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We consider multiple optimal stopping rules for a finite (with horizon  N ) sequence of independent random variables. We are interested in finding a stopping rule which maximises the expected sum of  k , 1 &lt;  k  &lt;  N , observations. The optimal stopping rule and the value of the game are obtained. This result can be applied in the house-selling problem and in behavioural ecology problems.

A multiple optimal stopping rule for sums of independent random variables