Strong equilibria in games with the lexicographical improvement property
Strong equilibria in games with the lexicographical improvement property
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具有词典改进特性的游戏中的强平衡
DOI：
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发表时间：
2013
影响因子：
0.6
通讯作者：
R. Möhring
中科院分区：
文献类型：
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作者：
T. Harks;Max Klimm;R. Möhring
我们研究了一类有限策略对策，其性质是：博弈者联盟的每一个对其成员都有利的偏差严格降低了定义在策略配置文件集合上的某个函数的词典顺序。我们将这一性质称为词典改进性质(LIP)，并证明了在有限对策中，它等价于广义强势函数的存在。利用这个刻画，我们得到了强均衡的存在性、效率和公平性。作为我们的主要结果，我们证明了一类重要的对策，我们称之为瓶颈拥塞对策，具有LIP，从而具有上述性质。对于无限对策，LIP既不意味着广义强势的存在，也不意味着SE的存在。因此，我们引入了更一般的成对唇形的概念，并证明了当成对唇形满足一个连续函数时，则存在一个SE。因此，我们证明了具有连续设施费用函数的可分瓶颈拥塞对策具有SE。
We study a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the lexicographical improvement property (LIP) and show that, in finite games, it is equivalent to the existence of a generalized strong potential function. We use this characterization to derive existence, efficiency and fairness properties of strong equilibria (SE). As our main result, we show that an important class of games that we call bottleneck congestion games has the LIP and thus the above mentioned properties. For infinite games, the LIP does neither imply the existence of a generalized strong potential nor the existence of SE. We therefore introduce the slightly more general concept of the pairwise LIP and prove that whenever the pairwise LIP is satisfied for a continuous function, then there exists a SE. As a consequence, we show that splittable bottleneck congestion games with continuous facility cost functions possess a SE.