billingsley (1995), Problem 34.10(b)), we have…”