Makes sense. I'd like to suggest the following modifications / additions -
1.) the reward (c) should be a linearly (or geometrically) decreasing function of N - Guy will not be indifferent to N = 2 and N = 100.
2.) N may not be homogenous, which means that (a) will not be uniform. However, a normal leptokurtic distribution does not seem like an unreasonable assumption for (a)
3.) (b) is essentially the opportunity cost - which is proportional to the perceived number of Carols in the bar. (b) can then be a normal distribution with mean (b)/m, where 'm' is a suitable whole number depending on person to person