Pricing group membership

TL;DR

This paper studies how agents with different types form groups under various decision-making processes, revealing conditions for efficient sorting and the impact of group competition on social welfare.

Contribution

It introduces the concept of top-down sorting equilibrium in group formation models and analyzes its existence, efficiency, and comparison with integration strategies.

Findings

Top-down sorting equilibrium exists under both centralized and decentralized choices.

Integration can be socially better than top-down sorting in certain conditions.

Top-down sorting remains efficient even with inter-group competition.

Abstract

We consider a model where agents differ in their `types' which determines their voluntary contribution towards a public good. We analyze what the equilibrium composition of groups are under centralized and centralized choice. We show that there exists a top-down sorting equilibrium i.e. an equilibrium where there exists a set of prices which leads to groups that can be ordered by level of types, with the first k types in the group with the highest price and so on. This exists both under decentralized and centralized choosing. We also analyze the model with endogenous group size and examine under what conditions is top-down sorting socially efficient. We illustrate when integration (i.e. mixing types so that each group's average type if the same) is socially better than top-down sorting. Finally, we show that top down sorting is efficient even when groups compete among themselves.