On the Coalitional Rationality of the Banzhaf Value and Other Non-Efficient Semivalues

In the Inverse Set relative to a Semivalue, we are looking for a new game for which the Semivalue of the original game is coalitional rational. The problem is solved by means of the Power Game of the given game. The procedures of building the new game, as well as the case of the Banzhaf Value are illustrated by means of some examples.

On the Coalitional Rationality and the Inverse Problem for Shapley Value and the Semivalues

In cooperative game theory, a central problem is to allocate fairly the win of the grand coalition to the players who agreed to cooperate and form the grand coalition. Such allocations are obtained by means of values, having some fairness properties, expressed in most cases by groups of axioms. In an earlier work, we solved what we called the Inverse Problem for Semivalues, in which the main result was offering an explicit formula providing the set of all games with an a priori given Semivalue, associated with a given weight vector. However, in this set there is an infinite set of games for which the Semivalues are not coalitional rational, perhaps not efficient, so that these are not fair practical solutions of the above fundamental problem. Among the Semivalues, coalitional rational solutions for the Shapley Value and the Banzhaf Value have been given in two more recent works. In the present paper, based upon a general potential basis, relative to Semivalues, for a given game and a given Semivalue, we solve the connected problem: in the Inverse Set, find out a game with the same Semivalue, which is also coalitional rational. Several examples will illustrate the corresponding numerical technique.

ANALYSIS OF GROUP MULTIUSER DETECTION BASED ON COALITION GAME THEORY

Coalition game theory is introduced to investigate the performance,fairness and stability of decorrelating group multiuser detection receiver,not only from the perspective of individual nodes,but also various coalitions and the whole system as well. Firstly,to derive how the system scale with coalition size,a stochastic model with transferable payoffs (stochastic TU-model) is provided. Secondly,to find the most preferred coalition structures from the view point of individual nodes,a model with Non-Transferable payoffs (NTU-model) is presented. Theoretical analysis and simulation results suggest that stochasticaly the grand coalition is payoff maximizing for the system as a whole,while individual nodes with good-conditioned channels may prefer local "win-win coalitions".

On the Coalitional Rationality and the Egalitarian Nonseparable Contribution

In earlier works we introduced the Inverse Problem, relative to the Shapley Value, then relative to Semivalues. In the explicit representation of the Inverse Set, the solution set of the Inverse Problem, we built a family of games, called the almost null family, in which we determined more recently a game where the Shapley Value and the Egalitarian Allocations are colalitional rational. The Egalitarian Nonseparable Contribution is another value for cooperative transferable utilities games (TU games), showing how to allocate fairly the win of the grand coalition, in case that this has been formed. In the present paper, we solve the similar problem for this new value: given a nonnegative vector representing the Egalitarian Nonseparable Contribution of a TU game, find out a game in which the Egalitarian Nonseparable Contribution is kept the same, but it is colalitional rational. The new game will belong to the family of almost null games in the Inverse Set, relative to the Shapley Value, and it is proved that the threshold of coalitional rationality will be higher than the one for the Shapley Value. The needed previous results are shown in the introduction, the second section is devoted to the main results, while in the last section are discussed remarks and connected problems. Some numerical examples are illustrating the procedure of finding the new game.

Game Analysis of Rational FRS on Market Admittance

The dynamic signaling game-model is employed to study countermeasures of Q, U and C for supply-demand on financial market. As the game result, the mixed equilibrium of Q and U exists naturally without FRS. It is concluded that FRS on market admittance is objective demand of financial market, also the rational management behavior of government FRSI. And in addition to the empirical criteria, the FRS agreements between FRSI and financial-institutions should be considered as one of advanced FRS techniques. These must cover:① the regulation conformed status investigation with sufficient frequency,② corresponding punitive measures with sufficient strength. Thus the information can be delivered FRSI have ensured only qualified and regulation-conformed financial-institutions could be allowed to enter. That could safeguard the steadiness of the financial market.

Maintenance of cooperation induced by punishment in public goods games

In this paper, we study the public goods games with punishment by adopting the well-known approximate best response dynamics. It shows that the evolution of cooperation is affected by two aspects when other parameters are fixed. One is the punishment mechanism which can avoid the dilemma of lacking investment, and the other is the degree of rationality. Theoretical analysis and numerical results indicate that the existence of punishment mechanism and distribution of rationality are the keys to the enhancement of cooperation level. We also testify that they can heavily influence the payoffs of system as well. The findings in this paper may provide a deeper understanding of some social dilemmas.

Evolution of Cooperation in Public Goods Games

We investigate the evolution of cooperation with evolutionary public goods games based on finite populations, where four pure strategies： cooperators, defectors, punishers and loners who are unwilling to participate are considered. By adopting approximate best response dynamics, we show that the magnitude of rationality not only quantitatively explains the experiment results in [Nature （London） 425 （2003） 390], but also it will heavily influence the evolution of cooperation. Compared with previous results of infinite populations, which result in two equilibriums, we show that there merely exists a special equilibrium cooperation. In addition, we characterize that loner＇s and the relevant high value of bounded rationality will sustain payoff plays an active role in the maintenance of cooperation, which will only be warranted for the low and moderate values of loner＇s payoff. It thus indicates the effects of rationality and loner＇s payoff will influence the cooperation. Finally, we highlight the important result that the introduction of voluntary participation and punishment will facilitate cooperation greatly.

A rational quantum state sharing protocol with semi-off-line dealer

A rational quantum state sharing protocol with the semi-off-line dealer is proposed.Firstly,the dealer Alice shares an arbitrary two-particle entangled state with the players by Einstein-Podolsky-Rosen(EPR)pairs and Greenberger-Horne-Zeilinger(GHZ)states.The EPR pairs are prepared by Charlie instead of the dealer,reducing the workload of the dealer.Secondly,all players have the same probability of reconstructing the quantum state,guaranteeing the fairness of the protocol.In addition,the dealer is semi-off-line,which considerably reduces the information exchanging between the dealer and the players.Finally,our protocol achieves security,fairness,correctness,and strict Nash equilibrium.

Egalitarian Allocations and the Inverse Problem for the Shapley Value

In a cooperative transferable utilities game, the allocation of the win of the grand coalition is an Egalitarian Allocation, if this win is divided into equal parts among all players. The Inverse Set relative to the Shapley Value of a game is a set of games in which the Shapley Value is the same as the initial one. In the Inverse Set, we determined a family of games for which the Shapley Value is also a coalitional rational value. The Egalitarian Allocation of the game is efficient, so that in the set called the Inverse Set relative to the Shapley Value, the allocation is the same as the initial one, but may not be coalitional rational. In this paper, we shall find out in the same family of the Inverse Set, a subfamily of games with the Egalitarian Allocation is also a coalitional rational value. We show some relationship between the two sets of games, where our values are coalitional rational. Finally, we shall discuss the possibility that our procedure may be used for solving a very similar problem for other efficient values. Numerical examples show the procedure to get solutions for the efficient values.

On the Gas Routing via Game Theory

The delivery of the natural gas obtained by drilling, fracking and sending the product to consumers is done usually in two phases: in the first phase, the gas is collected from all wells spread on a large area, and belonging to several companies, and is sent to a depot owned by the city;then, in the second phase, another company is taking the gas on a network of ducts belonging to the city, along the streets to the neighborhoods and the individual consumers. The first phase is managed by the gas producing companies on the ducts owned by each company, possibly also on some public ducts. In this paper, we discuss only this first phase, to show why the benefits of these companies depend on the cooperation of the producers, and further, how a fair allocation of the total gas obtained, to the drilling companies, is computed. Following the model of flow games, we generate a cooperative transferable utilities game, as shown in the first section, and in this game any efficient value gives an allocation of benefits to the owners of ducts in the total network. However, it may well happen that the chosen value is not coalitional rational, in the game, that is, it does not belong to the Core of the game. By using the results obtained in an earlier work of the author, sketched in the second section, we show in the last section how the same allocation may be associated to a new game, which has the corresponding value a coalitional rational value. An example of a three person flow game shows the game generation, as well as the procedure to be used for obtaining the new game in which the same value, a Shapley Value, will give a coalitional rational allocation.

Hierarchical Game Approach for Optimization of Regional Integrated Energy System Clusters Considering Bounded Rationality

Regional integrated energy system(RIES)cluster,i.e.,multi-source integration and multi-region coordination,is an effective approach for increasing energy utilization efficiency.The hierarchical architecture and limited information sharing of RIES cluster make it difficult for traditional game theory to accurately describe their game behavior.Thus,a hierarchical game approach considering bounded rationality is proposed in this paper to balance the interests of optimizing RIES cluster under privacy protection.A Stackelberg game with the cluster operator(CO)as the leader and multiple RIES as followers is developed to simultaneously optimize leader benefit and RIES utilization efficiency.Concurrently,a slight altruistic function is introduced to simulate the game behavior of each RIES agent on whether to cooperate or not.By introducing an evolutionary game based on bounded rationality in the lower layer,the flaw of the assumption that participants are completely rational can be avoided.Specially,for autonomous optimal dispatching,each RIES is treated as a prosumer,fexibly switching its market participation role to achieve cluster coordination optimization.Case studies on a RIES cluster verify effectiveness of the proposed approach.

Punishment in optional public goods games

In this work, the optional public goods games with punishment are studied. By adopting the approximate best response dynamics, a micro model is given to explain the evolutionary process. Simultaneously, the magnitude of rationality is also considered. Under the condition of bounded rationality which provides a light to interpret phenomena in human society, the model leads to two types of equilibriums. One is the equilibrium without punishers and the other is the equilibrium including only punishers and cooperators. In addition, the effects of rationality on equilibriums are briefly investigated.

The Generic Uniqueness and Well-Posedness of NashEquilibria for Stable Population Games

This paper aims at studying a new kind of stable population games introduced by J.Hofbauer and H.Sandholm in 2009.We first construct a complete distance space M consisting of stable population games and show that most of stable population games have unique Nash equilibrium point that according to Baire’s category theorem.It implies that every stable population game that possesses more than one Nash equilibrium can be approached arbitrarily by a sequence of the stable population game each of which has a unique Nash equilibrium.Then,we construct a bounded rationality function and deduce some results on the generic well-posedness implying Tikhonov well-posedness and Hadamard well-posedness for stable population games.

Cournot-Bertrand双寡头动态博弈模型的复杂性分析

提出了一个主从的Cournot-Bertrand双寡头混合博弈模型援寡头都是在有限理性期望下进行的博弈,并且上级寡头考虑产量,下级寡头考虑价格援分析了该模型的纳什均衡点和它的局部稳定性援通过数值模拟,利用稳定域图、分岔图、最大Lyapunov指数图以及奇异吸引子图研究了该模型的复杂动力学性质,且通过分析两寡头的利润分岔图。

Multi-agent reinforcement learning based on policies of global objective

In general-sum games, taking all agent＇s collective rationality into account, we define agents＇ global objective, and propose a novel multi-agent reinforcement learning（RL） algorithm based on global policy. In each learning step, all agents commit to select the global policy to achieve the global goal. We prove this learning algorithm converges given certain restrictions on stage games of learned Q values, and show that it has quite lower computation time complexity than already developed multi-agent learning algorithms for general-sum games. An example is analyzed to show the algorithm＇ s merits.

A Tree Formulation for Signaling Games with Noise

The paper provides an analysis of a sender-receiver sequential signaling game. The private information of the sender is transmitted with noise by a Machine, i.e. does not always correctly reflect the state of nature. Hence, a truthful revelation by the sender of his information does not necessarily imply that the signal he sends is correct. Also, the receiver can take a correct action even if the sender transmits an incorrect signal. The payoffs of the two players depend on their combined actions. Perfect Bayesian Equilibria which can result from different degrees of noise is analysed. The Bayesian updating of probabilities is explained. The fixed point theorem which makes the connection with the idea of rational expectations in economics is calculated. Given a number of equilibria, we comment on the most credible one on the basis of the implied payoffs for both players. The equilibrium signals are an example of the formation of a language convention discussed by D. Lewis.

博弈思维视角下儿童益智类数字玩具设计策略研究

针对学龄儿童博弈类数字玩具缺失、使用体验不佳的问题,探讨了博弈过程与游戏结合的适配度,并以五子棋为例进行实践研究,以期提升玩具设计质量。依据博弈思维视角提出设计角度,结合学龄儿童的认知发展规律和多感官发展特征得出棋类游戏衍生数字玩具的设计策略。通过外观设计、辅助信息设计和智能交互设计融入玩具设计中。将策略与思维流程进行结合,设计了一套帮助学龄儿童正确理解博弈概念、认知博弈技能的数字拼搭玩具。希望能为玩具研究人员和教育实践者提供如何从博弈思维角度来辅助儿童进行博弈概念学习和技能掌握。

考虑用户需求响应博弈推演的区域综合能源运营策略

随着工商业用户能源种类多样化及其耦合程度紧密化,通过激励消费者剩余价值引导综合能源用户参与需求响应,对于降低综合能源系统运行成本以及提高用户能效具有积极意义。该文设计了基于消费者剩余的体验估值函数,并将其考虑在用户侧目标函数中,通过演化博弈推导工商业用户参与需求响应的动态过程,从而克服传统分析方法对用户侧参与需求响应的定值设置。该文建立了基于用户侧需求响应演化博弈的综合能源系统优化运营模型,上层建立了区域综合能源系统优化模型,计算面向用户的用能价格;下层建立了考虑剩余价值的区域综合能源系统用户响应模型,并进行演化博弈推导。算例基于电-热-气综合能源系统,采用演化博弈分析了需求侧市场用户响应行为及其影响因素。结果表明,工商业两类用户参与需求响应使得综合能源系统的运行总成本降低5.5%,同时两类用户效用分别提高了51.91%和44.29%。所提模型和方法不仅可以模拟用户侧需求响应动态博弈过程,而且能够为综合能源系统中运营商和需求侧用户的策略选择提供有益参考。

考虑电动汽车用户有限理性的定制化电价套餐设计

考虑到售电公司对提高市场占有率和收益的需求,电动汽车用户对经济和舒适的追求,以及电动汽车保有量基数大且还在持续快速上升的情况,提出了一种考虑电动汽车用户有限理性的定制化电价套餐设计方法。首先,利用蒙特卡洛方法模拟生成一些电动汽车用户的充电需求以增加充电负荷数据,并采用k-medoids聚类算法对电动汽车用户按其充电负荷聚类出典型电动汽车用户的充电需求曲线。然后,通过熵权法计算电动汽车用户效用,并在此基础上应用演化博弈论分析电动汽车用户在有限理性情况下的电价套餐选择情况。最后,建立考虑电动汽车用户有限理性的电价套餐双层优化模型,上层模型优化目标为售电公司购售电收益最大,下层模型优化目标为电动汽车用户效用最大。算例结果表明该定制化电价套餐不但能够有效地提高售电公司的营业利润,而且能够降低用户用电成本。

基于合作博弈的虚拟电厂联盟策略与收益分配机制研究

虚拟电厂可通过资源互补提升潜在收益,但也面临合作联盟规模、主体利益保障及主体隐私保护3个关键问题。首先证明了虚拟电厂合作博弈的存在性以及主体理性假设下合作联盟整体参与市场的唯一性。其次基于非对称纳什议价方法,提出了以净功率输出为贡献度进行度量的合作收益分配机制,保障合作联盟稳定性。然后计及各虚拟电厂的隐私保护需求,提出了dual-block交替方向乘子法(ADMM)分布式求解方法,避免多主体ADMM迭代引起的收敛性问题。最后通过算例验证了所提合作收益机制的有效性和分布式求解算法的高效性。