Rent-seeking with non-identical sharing rules: An equilibrium rescued

Nitzan's (1991) analysis of differential sharing rules in a collective rent-seeking setting is reconsidered. Two groups, each with more than one member, are presumed to use different linear combinations of two sharing rules, one based on an equal-division of the prize, and the other on each member's relative effort. We show that an equilibrium always exists for this type of game, and then characterize the equilibrium. Our result is contrary to Nitzan's claims that (a) in the general case an equilibrium often does not exist, and (b) an equilibrium never exists when the groups use the polar extreme rules.