Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more complex behaviors. In fact, depending on the network structure, such games may even fail to have pure-strategy Nash equilibria. An example is represented by the well-known matching pennies (discoordination) game. In this work, we first provide graph-theoretic conditions for the existence of pure-strategy Nash equilibria in mixed network coordination/anti-coordination games of arbitrary size. For the case where such conditions are met, we then study the asymptotic behavior of best-response dynamics and provide sufficient conditions for finite-time convergence to the set of Nash equilibria. Our results build on an extension and refinement of the notion of network cohesiveness and on the formulation of the new concept of network indecomposibility.

翻译：尽管网络协调游戏和网络反协调游戏在文献中受到相当程度的注意,但已知与同时进行协调和反协调的玩家的网络游戏表现出更为复杂的行为。事实上,根据网络结构,这种游戏甚至可能没有纯粹的策略性Nash equilibria(Nash equilibria) 。一个有名的匹配硬币(discoordination)游戏就是例子。在这项工作中,我们首先为在任意规模的混合网络协调/反协调游戏中存在纯战略性Nash equilibria提供图形理论条件。对于满足这些条件的情况,我们接着研究最佳反应动态的无约束行为,并为与Nash equilibria 组合的不定期融合提供足够条件。我们的成果建立在网络凝聚力概念的扩展和完善以及网络不兼容性新概念的形成之上。