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.

中文翻译：

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超模块化游戏中的最佳定位

我们研究了具有二元动作和有限数量玩家的超模块化游戏的最佳定位问题。所考虑的问题在于选择最小尺寸的玩家子集，这样，当这些玩家的动作被迫达到受控值而其他玩家被留下重复执行最佳响应动作时，系统将收敛到最大博弈的纳什均衡。我们的主要贡献在于表明该问题是 NP 完全的，并提出了一种有效的迭代算法，该算法的解决方案具有可证明的收敛特性。我们详细讨论了网络协调博弈的特殊情况及其与凝聚力概念的关系。最后，我们通过模拟展示了我们的方法在基于经典网络中心性度量的朴素启发式方法方面的优势。