Optimal strategies for maximum-number games

Decision making in a sequential search task

“…In the individual situation, the experiment ends as soon as S stops; in the group situation he must remain until the slowest member of the group finishes. The cost of observations is therefore more likely to be salient for the Ss tested alone, an effect that would lower the optimal stopping number Zo (Ash & Jones, 1964;Rapoport & Tversky, 1966). Also, in a group, it may be embarrassing for S to stop too soon while others continue and win.…”

“…We define the state Sn as where Xu is the number written on the nth card, n:~, 2, ..• ,N. We then have P(Sn+1 =jISn=i)=O for j< i, = P(X n+1 = j) for j >I, A solution to the finite optimal stopping problem for large N was given by Ash and Jones (1964): sample until Zo = N -ka cards have been observed, and then stop after exposing the first card which is the largest of those seen so far (hereafter referred to as a candidate). Declare the candidate to be the largest in the deck.…”