AUCTIONING METHOD FOR AIRSPACE CONGESTING RESOURCE ALLOCATION AND GAME EQUILIBRIUM ANALYSIS

The airspace congestion is becoming more and more severe.Although there are traffic flow management（TFM）initiatives based on CDM widely applied,how to reschedule these disrupted flights of different airlines integrating TFM initiatives and allocate the limited airspace resources to these airlines equitably and efficiently is still a problem.The air traffic management（ATM）authority aims to minimizing the systemic costs of congested airspaces.And the airlines are self-interested and profit-oriented.Being incorporated into the collaborative decision making（CDM）process,the airlines can influence the rescheduling decisions to profit themselves.The airlines maybe hide the flight information that is disadvantageous to them,but is necessary to the optimal system decision.To realize the coincidence goal between the ATM authority and airlines for the efficient,and equitable allocation of airspace resources,this paper provides an auction-based market method to solve the congestion airspace problem under the pre-tactic and tactic stage of air traffic flow management.Through a simulation experiment,the rationing results show that the auction method can decrease the total delay costs of flights in the congested airspace compared with both the first schedule first service（FSFS）tactic and the ration by schedule（RBS）tactic.Finally,the analysis results indicate that if reallocate the charges from the auction to the airlines according to the proportion of their disrupted flights,the auction mechanism can allocate the airspace resource in economy equitably and decrease the delay losses of the airlines compared with the results of the FSFS tactic.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

Institutional Incentives, Game Equilibrium and Social Justice： Toward a Unified Theory of Pure Jurisprudence

This article seeks to make a constructive advance in jurisprudential theory by employing the unified analytical framework of modern social science. We first outline the main ideas of individual rational decision-making and game theory and of social choice and mechanism design, before offering a preliminary discussion of their application to legal issues. The core thesis is that the law in combination with other social norms provides institutional incentives to all actors in society. Legislators＇ social justice objectives can be reasonably enforced only as a result of behavioral equilibrium in the social game.

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.

Game Theory Model and Equilibrium Analysis of Peasant's Production Decision

Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took the game theory as an analyzed tool to describe the interactional processes among the peasants, and set up the game theory model of independent decision and joint decision by peasants. It was shown that the government＇s positive guide and the market environment macroscopically controlled by the government could effectively increased the peasants＇ income

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE

A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

A Scalar Compromise Equilibrium for N-Person Prescriptive Games

A scalar equilibrium (SE) is defined for n-person prescriptive games in normal form. When a decision criterion (notion of rationality) is either agreed upon by the players or prescribed by an external arbiter, the resulting decision process is modeled by a suitable scalar transformation (utility function). Each n-tuple of von Neumann-Morgenstern utilities is transformed into a nonnegative scalar value between 0 and 1. Any n-tuple yielding a largest scalar value determines an SE, which is always a pure strategy profile. SEs can be computed much faster than Nash equilibria, for example;and the decision criterion need not be based on the players’ selfishness. To illustrate the SE, we define a compromise equilibrium, establish its Pareto optimality, and present examples comparing it to other solution concepts.

基于Stackelberg Game模型的网络性能研究

通过对多局域世界模型(Multi-Local-World Model,MLWM)的分析,抽取出一个基本的拓扑子结构,并将主从博弈的思想引入到网络流量控制中,建立了一个基于网络拓扑的Stackelberg博弈模型.在该模型下,分析了Nash均衡的存在性与唯一性,求出了Nash均衡时最佳的链路价格和流量,给出了网络最佳运行状态的一种定量描述,最后分析了网络拓扑参数对网络最佳运行状态的影响,研究了该模型下网络拓扑变化引起的网络性能的演化特性.

银行货币储备博弈的强化学习方法

在大规模银行交互系统中,各银行可通过控制与中央银行的借贷率来使自身对数货币储备尽可能地接近样本均值,从而降低系统性风险发生的概率.然而当状态过程与目标函数的参数未知时,无法直接求解随机微分博弈问题得到纳什均衡.本文结合平均场博弈理论与连续时间强化学习的相关方法,构造了一组大规模银行借贷网络中的近似纳什均衡.首先通过求解向前向后耦合HJB-FPK方程,得到代表银行的平均场均衡策略;再通过所得策略的形式,设计出迭代参数的方法用以刻画参数未知时的近似最优策略;最后通过学到的参数,构造银行数量较大时的近似纳什均衡.

The Consistency Characterizations of Correlated Equilibria for Games in Strategic Form

１９９３年，Ｂ．Ｐｅｌｅｇ和Ｓ．Ｔｉｊｓ两位教授使用两种一致性公理系统分别对策略式对策的Ｎａｓｈ平衡做了公理化的描述．

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

Non-Cooperative Differential Game Based Energy Consumption Control for Dynamic Demand Response in Smart Grid

In this paper, we conduct research on the dynamic demand response problem in smart grid to control the energy consumption. The objective of the energy consumption control is constructed based on differential game, as the dynamic of each users’ energy state in smart gird can be described based on a differential equation. Concept of electricity sharing is introduced to achieve load shift of main users from the high price hours to the low price hours. Nash equilibrium is given based on the Hamilton equation and the effectiveness of the proposed model is verified based on the numerical simulation results.

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.

A Game Theory Analysis of the OPEC’s Influence on World Oil Price

Most studies concerning OPEC＇s behavior assumptions about oil market structure are either very were based on traditional market microstructure. However, the rigorous or rather fuzzy. This paper demonstrates the rationality and necessity of OPEC＇s price band policy by using the game theory. We conclude that OPEC has the incentive to limit its price within a specific range if the game period is sufficiently long. This incentive comes either from preference for long-term interest or from future expectations. In such a way, OPEC tries its best to maximize its profit with the quota-price dual policy and plays a price stabilizing role in the future world oil market.

Modeling and Analysis of Single Machine Scheduling Based on Noncooperative Game Theory

Considering the independent optimization requirement for each demander of modernmanufacture, we explore the application of noncooperative game in production scheduling research,and model scheduling problem as competition of machine resources among a group of selfish jobs.Each job has its own performance objective. For the single machine, multi-jobs and non-preemptivescheduling problem, a noncooperative game model is established. Based on the model, many prob-lems about Nash equilibrium solution, such as the existence, quantity, properties of solution space,performance of solution and algorithm are discussed. The results are tested by numerical example.

Differential Game Based Link Resource Management for Next Generation Optical Network

In this paper, we investigate the link resource management problem for optical networks, to achieve the resource cost during the information transmission. We use the differential game to formulate the cost control problem for the link resource management, to minimize the resource allocation cost functions, which dynamic behaviours are described by differential equations. Each link controls its transmission bandwidth based on the Nash equilibriums of the differential game. The effectiveness of the proposed model is given through numerical simulations.

Stochastic evolutionary public goods game with first and second order costly punishments in finite populations

We study the stochastic evolutionary public goods game with punishment in a finite size population. Two kinds of costly punishments are considered, i.e., first-order punishment in which only the defectors are punished, and second-order punishment in which both the defectors and the cooperators who do not punish the defective behaviors are punished. We focus on the stochastic stable equilibrium of the system. In the population, the evolutionary process of strategies is described as a finite state Markov process. The evolutionary equilibrium of the system and its stochastic stability are analyzed by the limit distribution of the Markov process. By numerical experiments, our findings are as follows.（i） The first-order costly punishment can change the evolutionary dynamics and equilibrium of the public goods game, and it can promote cooperation only when both the intensity of punishment and the return on investment parameters are large enough.（ii）Under the first-order punishment, the further imposition of the second-order punishment cannot change the evolutionary dynamics of the system dramatically, but can only change the probability of the system to select the equilibrium points in the ＂C＋P＂ states, which refer to the co-existence states of cooperation and punishment. The second-order punishment has limited roles in promoting cooperation, except for some critical combinations of parameters.（iii） When the system chooses＂C＋P＂ states with probability one, the increase of the punishment probability under second-order punishment will further increase the proportion of the ＂P＂ strategy in the ＂C＋P＂ states.

No-cooperative games for multiple emergency locations in resource scheduling

When an emergency happens, the scheduling of relief resources to multiple emergency locations is a realistic and intricate problem, especially when the available resources are limited. A non-cooperative games model and an algorithm for scheduling of relief resources are presented. In the model, the players correspond to the multiple emergency locations, strategies correspond to all resources scheduling and the payoff of each emergency location corresponds to the reciprocal of its scheduling cost. Thus, the optimal results are determined by the Nash equilibrium point of this game. Then the iterative algorithm is introduced to seek the Nash equilibrium point. Simulation and analysis are given to demonstrate the feasibility and availability of the model.