 Benefits are somewhat less lumpy in these two games than the previous two. Lumpiness can by further reduced by further flattening the curves. At the limit, we get the public goods game shown in the first graph of figure 4. Here the curves are straight lines. Each additional cooperator provides both defectors and cooperators with the same additional benefit of mc/n where c is the cost of donation, m is the stipulated multiplier and n is the number of players in the game. If the curves are sufficiently flat, they can intersect at most once. Altogether there are three possibilities: the game pictured in figure 4(a), where the two curves do not intersect, the one pictured in 4(b), where cooperators' utility is above the defectors' to the left of the intersection and below it to the right, and the one pictured in 4(c), where the defectors' utility starts above that of the cooperators' and ends up below it. In the 4(b), one benefits by cooperating when few of the others do and defecting when most of the others cooperate. Bovens plausibly suggests that this should be regarded as a many-player version of the game of chicken: go straight if your opponent swerves and swerve if your opponent goes straight. In 4(c), one benefits by defecting when most others do and cooperating when most others do. As Bovens suggests, this might be regarded as a many-person version of the stag hunt: hunt together or separately if your opponent does likewise.  (Stag hunt is further discussed in  section 8 below).  The first possibility, as we have seen, meets conditions plausibly associated with the PD. 