The equivalence of rent-seeking outcomes for competitive-share and strategic groups

In competitive-share groups, groups of players compete for a rent and members of the winning group share the prize according to a weighted average of relative outlay and egalitarian shares. In strategic groups, group members compete individually for a rent and the winner keeps a part of the rent, and divides the rest among group members. In this note, we show that these two portrayals of rent seeking with groups are equivalent.