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a/(1-w) ≥ c1p + c2(1 − p). This equilibrium condition has a natural interpretation as well:
in order to sustain CWOL, the long term gains to player 1 from the ongoing relationship
must suffice for player 1 to cooperate when player 1 expects the temptation to sometimes
be high. That is, not looking makes the expected–as opposed to realized–gains from
defection relevant, in a sense smoothing the temptation to defection. Thus, the range
where CWOL is an equilibrium and CWL is not, c1p + c2(1 − p) ≤ a/(1-w) < c2, has the
following interpretation: the expected temptation is low but the maximal temptation is
high. In the appendix, we confirm this result using our subgame perfections analysis. We
also use dynamics to show that, CWOL increases relative to CWL when we increase the
maximal temptation, but hold the mean temptation constant.

We identify a second condition under which people will be most likely to avoid and
detect looking by relaxing the assumption d > (p/(1-p))b. Then, in the region where d ≤ (p/(1-p))b,
there is a fourth equilibrium. It is the strategy pair where player 2 always continues if
player 1 cooperates when the temptation is low, and player 1 looks and cooperates only
when the temptation is low (we refer to this as the ONLYL equilibrium). In contrast,
CWOL is an equilibrium for all values of d. CWOL is thus the only cooperative equilibrium
in the parameter region d > (p/(1-p))b, which has the interpretation: defection is sufficiently
harmful to player 2 such that player 2 prefers to avoid the interaction if player 1 only
cooperates some of the time.

Note that CWOL is an equilibrium over a wider parameter region than both CWL
and ONLYL, and thus that the ability to avoid looking and to detect whether others look
increases the parameter space over which cooperation is feasible. To see this, consider re-
moving player 1’s strategy which consists of not looking. Alternatively, consider removing
player 2’s strategy where he conditions his behavior on whether player 1 has looked. In
either case, cooperation is only sustained in a Nash Equilibrium if a/(1-w) ≥ ap + c2(1 − p) or

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