To Skip or Not to Skip

So you’re stuck in a line… it is x people long.  You must now decide whether to wait or skip, and how many people to skip. The model is as follows:

For every person skipped, payoff increases by a(x), a constantly increasing function where payoff/person skipped increases as the number of ppl in line increases. Waiting results in a disutility of b(x). Every person skipped experiences a disutility of b’(x)= b(r)+c, where c is a constant representing psychological disutility from being skipped and r is the number of people in front of the individual in line

However, if skipping is unsu

So you’re stuck in a line… it is x people long.  You must now decide whether to wait or skip, and how many people to skip. The model is as follows:

For every person skipped, payoff increases by a(x), a constantly increasing function where payoff/person skipped increases as the number of ppl in line increases. Waiting results in a disutility of b(x). Every person skipped experiences a disutility of b’(x)= b(r)+c, where c is a constant representing psychological disutility from being skipped and r is the number of people in front of the individual in line

However, if skipping is unsuccessful, the skipper will be sent to the back of the line and incur a reputation cost b”(x) = b(x+(h-c))+d . b” uses b evaluated at x+(h-c) because it is assumed that h people are being added to the line while c people exit.   

or

You should will skip x number of people such that the expected value of skipping is maximised and greater than -b(x).

If no such solution exists, you should wait. 

The next logical step would be to calculate how to maximize “social welfare”, but let’s be honest, you’re probably more concerned about your own wait time anyways. It will be left as an exercise to the reader.

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