Repeated Multimarket Contact with Private Monitoring: A Belief-Free Approach

TL;DR

This paper develops a belief-free strategy framework for repeated multimarket contact games with private monitoring, demonstrating conditions under which collusion can be sustained with simple, mild punishment strategies.

Contribution

It introduces a novel class of belief-free automaton strategies that support collusion in multimarket contact with private signals, highlighting the role of partial indifference.

Findings

Collusive equilibria can be sustained with simple strategies.

Mild punishment strategies do not harm minimum cartel profits.

Partial indifference condition ensures optimal collusive payoffs.

Abstract

This paper studies repeated games where two players play multiple duopolistic games simultaneously (multimarket contact). A key assumption is that each player receives a noisy and private signal about the other's actions (private monitoring or observation errors). There has been no game-theoretic support that multimarket contact facilitates collusion or not, in the sense that more collusive equilibria in terms of per-market profits exist than those under a benchmark case of one market. An equilibrium candidate under the benchmark case is belief-free strategies. We are the first to construct a non-trivial class of strategies that exhibits the effect of multimarket contact from the perspectives of simplicity and mild punishment. Strategies must be simple because firms in a cartel must coordinate each other with no communication. Punishment must be mild to an extent that it does not hurt even the minimum required profits in the cartel. We thus focus on two-state automaton strategies such that the players are cooperative in at least one market even when he or she punishes a traitor. Furthermore, we identify an additional condition (partial indifference), under which the collusive equilibrium yields the optimal payoff.