Optimal Targeting in Super-Modular Games

TL;DR

This paper addresses the problem of optimally selecting a minimal set of players to influence in super-modular games to ensure convergence to the highest Nash equilibrium, introducing an NP-complete problem and an efficient solution algorithm.

Contribution

It formulates the optimal targeting problem in super-modular games, proves its NP-completeness, and proposes a convergent iterative algorithm, with applications to network coordination games.

Findings

The targeting problem is NP-complete.

The proposed algorithm converges efficiently.

Simulations show improved performance over classical heuristics.

Abstract

We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these players are forced to a controlled value while the others are left to repeatedly play a best response action, the system will converge to the greatest Nash equilibrium of the game. Our main contributions consist in showing that the problem is NP-complete and in proposing an efficient iterative algorithm with provable convergence properties for its solution. We discuss in detail the special case of network coordination games and its relation with the notion of cohesiveness. Finally, we show with simulations the strength of our approach with respect to naive heuristics based on classical network centrality measures.