异构无线网络用户网络关联优化:一种基于群体博弈的方法

针对异构无线网络(Heterogeneous Wireless Networks,HWNs)负载平衡问题,提出了一种基于群体博弈的用户网络关联方案.首先将HWNs系统用户网络关联问题抽象成一个群体博弈模型,根据用户在网络中得到的收益函数,证明该群体博弈满足势博弈的条件.利用复制动态作为演化动态工具,证明演化的结果最终会收敛到纳什均衡,这个特性确保了每个用户关联到一个效用最优的网络.然后证明纳什均衡点能最大化整个HWNs系统的吞吐量,保证了纳什均衡的有效性.最后,基于复制动态原理提出了用户网络关联算法.仿真实验模拟了用户网络选择过程,得到了均衡点,验证了理论分析的结果.     

供应链中分享真实信息的激励机制

展示了古诺竞争模型中一个供应商和多个零售商的3阶段博弈模型,并证实了如果零售商能真实地分享预测信息,则供应商往往会获利,而零售商的利润将下降.分享信息时零售商会有动机透露较少的需求预测,这种信息失真现象是各方利用私人信息获取自身利益的结果.如果供应商和零售商分享信息前,能够就相对利润率或利润达成协议,则信息共享的阻碍因素和扭曲信息的动机会消失,零售商将如实地分享信息,双方都能够从信息共享的行为中获利.     

供应链中分享真实信息的激励机制

展示了古诺竞争模型中一个供应商和多个零售商的3 阶段博弈模型, 并证实了如果零售商能真实地分享预测信息, 则供应商往往会获利, 而零售商的利润将下降. 分享信息时零售商会有动机透露较少的需求预测, 这种信息失真现象是各方利用私人信息获取自身利益的结果. 如果供应商和零售商分享信息前, 能够就相对利润率或利润达成协议, 则信息共享的阻碍因素和扭曲信息的动机会消失, 零售商将如实地分享信息, 双方都能够从信息共享的行为中获利.     

基于乘法偏好关系的群一致性偏差熵多属性群决策方法研究

在多属性群决策中, 针对每一个属性下决策者都有一个关于决策方案的乘法偏好关系的决策问题, 提出一种基于乘法偏好关系的群一致性偏差熵多属性群决策方法. 此方法考虑到不同属性下的决策者具有不同的权重, 并通过迭代运算可以达到群一致性水平, 从而得出最终的不同属性下决策者的权重; 同时, 可以利用偏差熵模型来求解属性权重, 利用这两个权重最终获得一个综合各方意见的群一致性乘法偏好关系. 最后通过算例分析验证了所提出方法的有效性.     

多吃纤维食物能抑制女性食欲

我们每一个人都知道,如果你吃了一盘豆角或是一碗糠麸类东西,你很快就会感到吃饱了.最近由美国<临床营养学>杂志发表的一份研究报告指出,膳食中纤维量的增加会使妇女更易有吃饱了的感觉,并且会增加人体中某种与吃饱有关的荷尔蒙的含量.     

基于密度峰值聚类理念的大群体应急模糊决策模型

针对决策者权重未知情形下重大突发事件应急决策问题,提出一种SFN-CFSFDP-Borda-MULTIMOORA模型.首先,采用球形模糊数描述决策者对应急备选方案的评价信息;其次,基于密度峰值聚类理念对大决策群体进行聚类;然后,提出可扩展的群体综合冲突优化模型,根据聚类结果进行冲突测度,求解决策者及聚集的权重并实现意见融合;再次,利用改进Borda-MULTIMOORA法决策最优方案;最后,以黑龙江东湖水库事件为例,对模型的有效性与实用性给予验证.结果表明,SFN-CFSFDP-Borda-MULTIMOORA模型能够充分考虑决策者的心理特征,强化在重大突发不确定情景下决策者的知识表达能力,同时明确聚类中心的选择方法,达到聚集内部差异小、聚集间差异大的聚类效果,通过考虑群体综合冲突及实际决策情形对决策者权重和聚集权重进行设置更符合实际,有效实现群体冲突融合,并提高决策效率,为重大突发事件大群体应急决策提供理论支持.     

基于方案修订的群决策一致性形成的研究

层次分析法(AHP)是群决策中经常使用的一种方法,利用AHP进行群决策的过程实质上也是决策者个体偏好集结的过程。针对如何将不同形式的偏好信息进行有效集结以形成群决策一致性方案的问题,提出一种通过活用AHP修订决策方案达到决策者群体的一致性偏好最终得以形成的方法,在利用决策者的决策信息进行群组划分的基础上明确各个划分的决策偏好差异,提出了活用AHP进行群决策一致性形成的方向,并形成了有效的动态群决策过程。     

群体环境下基于随机对策的多Agent局部学习算法

基于群体环境中个体agent局部感知和交互的生物原型,提出一种随机对策框架下的多agent局部学习算法．算法在与局部环境交互中采用贪婪策略最大化自身利益．分别在零和、一般和的单个平衡点和多个平衡点情形下改进了Nash-Q学习算法;提出了行为修正方法,并证明了算法收敛、计算复杂度降低．     

基于能效的多小区LTE系统资源分配算法

针对多小区LTE移动通信系统,考虑用户的最小速率要求,以最大化系统能效为目标,提出了一种迭代式的资源分配算法,通过不断迭代子信道分配和功率控制两个子过程来优化系统能效.针对子信道分配问题,提出了一种基于三种基本模式的子信道调整算法;针对功率控制问题,建立了多小区非合作博弈模型,理论证明了纳什均衡点的存在性,并设计了算法收敛于该纳什均衡点.仿真结果表明,与多小区最大化系统吞吐量算法相比,提出的算法获得了明显的能效增益,同时也达到了较好的系统吞吐量,尤其在强干扰环境下该算法的优势更加明显.     

社会网络环境下基于公众行为大数据属性挖掘的大群体应急决策方法及应用

针对社会网络环境下复杂大群体应急决策中决策属性信息难以获得问题,提出社会网络环境下公众行为大数据驱动的大群体应急决策方法.首先,通过挖掘社交平台上的公众行为大数据,利用TF-IDF、Word2vec技术进行关键词提取、聚类及其影响力分析,从大量行为数据中挖掘大群体决策属性信息以辅助专家决策,使决策结果具有更高的科学性和有效性;其次,构建决策者间基于信任关系和观点相似度的社会网络,采用同时考虑信任和相似度的聚类方法对决策者进行聚类,并基于社会网络分析获得决策者权重;然后,提出基于决策者间信任关系的共识调整方法进行共识调整以获得最终群体决策矩阵和方案排序,通过引入决策者客观自信度避免个别决策者过分自信行为的影响;最后,通过一个新冠疫情案例分析说明方法的可行性和有效性.     

Road Pricing Design Based on Game Theory and Multi-agent Consensus

Consensus theory and noncooperative game theory respectively deal with cooperative and noncooperative interactions among multiple players/agents. They provide a natural framework for road pricing design, since each motorist may myopically optimize his or her own utility as a function of road price and collectively communicate with his or her friends and neighbors on traffic situation at the same time. This paper considers the road pricing design by using game theory and consensus theory. For the case where a system supervisor broadcasts information on the overall system to each agent, we present a variant of standard fictitious play called average strategy fictitious play (ASFP) for large-scale repeated congestion games. Only a weighted running average of all other players' actions is assumed to be available to each player. The ASFP reduces the burden of both information gathering and information processing for each player. Compared to the joint strategy fictitious play (JSFP) studied in the literature, the updating process of utility functions for each player is avoided. We prove that there exists at least one pure strategy Nash equilibrium for the congestion game under investigation, and the players' actions generated by the ASFP with inertia (players' reluctance to change their previous actions) converge to a Nash equilibrium almost surely. For the case without broadcasting, a consensus protocol is introduced for individual agents to estimate the percentage of players choosing each resource, and the convergence property of players' action profile is still ensured. The results are applied to road pricing design to achieve socially local optimal trip timing. Simulation results are provided based on the real traffic data for the Singapore case study.      

Forward looking Nash equilibrium for keyword auction

We introduce the concept of forward looking Nash equilibrium for the position auction (also called the generalized second price auction), a widely studied protocol for Internet advertisement bidding processes. We show that it has a unique solution for the position auction. Most importantly, the cost each bidder pays and the revenue of the auctioneer under the equilibrium are all equal to those under VCG mechanism. As the position auction is not an incentive compatible protocol, the fact that the forward looking Nash equilibrium results in the same payoff for everyone as in the VCG protocol justifies the practical protocol.     

Matrix games with missing,interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.     

Equilibria of graphical games with symmetries

We study graphical games where the payoff function of each player satisfies one of four types of symmetry in the actions of his neighbors. We establish that deciding the existence of a pure Nash equilibrium is NP-hard in general for all four types. Using a characterization of games with pure equilibria in terms of even cycles in the neighborhood graph, as well as a connection to a generalized satisfiability problem, we identify tractable subclasses of the games satisfying the most restrictive type of symmetry. Hardness for a different subclass leads us to identify a satisfiability problem that remains NP-hard in the presence of a matching, a result that may be of independent interest. Finally, games with symmetries of two of the four types are shown to possess a symmetric mixed equilibrium which can be computed in polynomial time. We thus obtain a natural class of games where the pure equilibrium problem is computationally harder than the mixed equilibrium problem, unless P=NP.     

On the complexity of constrained Nash equilibria in graphical games

A widely accepted rational behavior for non-cooperative players is based on the notion of Nash equilibrium. Although the existence of a Nash equilibrium is guaranteed in the mixed framework (i.e., when players select their actions in a randomized manner) in many real-world applications the existence of “any” equilibrium is not enough. Rather, it is often desirable to single out equilibria satisfying some additional requirements (in order, for instance, to guarantee a minimum payoff to certain players), which we call constrained Nash equilibria.In this paper, a formal framework for specifying these kinds of requirement is introduced and investigated in the context of graphical games, where a player p may directly be interested in some of the other players only, called the neighbors of p. This setting is very useful for modeling large population games, where typically each player does not directly depend on all the players, and representing her utility function extensively is either inconvenient or infeasible.Based on this framework, the complexity of deciding the existence and of computing constrained equilibria is then investigated, in the light of evidencing how the intrinsic difficulty of these tasks is affected by the requirements prescribed at the equilibrium and by the structure of players’ interactions. The analysis is carried out for the setting of mixed strategies as well as for the setting of pure strategies, i.e., when players are forced to deterministically choose the action to perform. In particular, for this latter case, restrictions on players’ interactions and on constraints are identified, that make the computation of Nash equilibria an easy problem, for which polynomial and highly-parallelizable algorithms are presented.     

Competing for consumer's attention

We consider an infinite-horizon differential game played by two direct marketers. Each player controls the number of emails sent to potential customers at each moment in time. There is a cost associated to the messages sent, as well as a potential reward. The latter is assumed to depend on the state variable defined as the level of the representative consumer's attention. Two features are included in the model, namely, marginal decreasing returns and bounded rationality. By the latter, we mean that the representative consumer has a limited capacity for processing the information received. The evolution of this capacity depends on its level, as well as on the emails sent by both players. This provides environmental flavour where, usually, one player's pollution emissions (here emails) also affect the payoff of the other player by damaging the common environment (here, the stock of consumer attention).We characterize competitive equilibria for different scenarios based on each player's type, i.e., whether the player is a spammer or not. We define a spammer as a myopic player, i.e., a player who cares only about short-term payoff and ignores the impact of her action on the state dynamics. In all scenarios, the game turns out to be of the linear-quadratic variety. Feedback Nash equilibria for the different scenarios are characterized and the equilibrium strategies and outcomes are compared.Finally, we analyze the game in normal form, where each player has the option of choosing between being a spammer or not, and we characterize Nash equilibria.     

多人非合作随机自适应博弈

本文考虑系数未知的离散时间线性随机系统多人非合作的自适应博弈问题,每个参与者运用最小二乘算法和"必然等价原则"来设计博弈策略组合,目的是自适应优化自身的一步超前收益函数.本文证明此自适应策略组合使得闭环系统全局稳定,并且在一定意义下是该博弈问题的渐近纳什均衡解.     

Equilibria problems on games: Complexity versus succinctness

We study the computational complexity of problems involving equilibria in strategic games and in perfect information extensive games when the number of players is large. We consider, among others, the problems of deciding the existence of a pure Nash equilibrium in strategic games or deciding the existence of a pure Nash or a subgame perfect Nash equilibrium with a given payoff in finite perfect information extensive games. We address the fundamental question of how can we represent a game with a large number of players? We propose three ways of representing a game with different degrees of succinctness for the components of the game. For perfect information extensive games we show that when the number of moves of each player is large and the input game is represented succinctly these problems are PSPACE-complete. In contraposition, when the game is described explicitly by means of its associated tree all these problems are decidable in polynomial time. For strategic games we show that the complexity of deciding the existence of a pure Nash equilibrium depends on the succinctness of the game representation and then on the size of the action sets. In particular we show that it is NP-complete, when the number of players is large and the number of actions for each player is constant, and that the problem is -complete when the number of players is a constant and the size of the action sets is exponential in the size of the game representation. Again when the game is described explicitly the problem is decidable in polynomial time.     

Random Bimatrix Games Are Asymptotically Easy to Solve (A Simple Proof)

We focus on the problem of computing approximate Nash equilibria and well-supported approximate Nash equilibria in random bimatrix games, where each player’s payoffs are bounded and independent random variables, not necessarily identically distributed, but with almost common expectations. We show that the completely mixed uniform strategy profile, i.e., the combination of mixed strategies (one per player) where each player plays with equal probability each one of her available pure strategies, is with high probability a $\sqrt{\frac{\ln n}{n}}$ -Nash equilibrium and a $\sqrt{\frac{3\ln n}{n}}$ -well supported Nash equilibrium, where n is the number of pure strategies available to each player. This asserts that the completely mixed, uniform strategy profile is an almost Nash equilibrium for random bimatrix games, since it is, with high probability, an ?-well-supported Nash equilibrium where ? tends to zero as n tends to infinity.     

Optimal arrivals in a two-server random access system with loss

This paper considers a two-server random access system with loss that receives requests on a time interval [0, T]. The users (players) send their requests to the system, and then the system provides a random access to one of its two servers with some known probabilities. We study the following non-cooperative game for this service system. As his strategy, each player chooses the time to send his request to the system, trying to maximize the probability of servicing. The symmetric Nash equilibrium acts as the optimality criterion. Two models are considered for this game. In the first model the number of players is deterministic, while in the second it obeys the Poisson distribution. We demonstrate that there exists a unique symmetric equilibrium for both models. Finally, some numerical experiments are performed to compare the equilibria under different values of the model parameters.