A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting.
We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.
Mixing Time and Stationary Expected Social Welfare of Logit Dynamics
我们研究战略博弈的“logit动态”[Blume，Games and Economic Behavior，1993]。这种动态的工作原理如下：在游戏的每个阶段，玩家被随机地均匀选择，并且她根据“噪声”最佳响应进行游戏，其中噪声水平由参数$β$调整。这样的动态定义了一个家庭的遍历马尔可夫链，索引为$β$，在一组策略配置文件。我们相信，这些马尔可夫链的平稳分布给出了一个有意义的描述的长期行为的系统，其代理人是不完全理性的。我们的目标是双重的：一方面，我们感兴趣的是评估博弈在均衡时的表现，即当策略分布是随机的时，根据平稳分布的期望社会福利。另一方面，我们想估计一个系统从任意分布开始并运行logit动态需要多长时间才能接近其平稳分布;即，链的“混合时间”。本文研究了三人CK对策、二人协调对策和两个简单的$n$对策的平稳期望社会福利。对于所有这些游戏，我们也给几乎紧的上界和下界的混合时间的logit动态。我们的结果显示了两种不同的行为：在某些游戏中的混合时间指数依赖于$β$，而对于其他游戏，它可以由一个独立于$β$的函数的上界。
We initiate the study of congestion games with variable demands where the (variable) demand has to be assigned to exactly one subset of resources. The players' incentives to use higher demands are stimulated by non-decreasing and concave utility functions. The payoff for a player is defined as the difference between the utility of the demand and the associated cost on the used resources. Although this class of non-cooperative games captures many elements of real-world applications, it has not been studied in this generality, to our knowledge, in the past. We study the fundamental problem of th…
Evolutionary Dynamics of Variable Games in Structured Populations
University of Electronic Science and Technology of China（电子科技大学）；Southwest University（西南大学）；Institute of Technical Physics and Materials Science, Centre for Energy Research（能源研究中心技术物理与材料科学研究所）
Game of Thrones: Fully Distributed Learning for Multi-Player Bandits
我们考虑了一个N人多臂强盗博弈，每个人从M个武器中选择一个进行T轮。每个参与人对武器有不同的期望奖励，并且瞬时奖励是独立同分布的或马尔可夫的。当两个或两个以上的玩家选择同一只手臂时，他们都获得零奖励。表现是用预期的后悔总和来衡量的，与最大化预期奖励总和的最佳武器分配给玩家相比。我们假设每个玩家只知道自己的行动和每回合获得的奖励。玩家无法观察其他玩家的行为，玩家之间也无法进行交流。我们提出了一个分布式算法，并证明它达到了预期的近O \left（\log T \right）的遗憾之和。这是第一个算法，以实现近秩序的最佳遗憾，在这个完全分布的情况下。所有其他作品都假设所有参与者都有相同的预期回报向量，或者参与者之间的沟通是可能的。
Carnegie Mellon University（卡内基梅隆大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Oxford（牛津大学）；Strategy Robot, Inc.（战略机器人公司）；Strategic Machine, Inc.（战略机器公司）；Optimized Markets, Inc.（优化市场公司）
