provide sufficient conditions so that the equilibrium set includes the efficient outcome,
following the work of Kandori (1992) and Ellison (1994). This is achieved when
everyone cooperates in every match and in every period.
The private monitoring treatment is characterized by two informational frictions.
Players cannot observe identities of opponents, so we say that players are strangers.
Second, players can neither communicate with each other nor observe action histories of
others; they can only observe the outcome resulting from actions taken in their pair.
Clearly, the inefficient outcome can be supported as a sequential equilibrium through
the strategy “defect forever.” Because repeated play does not decrease the set of
equilibrium payoffs, Z is always a best response to play of Z by any randomly selected
opponent. In this case the players’ payoff in the indefinitely repeated game is the present
discounted value of the minmax payoff forever z/(1-δ).
If δ is sufficiently high, however, then the efficient outcome can be sustained as a
sequential equilibrium. Formally, we have the following result.
Lemma 1. Let δ* ∈(0,1) be the unique value of δthat satisfies
δ2(h- z) + δ(2h - y - z) - 3(h - y) = 0.
If δ ≥ δ *, then the efficient outcome can be sustained as a sequential equilibrium. In an
economy with full cooperation, every player receives payoff y / (1-δ).
The proof is in Appendix A and follows that found in Kandori (1992). Here, we
provide intuition. Conjecture that players behave according to actions prescribed by a
social norm; a social norm is simply a rule of behavior that identifies “desirable” play and
a sanction to be selected if a departure from the desirable action is observed. We identify
the desirable action by Y and the sanction by Z. Thus, every player must cooperate as
long as she has never played Z or has seen anyone select Z. However, as soon as a player
observes Z, then she must select Z forever after. This is known as a grim trigger strategy.
In our experiments, this strategy is equivalent to what we call a reactive strategy (i.e., a
player will choose Z if and only if one of his opponents has chosen Z).
Given this social norm, on the equilibrium path everyone cooperates so the payoff to
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