# Sensitivity analysis for network aggregative games

## TL;DR

This paper analyzes how the Nash equilibrium in constrained network aggregative games responds to parameter changes, providing a primal-based sensitivity characterization and conditions for strong monotonicity, with applications in social planning and network routing.

## Contribution

It introduces a primal reformulation for sensitivity analysis in network aggregative games and establishes conditions for strong monotonicity, enabling systematic study of equilibrium changes.

## Key findings

- Characterization of Nash equilibrium sensitivity using primal variables
- Conditions guaranteeing strong monotonicity in network aggregative games
- Application framework for social planning and network routing scenarios

## Abstract

We investigate the sensitivity of the Nash equilibrium of constrained network aggregative games to changes in exogenous parameters affecting the cost function of the players. This setting is motivated by two applications. The first is the analysis of interventions by a social planner with a networked objective function while the second is network routing games with atomic players and information constraints. By exploiting a primal reformulation of a sensitivity analysis result for variational inequalities, we provide a characterization of the sensitivity of the Nash equilibrium that depends on primal variables only. To derive this result we assume strong monotonicity of the mapping associated with the game. As the second main result, we derive sufficient conditions that guarantee this strong monotonicity property in network aggregative games. These two characterizations allows us to systematically study changes in the Nash equilibrium due to perturbations or parameter variations in the two applications mentioned above.