检索结果-内蒙古大学图书馆

AFFINE RELAXATIONS OF THE best response algorithm: GLOBAL CONVERGENCE IN RATIO-BOUNDED GAMES

SIAM JOURNAL ON OPTIMIZATION 2023年第3期33卷 1914-1942页

作者： Caruso, Francesco Ceparano, Maria Carmela Morgan, Jacqueline Univ Naples Federico II Dept Econ & Stat I-80126 Naples Italy Univ Naples Federico II Dept Econ & Stat Ctr Studies Econ & Finance CSEF I-80126 Naples Italy

In a two-player noncooperative game framework, we deal with the affine relaxations of the best response algorithm (where a player's strategy is a best response to the strategy of the other player that comes from the previous step), motivated by the first results obtained for convex relaxations in zero-sum games (J. Morgan, Int. J. Comput. Math., 4 (1974), pp. 143-175) and for nonconvex affine relaxations in non-zero-sum games (F. Caruso, M. C. Ceparano, and J. Morgan, SIAM J. Optim., 30 (2020), pp. 1638-1663). In order to be able to specify the convergence of any type of affine relaxation of the best response algorithm, we define a new class of games, called ratio-bounded games. This class contains games broadly used in literature (such as weighted potential and zero-sum games), both in finite and infinite dimensional settings. Its definition relies on a unifying property and on three associate key parameters explicitly related to the data. Depending on how the parameters are ordered, we provide a classification of the ratio-bounded games in four subclasses such that, for each of them, the following issues are answered when the strategy sets are real Hilbert spaces: existence and uniqueness of the Nash equilibria, global convergence of the affine relaxations of the best response algorithm, estimation of the related errors, determination of the algorithm with the highest speed of convergence, and comparison with the known results. Moreover, the investigation is supplemented by illustrating numerical examples and by describing a black-box model with a first-order oracle for an implementation of the algorithm.

关键词： two-player noncooperative game Nash equilibrium existence and uniqueness fixed point contraction mapping nonexpansive mapping super monotone operator best response algorithm convex relaxation nonconvex affine relaxation global convergence error bound speed of convergence potential game zero-sum game

来源：评论

学校读者我要写书评

暂无评论

AN INVERSE-ADJUSTED best response algorithm FOR NASH EQUILIBRIA

引用

SIAM JOURNAL ON OPTIMIZATION 2020年第2期30卷 1638-1663页

作者： Caruso, Francesco Ceparano, Maria Carmela Morgan, Jacqueline Univ Naples Federico II Dept Econ & Stat Naples Italy Univ Naples Federico II Ctr Studies Econ & Finance CSEF Naples Italy

Regarding the approximation of Nash equilibria in games where the players have a continuum of strategies, there exist various algorithms based on best response dynamics and on its relaxed variants: from one step to the next, a player's strategy is updated by using explicitly a best response to the strategies of the other players that come from the previous steps. These iterative schemes generate sequences of strategy profiles which are constructed by using continuous optimization techniques and they have been shown to converge in the following situations: in zero-sum games or, in non-zero-sum ones, under contraction assumptions or under linearity of best response functions. In this paper, we propose an algorithm which guarantees the convergence to a Nash equilibrium in two-player non-zero-sum games when the best response functions, called r(1) and r(2), are not necessarily linear, neither the composition r(1) circle r(2) nor r(2) circle r(1) is a contraction, and the strategy sets are Hilbert spaces. First, we address the issue of uniqueness of the Nash equilibrium extending to a more general class the result obtained by Caruso, Ceparano, and Morgan [J. Math. Anal. Appl., 459 (2018), pp. 1208-1221] for weighted potential games. Then, we describe a theoretical approximation scheme based on a nonstandard (nonconvex) relaxation of best response iterations which converges to the unique Nash equilibrium of the game. Finally, we define a numerical approximation scheme relying on a derivative-free continuous optimization technique applied in a finite dimensional setting and we provide convergence results and error bounds.

关键词： zero-sum game saddle point noncooperative non-zero-sum game Nash equilibrium uniqueness theoretical and numerical approximations fixed point super monotone operator best response algorithm convex and nonconvex relaxation local variation method error bound

来源：评论

学校读者我要写书评

暂无评论

Credit rating based real-time energy trading in microgrids

引用

APPLIED ENERGY 2019年 236卷 985-996页

作者： Zhang, Xiaoyan Zhu, Shanying He, Jianping Yang, Bo Guan, Xinping Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Minist Educ China Key Lab Syst Control & Informat Proc Shanghai 200240 Peoples R China

In this paper, we investigate the problem of credit rating management in energy trading among microgrids subject to transmission losses and wheeling cost. The main concern is how to constrain the default behaviors of retailers to enable all the consumers and retailers to be actively involved in the energy trading. By endowing retailers as leaders and consumers as followers, we establish a multi-leader multi-follower dynamic game model and propose a scorecard model based on logistic regression to evaluate retailers' credit ratings. The concept of trust degree is then introduced for all the retailers as a punitive measure to relate their credit ratings with the reduction in the profit. With such a strategy, we can theoretically show that a unique equilibrium exists for the dynamic game model. Moreover, a best response algorithm is proposed to make the consumers and retailers achieve the equilibrium iteratively. Numerical simulations are provided to demonstrate the effectiveness and efficiency of the proposed method. It is found that default behaviors of selfish retailers can be greatly constrained with only a slight degradation of the interests of other participants, thereby promoting the establishment of a trustworthy trading market. We also discuss the influence level of transmission losses on trading behaviors of retailers and consumers.

关键词： Real-time energy trading Credit rating management Leader-follower dynamic game Transmission loss best response algorithm

来源：评论

学校读者我要写书评

暂无评论

A Stackelberg game approach for multiple energies trading in integrated energy systems

引用

APPLIED ENERGY 2017年第Aug.15期200卷 315-329页

作者： Wei, F. Jing, Z. X. Wu, Peter Z. Wu, Q. H. South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Guangdong Peoples R China Univ Liverpool Dept Phys Liverpool L69 3GJ Merseyside England Univ Liverpool Dept Elect Engn & Elect Liverpool L69 3GJ Merseyside England

In this paper, we propose a novel game model based on the hierarchical Stackelberg game for analyzing the multiple energies trading (MET) problem in integrated energy systems (IESs). In the proposed game model, a number of distributed energy stations (DESs) lead the game deciding the unit prices of electricity and cooling energies they generated, while multiple energy users (EUs) perform as followers determining the amounts of energies to consume. In addition to maximizing the profit of each DES, the proposed hierarchical game model also considers the benefit of each EU, who actively participates in the MET. We prove that, for the first time, there exists a unique Stackelberg Equilibrium (SE) in the MET, so that the existence of an equilibrium strategy optimizing the objectives of all participants can be guaranteed. Moreover, we found that the price setting game played by DESs is a submodular game when energy dispatching is performed during their generation process, which indicates that the behaviors of DESs are strategic substitutes. Furthermore, the SE is obtained in a closed-form, by which the effects of coupling generation of multiple energies are analyzed. Finally, a best response algorithm is provided to obtain the SE in an iterative way. Numerical studies demonstrate the convergency of the proposed best response algorithm, corroborate the jointly effects of market scale and exogenous parameter on the SE and verify the practicability of the proposed game-theoretic approach. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Integrated energy system Strategic substitutes Submodular Stackelberg game best response algorithm

来源：评论

学校读者我要写书评

暂无评论

Green-oriented user-satisfaction aware WiFi offloading in HetNets

引用

IET COMMUNICATIONS 2018年第5期12卷 501-508页

作者： Xu, Jiao Wu, Shaohua Xu, Luyao Zhang, Ning Zhang, Qinyu Harbin Inst Technol Shenzhen Grad Sch Shenzhen Peoples R China Univ Waterloo Dept Elect Comp Engn Waterloo ON Canada

To cope with the tremendous growth of data traffic and obtain a given communication service with minimal energy use, traffic offloading and energy efficiency (EE) improving are two important issues to address for green cellular networks. The authors investigate downlink WiFi offloading in a heterogeneous network consisting of one long term evolution eNodeB (eNB) and multiple overlaid WiFi access points to maximise the user satisfaction of the whole system. In addition, a designed resource reallocation scheme after offloading is jointly considered to improve the EE of the eNB. In the offloading model, two constraints are considered to guarantee the rate promotion of the offloaded users and less impact on WiFi networks. Moreover, the authors transform the model into a combinatorial optimisation problem and adopt the best response (BR) algorithm based on game-theoretic approach to obtain the optimal offloading user set. Numerical results show that the proposed WiFi-offloading model can significantly improve the aggregate user satisfaction as well as EE of the eNB. Also, the BR algorithm can converge to the optimal solution same as the exhaustive search algorithm through several iterations.

关键词： green computing cellular radio wireless LAN telecommunication traffic combinatorial mathematics game theory optimisation search problems energy conservation telecommunication power management green-oriented user-satisfaction aware WiFi offloading HetNet data traffic communication service minimal energy use traffic offloading energy efficiency green cellular networks downlink WiFi offloading heterogeneous network LTE eNodeB eNB multiple overlaid WiFi access points user satisfaction maximisation rate promotion WiFi networks combinatorial optimisation problem best response algorithm BR algorithm game-theoretic approach optimal offloading user set user satisfaction aggregation exhaustive search algorithm

来源：评论

学校读者我要写书评

暂无评论

Invariant Nash Equilibrium for Large Player Games in Multiple Access Channels 18

Invariant Nash Equilibrium for Large Player Games in Multipl...

引用

18th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOPT)

作者： Narayanan, Prashant Theagarajan, Lakshmi Narasimhan Indian Inst Technol Palakkad Dept EE Kozhippara 678557 Kerala India

ISBN: (纸本)9783903176294

We consider a wireless multiple access channel (MAC) with N users. Associated with each user is their time varying channel state and a finite-length queue which varies with time. In MAC, a receiver decodes the signals of each user by treating the other users' signals as noise. Each user decides their transmit power and the queue-admission control variable dynamically to maximize their expected throughput without any knowledge of the states and actions of other users. This decision problem is formulated as a Markov game for which we show the existence of equilibrium and an algorithm to compute the equilibrium policies. We show that, when the number of users exceeds a given threshold, the expected throughput of all users at all the equilibria points are the same. Furthermore, we show that the equilibrium policies of the users are invariant as long as the number of users remain above the latter threshold, which is referred to as the infinitely invariant Nash equilibrium (LINE). For the considered system, we prove that LINE exists and show that each user can compute these policies using a sequence of linear programs which does not depend upon the parameters of the other users. We also provide the necessary and sufficient conditions for the existence of LINE. Finally, we validate our analysis using numerical simulations.

关键词： Multiple access channel stochastic games Nash equilibrium Markov games best response algorithm power control queue constraints resource allocation

来源：评论

学校读者我要写书评

暂无评论

Energy-efficient Power Allocation in Cognitive Sensor Networks: A Game Theoretic Approach

Energy-efficient Power Allocation in Cognitive Sensor Networ...

引用

IEEE Global Communications Conference (GLOBECOM)

作者： Chai, Bo Deng, Ruilong Cheng, Peng Chen, Jiming Zhejiang Univ State Key Lab Ind Control Technol Hangzhou Zhejiang Peoples R China

ISBN: (纸本)9781467309219;9781467309202

In this paper, we study power allocation in cognitive sensor networks where cognitive users (cognitive enabled sensor nodes) opportunistically share a common spectrum with primary users (licensed devices). We define an energy efficiency-oriented utility function as a new metric to evaluate power allocation. Consider that sensor nodes are self-interested to maximize their own utility, we formulate the energy efficient power allocation problem as a non-cooperative game. We firstly prove that there exist Nash equilibriums in the proposed game. Secondly, we prove that the power allocation game is a supermodular game with some conditions. Finally, we use best response algorithm to identify the Nash equilibrium. Simulations are conducted to demonstrate that the proposed power allocation strategy can achieve satisfactory performance in terms of energy efficiency, convergence speed and fairness in cognitive sensor networks.

关键词： Energy efficiency cognitive radio game theory supermodular game best response algorithm

来源：评论

学校读者我要写书评

暂无评论

Energy Harvesting Time Coefficient Analyze for Cognitive Radio Sensor Network Using Game Theory 3rd

Energy Harvesting Time Coefficient Analyze for Cognitive Rad...

引用

3rd International Conference on Human Centered Computing (HCC)

作者： Zhao, Mengyu Wei, Yifei Li, Qiao Song, Mei Liu, Ningning Beijing Univ Posts & Telecommun Sch Elect Engn Beijing 100876 Peoples R China

ISBN: (纸本)9783319745213;9783319745206

In this paper, the cognitive radio sensor node can harvest energy from the radio frequency signal which is transmitted by the primary user. A time switching protocol was used to divide cognitive users' time into three phases: spectrum sensing mode, energy harvesting mode and data transmission mode. Therefore, the optimal energy harvesting mode time selection is a question to be solved. We consider a non-cooperative game model in which cognitive users are regarded as selfish players aiming to maximize their own energy efficiency. Then we prove the existence and uniqueness of Nash Equilibrium. A distributed best response algorithm is used to obtain the Nash Equilibrium. The simulation results prove that this algorithm can converge to the same equilibrium from different initial values. At last, we analysis the influence of various system parameters on the results of Nash Equilibrium and energy efficiency.

关键词： Energy harvesting Energy efficiency Cognitive radio sensor network Non-cooperative game best response algorithm

来源：评论

学校读者我要写书评

暂无评论

The Invariant Nash Equilibrium for Stochastic Games in Multiple Access Channel 16

The Invariant Nash Equilibrium for Stochastic Games in Multi...

引用

16th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

作者： Narayanan, Prashant Theagarajan, Lakshmi Narasimhan Indian Inst Informat Technol Sri City Sri City India Indian Inst Technol Palakkad Palakkad India

ISBN: (纸本)9783903176003

In this paper, we present an iterative best-response algorithm to compute the Nash equilibrium of a power allocation game in a multiple access channel (MAC), where each user greedily chooses a power allocation policy to maximize their average transmission rate. We consider a MAC where the fading channel gains are assumed to be stationary and ergodic processes, taking values from a finite set. The receiver decodes the message of a user by assuming the messages of the rest of the users as noise. The Shannon capacity of a user is considered to be the achievable rate of that user. A user transmits with a transmit power chosen from a finite set of power values, in a selfish manner, such that their average rate of transmission is maximized We show that the Nash equilibrium of this game is unique, provided the number of users in the system is sufficiently large, but finite. Under this condition, we also show that the equilibrium policy does not change with more number of users coming into the system. We propose a simple greedy algorithm to compute the Nash equilibrium when the number of users is sufficiently large, but finite. The proposed algorithm does not depend upon the parameters of other users and hence, can be computed without any feedback or side-information from other users. We also present numerical results to illustrate the performance of the proposed algorithm.

关键词： Multiple Access Channel Stochastic Games Nash equilibrium Markov Decision process Potential Games best response algorithm

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：