Effort Provision and Incentivisation in Tullock Group-Contests with Many Groups: An Explicit Characterisation

We study effort provision and incentivisation in a Tullock group-contest with m ≥ 2 groups that differ in size. A novel algorithmic procedure is presented that, under a symmetry assumption, explicitly characterises the equilibrium. Endogenous, optimal incentivisation schemes are then determined. Four results ensue. First, strategic interactions endogenously come in mean-field form: individual effort provision responds to the aggregate effort and average egalitarianism across groups. Therefore, the game is aggregative. Second, individuals endlessly cycle between zero and positive effort provision at some incentivisation schemes: no pure-strategy equilibria exist in these cases. Third, group size determines whether the egalitarianism of endogenous schemes increases or decreases in the average egalitarianism across groups. Fourth, all groups provide effort at the endogenous schemes if incentivisation is properly restricted.