Collective action problem in heterogeneous groups

Abstract

I review the theoretical and experimental literature on the collective action problem in groups whose members differ in various characteristics affecting individual costs, benefits and preferences in collective actions. I focus on evolutionary models that predict how individual efforts and fitnesses, group efforts and the amount of produced collective goods depend on the group's size and heterogeneity, as well as on the benefit and cost functions and parameters. I consider collective actions that aim to overcome the challenges from nature or win competition with neighbouring groups of co-specifics. I show that the largest contributors towards production of collective goods will typically be group members with the highest stake in it or for whom the effort is least costly, or those who have the largest capability or initial endowment. Under some conditions, such group members end up with smaller net pay-offs than the rest of the group. That is, they effectively behave as altruists. With weak nonlinearity in benefit and cost functions, the group effort typically decreases with group size and increases with within-group heterogeneity. With strong nonlinearity in benefit and cost functions, these patterns are reversed. I discuss the implications of theoretical results for animal behaviour, human origins and psychology.

Keywords: altruism; collaboration; cooperation; evolutionarily stable strategies; mathematical modelling.

Figure 1.

Dependence of the share of benefit v_i going to an individual of rank i on parameter δ in the models used in numerical simulations with n = 8. (Online version in colour.)

Figure 2.

Collective action in the ‘us versus nature’ game with production function (2.4) without (a) and with (b) group extinction. Additive impact and cost functions. Summary results over all runs for one set of parameters, with B = 4, X₀ = 1, c = 1, G = 1000. For each run, the values are averages over individuals of rank i in all groups in the population. Colours show the relevant amounts for individuals of different ranks, from the rank-1 individual at the bottom (red) to the rank-n individual at the top. Each set of bars corresponds to a specific value of group size n. Each bar within a set corresponds to a specific value of within-group inequality δ, from the smallest on the left (δ = 0.25; low inequality) to the largest on the right (δ = 4; high inequality). Top half of graphs: individual efforts x_i; the total height of each bar gives the group effort. Bottom half of graphs: fertilities, i.e. individual shares of reproduction (). (Online version in colour.)

Figure 3.

Effects of nonlinear costs in the ‘us versus nature’ game. First column (a,c): γ = 1.5, second column (b,d): γ = 2.5. (a,b) No group extinction, (c,d) with group extinction. (Online version in colour.)

Figure 4.

Effects of synergicity in the ‘us versus nature’ game. First column (a,c): α = 1.5, second column (b,d): α = 2.5. (a,b) No group extinction, (c,d) with group extinction. The dashes show the group effort on the logarithmic scale specified on the right y-axis. (Online version in colour.)

Figure 5.

Collective action in the ‘us versus them’ game with production function (2.5) without (a) and with (b) group extinction. Additive impact function, linear costs function. (Online version in colour.)

Figure 6.

Effects of nonlinear costs in the ‘us versus them’ game. First column (a,c): γ = 1.5, second column (b,d): γ = 2, second column γ = 2.5. (a,b) No group extinction, (c,d) with group extinction. (Online version in colour.)

Figure 7.

Effects of synergicity in the ‘us versus them’ game. First column (a,c): α = 1.5, second column (b,d): α = 2, second column α = 2.5. (a,b) No group extinction, (c,d) with group extinction. The dashes show the group effort on the logarithmic scale specified on the right y-axis. (Online version in colour.)