恶意对线性负载均衡博弈中社会最优解的影响
The Effect of Malice on the Social Optimum in Linear Load Balancing Games
摘要：
本文研究了恶意玩家对负载均衡博弈中社会最优性的影响：考虑两个玩家SOC和MAL控制负载均衡博弈中流量的（1-f）和f部分。SOC试图最小化她的球员所面临的总成本，而MAL试图最大化相同的。如果两人的博弈是线性的，我们证明了这个两人零和博弈有一个纯策略纳什均衡。此外，我们表明，MAL的最佳策略之一是发挥自私：让f部分的流量被发送时，流量控制的无穷小球员发挥自私，并达到纳什均衡。这表明，在这个博弈中，一个恶意的参与者不会比一组自私的代理人造成更大的伤害。我们还引入了恶意成本的概念-SOC在均衡时所面临的成本与（1-f）OPT的比率，其中OPT是最小化所有参与者成本的社会最优值。在线性负载均衡游戏中，我们将恶意成本限制为（1+f/2）。
英文摘要：
In this note we consider the following problem to study the effect of malicious players on the social optimum in load balancing games: Consider two players SOC and MAL controlling (1-f) and f fraction of the flow in a load balancing game. SOC tries to minimize the total cost faced by her players while MAL tries to maximize the same. If the latencies are linear, we show that this 2-player zero-sum game has a pure strategy Nash equilibrium. Moreover, we show that one of the optimal strategies for MAL is to play selfishly: let the f fraction of the flow be sent as when the flow was controlled by infinitesimal players playing selfishly and reaching a Nash equilibrium. This shows that a malicious player cannot cause more harm in this game than a set of selfish agents. We also introduce the notion of Cost of Malice - the ratio of the cost faced by SOC at equilibrium to (1-f)OPT, where OPT is the social optimum minimizing the cost of all the players. In linear load balancing games we bound the cost of malice by (1+f/2).
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