Personalised incentives with constrained regulator's budget

We consider a regulator driving individual choices towards increasing social welfare by providing personal incentives. We formalise and solve this problem by maximising social welfare under a budget constraint. The personalised incentives depend on the alternatives available to each individual and on her preferences. A polynomial time approximation algorithm computes a policy within few seconds. We analytically prove that it is boundedly close to the optimum. We efficiently calculate the curve of social welfare achievable for each value of budget within a given range. This curve can be useful for the regulator to decide the appropriate amount of budget to invest. We extend our formulation to enforcement, taxation and non-personalised-incentive policies. We analytically show that our personalised-incentive policy is also optimal within this class of policies and construct close-to-optimal enforcement and proportional tax-subsidy policies. We then compare analytically and numerically our policy with other state-of-the-art policies. Finally, we simulate a large-scale application to mode choice to reduce CO2 emissions.