  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.
