everyone is the present discounted value of y forever: y/(1-δ). A complication arises
when a player might want to defect since h> y . Hence, since z< y , it must be the threat
of minmax forever that deters a player from defecting. Notice that a player deviates in
several instances—first, in equilibrium, if she has not observed play of Z in the past but
chooses Z currently, and second, off-equilibrium, if she has observed play of Z in the past
but plays Y currently.
Consider one-time deviations by a single player (unimprovability criterion). It should
be clear that cooperating when no defection has ever been observed is optimal only if the
agent is sufficiently patient. The future reward from cooperating today must be greater
than the extra utility generated by defecting today. Instead, if a defection occurs and
everyone plays according to the social norm, then everyone will end up defecting since
the initial defection will spread by contagion. Given that the economy has only four
players, this contagion in our experimental economies should occur very quickly. This is
illustrated in Figure 1, by the line labeled reactive strategy.
Cooperating after observing a defection should also be suboptimal. Choosing Y in this
instance can delay the contagion but cannot stop it. To see why, suppose a player has
observed Z. If he meets a cooperator in the following period, then choosing Y generates a
current loss to the player because he earns y (instead of h). If he meets a deviator,
choosing Y also generates a current loss because he earns l rather than z . Therefore, the
player must be sufficiently impatient to prefer play of Z to Y. The smaller are l and y ,
the greater is the incentive to play Z. Our parameterization ensures this incentive exists
for all δ∈ (0, 1) so it is a dominant strategy to play Z after observing (or selecting) Z.
Assuming a homogenous population in our experimental economies, the preceding
discussion has two immediate predictions, which are put forward below.
Proposition 2. In our experimental economies with private monitoring, the efficient
outcome can be sustained as an equilibrium.
Proposition 2 follows directly from Lemma 1. For the efficient outcome to be a feasible,
we need δ ≥ δ* . In our experimental design δ = 0.95 and δ* = 0.443 , a value that
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