Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. In such games, agents maximize their utility by choosing actions that differ from their neighbors' actions. Two important problems concerning evolutionary games are the existence of a pure Nash equilibrium (NE) and the convergence time of the dynamics. In this work, we study these two problems for anti-coordination games under sequential and synchronous update schemes. For each update scheme, we examine two decision modes based on whether an agent considers its own previous action (self essential ) or not (self non-essential ) in choosing its next action. Using a relationship between games and dynamical systems, we show that for both update schemes, finding an NE can be done efficiently under the self non-essential mode but is computationally intractable under the self essential mode. To cope with this hardness, we identify special cases for which an NE can be obtained efficiently. For convergence time, we show that the best-response dynamics converges in a polynomial number of steps in the synchronous scheme for both modes; for the sequential scheme, the convergence time is polynomial only under the self non-essential mode. Through experiments, we empirically examine the convergence time and the equilibria for both synthetic and real-world networks.

翻译：网络上的演化反协调博弈捕捉了交通路由和市场竞争等现实世界的策略情境。在此类博弈中，智能体通过选择与其邻居行动不同的策略来最大化自身效用。演化博弈的两个重要问题是纯纳什均衡的存在性以及动力学的收敛时间。本研究针对顺序更新和同步更新两种方案，研究了反协调博弈的这两个问题。对于每种更新方案，我们考察了两种决策模式：智能体在选择下一行动时是否考虑自身先前行动（自我必要模式）或不考虑（自我非必要模式）。利用博弈与动力系统之间的关系，我们证明在两种更新方案下，自我非必要模式可以高效地找到纳什均衡，而自我必要模式在计算上则难以处理。为应对这种困难，我们识别出能够高效获得纳什均衡的特殊情形。在收敛时间方面，我们证明在同步方案两种模式下，最佳响应动力学在多项式步数内收敛；而在顺序方案中，仅自我非必要模式下的收敛时间为多项式。通过实验，我们在合成网络和真实网络上实证考察了收敛时间与均衡状态。