论文标题
随机图上的最佳响应动力学
Best response dynamics on random graphs
论文作者
论文摘要
我们考虑在人群上的进化游戏，其基本互动拓扑由二项式随机图$ g（n，p）$确定。我们的重点是两名玩家对称游戏，在此类人群的事件成员之间进行了两种策略。玩家同步更新他们的策略。在每个回合中，每个玩家都会选择对邻居发挥的当前策略的最佳反应策略。我们表明，这种系统减少了普遍的多数和少数派动态。我们显示了$ p $的快速融合在取决于收益矩阵特征的范围内。在游戏的纯纳什平衡之间存在偏见的情况下，我们确定$ p $的急剧阈值，高于最大的连接组件以很高的可能性达到一致性。对于低于此临界值的$ P $，在没有发生的情况下，我们确定最大组件内的那些子结构在整个系统的演变过程中保持不一致。
We consider evolutionary games on a population whose underlying topology of interactions is determined by a binomial random graph $G(n,p)$. Our focus is on 2-player symmetric games with 2 strategies played between the incident members of such a population. Players update their strategies synchronously. At each round, each player selects the strategy that is the best response to the current set of strategies its neighbours play. We show that such a system reduces to generalised majority and minority dynamics. We show rapid convergence to unanimity for $p$ in a range that depends on a certain characteristic of the payoff matrix. In the presence of a bias among the pure Nash equilibria of the game, we determine a sharp threshold on $p$ above which the largest connected component reaches unanimity with high probability. For $p$ below this critical value, where this does not happen, we identify those substructures inside the largest component that remain discordant throughout the evolution of the system.
