路由博弈中从利他到不合作
From Altruism to Non-Cooperation in Routing Games
摘要：
研究了多用户共享网络中的路由问题。每个用户试图通过控制其给定流需求的路由来优化其自身的性能或其自身的性能与其他用户的性能之间的某种组合。我们参数化的合作程度，允许覆盖完全非合作行为，完全合作的行为，甚至更多，完全利他的行为，所有这些作为参数的选择的特殊情况。很大一部分的工作包括在探索的合作程度的均衡的影响。我们的第一个发现是确定多个纳什均衡的合作行为，不发生在非合作的情况下，在相同的条件下（成本，需求和拓扑结构）。然后，我们发现了Braess悖论（增加网络容量或增加网络链接会导致所有用户的性能变差），并研究了合作程度对它的影响。我们确定，当我们增加一个用户的合作程度，而其他用户保持不变的合作程度，导致该用户的性能改善。然后，我们继续探索，并将其进行到混合均衡的设置（即一些用户是非原子的-他们有无穷小的需求，其他人有有限的固定需求）。最后，我们得到了一些理论结果，表明低合作度的均衡是唯一的，证实了我们的数值研究的结果。
英文摘要：
The paper studies the routing in the network shared by several users. Each user seeks to optimize either its own performance or some combination between its own performance and that of other users, by controlling the routing of its given flow demand. We parameterize the degree of cooperation which allows to cover the fully non-cooperative behavior, the fully cooperative behavior, and even more, the fully altruistic behavior, all these as special cases of the parameter's choice. A large part of the work consists in exploring the impact of the degree of cooperation on the equilibrium. Our first finding is to identify multiple Nash equilibria with cooperative behavior that do not occur in the non-cooperative case under the same conditions (cost, demand and topology). We then identify Braess like paradox (in which adding capacity or adding a link to a network results in worse performance to all users) and study the impact of the degree of cooperation on it. We identify another type of paradox in cooperation scenario. We identify that when we increase the degree of cooperation of a user while other users keep unchanged their degree of cooperation, leads to an improvement in performance of that user. We then pursue the exploration and carry it on to the setting of Mixed equilibrium (i.e. some users are non atomic-they have infinitesimally small demand, and other have finite fixed demand). We finally obtain some theoretical results that show that for low degree of cooperation the equilibrium is unique, confirming the results of our numerical study.
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