We analyze a game-theoretic abstraction of epidemic containment played on an undirected graph $G$: each player is associated with a node in $G$ and can either acquire protection from a contagious process or risk infection. After decisions are made, an infection starts at a random node $v$ and propagates through all unprotected nodes reachable from $v$. It is known that the price of anarchy (PoA) in $n$-node graphs can be as large as $\Theta(n)$. Our main result is a tight bound of order $\sqrt{n\Delta}$ on the PoA, where $\Delta$ is the maximum degree of the graph. We also study additional factors that can reduce the PoA, such as higher thresholds for contagion and varying the costs of becoming infected vs. acquiring protection.

翻译：我们分析了在无向图$G$上进行的流行病遏制博弈论抽象：每个玩家与$G$中的一个节点相关联，可以选择从传染过程中获得保护，也可以承担感染风险。在做出决策后，感染从随机节点$v$开始，并通过所有从$v$可到达的未保护节点传播。已知在$n$节点图中，无政府状态代价（PoA）可高达$\Theta(n)$。我们的主要结果是PoA的一个紧密界，数量级为$\sqrt{n\Delta}$，其中$\Delta$是图的最大度。我们还研究了其他可降低PoA的因素，例如更高的传染阈值以及改变感染成本与获得保护成本之间的差异。