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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