ABSTRACT
In their entertaining and informative book The Art of Strategy, Avinash Dixit and Barry Nalebuff (New York: W.W. Norton, 2009) recount a contest between two competing teams, euphemistically labeled Red and Blue here, on the TV series Survivor in which 21 flags are planted in the sand. Each team, beginning with Red, must in sequence, take 1, 2 or 3 flags (a team cannot choose to take no flags, nor can it take 4 or more), and the team taking the last flag, whether it be alone or in combination with one or two others, is declared the winner. We leave it for the reader to consult Dixit and Nalebuff for the details on how this contest actually unfolded in the TV series; here we note simply that if one considers this contest an extensive form game, team Red should, if possible, maneuver things so that Blue is confronted with 4 flags on its last move. In this case, regardless of whether Blue chooses 1, 2 or 3 flags, Red will win by taking the remaining 3, 2 or 1 flags. But that means Red should maneuver to leave Blue with 8 flags on its move before that, since with 8 flags, regardless of Blue’s subsequent choice, Red can ensure that Blue confronts 4 flags on its last move. Moving further back on the extensive form, this implies that Red should maneuver to have Blue confront 12 flags before that, 16 before that and 20 before that. In other words, Red should choose 1 flag on the first move and counter any selection by Blue thereafter so that the number of flags chosen by Blue + Red on each successive pair of moves sums to 4.
