Consider a class consisting of $n$ students with their CPI ranging from $0$ to $10$. All of them are scored on a test given by an instructor. Each student in the class knows the CPI and test marks of every student. Following the scoring process, each student is given a choice in the method of evaluation.
Either a student can opt for no evalution, in case of which, the CPI of the student remains the same as before. Or, a student can submit for the evaluation process. The evaluation process is as follows: consider that a total of m students apply for evaluation. If a student has a position of $i$(out of the $m$) in the rank list, the student is awarded a CPI of $10({1−{i\over m+1}})$.
What should be the strategy of each student assuming every student wants to improve one's own CPI?
I realise that this would strongly depend on the distribution of the initial CPIs as well. Also, there can be certain situations where everyone being greedy is helpful for everybody. But for the general case, even if a student enumerates all the possible $2^n$ outcomes along with the payoffs of every other player, what should a student choose?
If we assume that the student cares about his/her ranking among everyone who took the test, it doesn't really matter. The conversion does not alter the ranking of the student; if the student has a lower score than another before conversion he/she/it will also have a lower score than the other after conversion. As the ranking is constant, the only difference is the score itself.
Assuming the student only cares about his / her own score, the student would opt to submit if the conversion positively affects the score, i.e. $$ 10(1- \frac{i}{m+1}) \geq \text{CPI}_i $$ where $\text{CPI}_i$ is the mark for the student.