Alireza Mohammadi Sepahvand

Across many settings, from social transfers to education and health services, reforms that aim to make access uniformly easier for everyone often exacerbate inequality. When access to the redistributive surplus is determined through competition, such reforms increase players’ efficiency in the contest but also raise the endogenous efficiency threshold for participation. I formalize this threshold-shifting mechanism in a model of decentralized redistribution, where heterogeneous efficiencies determine both who competes and how the redistributive surplus is allocated. The model delivers two main results. First, a uniform efficiency gain—i.e., equal reductions in access costs—does not expand participation. Instead, it amplifies inequality among participants by reinforcing the relative efficiency of those who were already highly efficient prior to the reform. Yet, such a reform also reduces contest-induced welfare loss, thereby giving rise to an equity–efficiency trade-off. Second, a participation-expanding reform that brings excluded players into the contest can reduce both inequality and welfare loss, particularly when: (i) the new entrants are sufficiently efficient relative to the average participant; and (ii) the Herfindahl–Hirschman Index (HHI) of endogenous contest strengths—measuring the extent to which players’ efficiencies exceed the participation threshold—is sufficiently high before the reform; for example, when a few strong participants dominate the competition for redistributive surplus.

This paper studies simultaneous intervention by a social planner in a network game with strategic complementarities. Players belong to degree classes and choose effort. The social planner targets players under a budget constraint, reducing the probability that their activity survives. Effort and intervention are chosen simultaneously, before realised links are observed. Under no assortative mixing—that is, beliefs about future neighbours are independent of own degree class—we show that there is a unique type-symmetric pure-strategy equilibrium. The equilibrium has a degree-threshold structure: sufficiently high-degree classes are targeted, and higher-degree targeted classes face lower survival probabilities. It also equalises effort across partially targeted classes. This is optimal when the planner takes effort as fixed, but it omits how survival probabilities affect effort through network amplification. We use a sequential benchmark to isolate this omitted margin and define a class-specific amplification score. The score captures how strongly a marginal increase in a class’s survival probability raises total surviving effort through network spillovers. If scores differ across targeted classes, simultaneous targeting is not sequentially optimal. Under degree-biased neighbour beliefs, as implied by the friendship paradox, scores are strictly ordered by degree. Thus, when simultaneous policy targets at least two classes, the sequential planner strictly improves by shifting intervention toward higher-degree targeted classes. Simultaneous policy is directionally correct in degree space, but too diffuse within the targeted block.

We construct a general axiomatic approach to measuring spatial concentration around a center or capital point of interest. Building on expected utility theory, we propose a basic axiom of independence (subgroup consistency), and show that it implies an expected influence representation of the concentration order. We prove that two additional axioms (monotonicity and rank invariance) imply that the associated influence function is a decreasing isoelastic function of the distance to the capital. We apply our index to measure the concentration of population around capital cities, show its advantages over alternative measures, and explore its correlations with many variables of interest.