Conflict between non-exclusive groups

How is group conflict over a public-good prize affected when individuals are active members of multiple groups simultaneously? To investigate this question, I introduce a simple model of Tullock group contest: individuals are partitioned into two groups in two dimensions each, the group-level impact function is concave, and effort cost convex. The additional partition dimension does not alter the level of aggregate and individual effort. Asymmetries in group size and effort cost have non-monotonic effects on individual efforts and expected utilities. The formation of an active additional group is beneficial for its members and detrimental to outsiders. I generalise the model to an arbitrary number of symmetric groups in an arbitrary number of dimensions and briefly investigate the full positive range of the Tullock exponent. Additional group dimensions do not alter expected utilities of existing equilibria. (C) 2020 Elsevier B.V. All rights reserved.