Asymmetric probabilistic prospects of Stackelberg players

Abstract

Alkanet al. (Ref. 1) consider the family of all bimatrix games with ordinal payoffs and conclude that the average leader and follower enjoy symmetric prospects under the Stackelberg solution concept. In contrast, economics lore stresses the asymmetry between leader and follower, the leader generally enjoying the more favored position. We replace the computational analysis of Ref. 1 by a simple probabilistic combinatorial argument. We then impose monotonicity conditions on the player preferences. With this regularity condition, the symmetry between leader and follower breaks down, and most of the resultant advantage accrues to the leader. Thus, the monotonicity largely restores the advantage ascribed by economics folklore to the leader. Our analysis extends to nonordinal payoff matrices.