Geodesic
A multiple optimal stopping rule for sums of independent random variables
Diskretnaya Matematika, Tome 19 (2007) no. 4, pp. 42-51.

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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 $k$, $1$, 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. 
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M. L. Nikolaev; G. Yu. Sofronov. A multiple optimal stopping rule for sums of independent random variables. Diskretnaya Matematika, Tome 19 (2007) no. 4, pp. 42-51. http://geodesic.mathdoc.fr/item/DM_2007_19_4_a2/

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