We study binary-action pairwise-separable graphical games that encompass both coordination and anti-coordination network games. Our model is grounded in an underlying directed signed graph, where each link is associated with a signed weight that describes both nature and the strength of the strategic pairwise interaction. Specifically, positive link weight corresponds to a strategic complement type interaction, whereas negative link weight corresponds to strategic substitute type interaction. The utility for each player is then an aggregation of pairwise terms determined by the weights of the signed graph in addition to an individual bias term. We consider a scenario that assumes the presence of a prominent cohesive subset of players, who are either connected exclusively by positive weights, or form a structurally balanced subset that can be bipartitioned into two adversarial subcommunities with positive intra-community and negative inter-community edges. Under suitable properties of the game restricted to the remaining players, our results guarantee the existence of Nash equilibria characterized by either consensus or polarization within the first group, as well as their stability under best response transitions. Our results can be interpreted as robustness results, building on the super-modular properties of network coordination games and on a novel use of the concept of graph cohesiveness.

翻译：我们研究包含协调与反协调网络博弈的二元行动成对可分离图博弈。该模型基于底层有向带符号图，每条边关联一个符号权重，同时描述策略性成对交互的性质与强度。具体而言，正边权重对应策略互补型交互，而负边权重对应策略替代型交互。每个博弈方的效用由带符号图权重与个体偏差项共同决定的成对项聚合构成。我们考虑存在显著凝聚性子集的情形：该子集内的博弈方要么仅通过正权重连接，要么形成结构平衡子集——可二分为两个对抗性子社群，各社群内部含正边、社群间含负边。在限定剩余博弈方满足适当性质的前提下，我们的结果保证了第一群体内存在以共识或极化表征的纳什均衡，及其在最优反应动态下的稳定性。这些结果可解读为基于网络协调博弈超模性质与图凝聚性概念创新应用的鲁棒性结论。