Optimal Intervention in Non-Binary Super-Modular Games

We study intervention design problems for general finite non-binary super-modular games. The considered interventions consist in constraining or incentivizing the players to play actions above designed lower bounds, with a cost for the system planner that is a separable increasing function of such bounds. We study the intervention of minimum cost for which a best response learning algorithm leads the system to its greatest Nash equilibrium. We show that, if the utility functions are unimodal, then the optimal intervention problem can be reformulated in terms of improvement paths, leading to a low complexity distributed iterative algorithm for its solution.