１　Faculty of Economics, Gakushuin University, Tokyo, Japan.  Comments on an early version of this work by Ryuichiro Ishikawa, Mitsunobu Miyake and Mamoru Kaneko are gratefully acknowledged.

２　We do not analyze the special case of q = 0.

３　Geometrically, in Figure 1 player 1 maximizes expected utility by finding the narrowest rectangle that includes the largest possible number of vertices below the 45° line whereas player 2 seeks the shortest rectangle that includes the largest possible number of vertices above the 45° line.

４　However, when q>0 and DA>A^o, player 2 is indifferent between being the leader or the follower.

５　Separate from the absolute rich/poor distinction, we will refer to a player i as “richer” (or “poorer”) than player j if A_i >A _j (or A_i <A _j).

６　We are continuing to assume that a single lottery is to be used for all players in the contest.