Collective action and the group size paradox

According to the Olson paradox, larger groups may be less successful than smaller groups in furthering their interests. We address the issue in a model with three distinctive features: explicit intergroup interaction, collective prizes with a varying mix of public and private characteristics, and nonlinear lobbying costs. The interplay of these features leads to new results. When the cost of lobbying has the elasticity of a quadratic function, or higher, larger groups are more effective no matter how private the prize. With smaller elasticities, a threshold degree of publicness is enough to overturn the Olson argument, and this threshold tends to zero as the elasticity approaches the value for a quadratic function. We also demonstrate that these results are true, irrespective of whether we examine group sizes over the cross-section in some given equilibrium or changes in the size of a given group over different equilibria.