Lambdaphagy

Your professor announces the following homework policy:

“Technically your paper is due at five o'clock. However, what I really care about is being able to grade all the papers in one sitting. So I will begin grading at five, and as long as your paper is submitted before I run out of papers to grade, I will accept it. Otherwise, you get a zero. Sitting down to grade twice just messes with my executive function.

"Each paper takes me 10 minutes to grade. You receive a normalized utility of 1 for submitting your paper on time, plus a benefit b*t for submitting at time t, where t is the number of grading periods that have elapsed, provided that I still have other papers to grade during that time. That is, a paper submitted at 5:00 earns its author 1 util, a paper submitted at 5:10 earns 1 + b utils, 5:20 gets you 1 + 2b utils, and so on.

"But I remind you that if I ever run out of papers to grade at any point, all papers received afterwards will receive zeros. And let us assume that if your paper receives a zero, you will be so stricken with remorse for your sophomoric game-theoretical cleverness that your total payoff will be 0 utils, regardless of your submission time.

"You must decide when to submit without communicating with your classmates. And by the way, every student has the same utility function and now you have common knowledge of this fact.”

If there are N students in the class, when should you submit your paper?