Before revision:  The presence of additional physical constraints that arise in public goods allocation problems motivates the need for modifications to the Fisher market framework to account for these more general set of constraints . In our market mechanism, we specifically modify the Fisher market social optimization problem through a perturbation of the budgets of agents .
After revision:  The presence of additional physical constraints that arise in public goods allocation problems motivates the need for modifications to the Fisher market framework to account for additional constraints we introduce a social convex optimization problem where we perturb the budgets of agents .