On the Relative Sequencing of Internal and External Rent-Seeking Contests

We consider rent-seeking contests between and within two equal-sized groups. Each group adopts one of three sequences: first internal then external contest, first external then internal contest, and simultaneous internal and external contests. Groups cannot unilaterally postpone a contest without losing. We rank the nine possible combinations according to rent-seeking expenditure and expected utilities. Rent-seeking is maximum when both internal contests either precede, or occur simultaneously with, the external contest. These forms have identical, Pareto-dominated, welfare consequences. Among contest forms which offer both groups a positive win probability, rent-seeking is minimized if the between-group contest precedes both within-group contests; this also induces Pareto-efficiency. When the groups independently choose the contest sequence, the unique Nash equilibrium involves simultaneous occurrence of all contests. Results due to Warneryd (1998) and Amegashie (1999) fall out. When a multi-member group battles a single-member one, unity against the common enemy (an efficient sequence choice) can be sustained if the larger group can resolve its internal coordination problem. With unequal groups and symmetric contest sequencing, the one-tier contest form may be Pareto-efficient, despite generating greater rent-seeking than all symmetric two-tier forms.