Supplier evaluation based on Nash bargaining game model

Traditional DEA method is improper for supplier evaluation and selection, as it adopts varying weights in evaluation, and fails to consider competition among the suppliers. In order to solve these two problems, Nash bargaining game DEA model is applied to supplier evaluation in present paper. However, there is a non-uniqueness problem with Nash bargaining game efficiency of supplier in existing Nash bargaining game DEA model. The existing Nash bargaining game DEA model is improved in present paper on this issue, then the improved model is applied to the third party logistics service provider evaluation. The result of supplier evaluation based on the improved model is more persuasive compared with the existing research achievement, owing to adopting common weights in evaluation, and the game between suppliers being taken account.     

A probabilistic approach to quantum Bayesian games of incomplete information

A Bayesian game is a game of incomplete information in which the rules of the game are not fully known to all players. We consider the Bayesian game of Battle of Sexes that has several Bayesian Nash equilibria and investigate its outcome when the underlying probability set is obtained from generalized Einstein–Podolsky–Rosen experiments. We find that this probability set, which may become non-factorizable, results in a unique Bayesian Nash equilibrium of the game.     

Solution of multiobjective optimization problems: coevolutionary algorithm based on evolutionary game theory

When attempting to solve multiobjective optimization problems (MOPs) using evolutionary algorithms, the Pareto genetic algorithm (GA) has now become a standard of sorts. After its introduction, this approach was further developed and led to many applications. All of these approaches are based on Pareto ranking and use the fitness sharing function to keep diversity. On the other hand, the scheme for solving MOPs presented by Nash introduced the notion of Nash equilibrium and aimed at solving MOPs that originated from evolutionary game theory and economics. Since the concept of Nash Equilibrium was introduced, game theorists have attempted to formalize aspects of the evolutionary equilibrium. Nash genetic algorithm (Nash GA) is the idea to bring together genetic algorithms and Nash strategy. The aim of this algorithm is to find the Nash equilibrium through the genetic process. Another central achievement of evolutionary game theory is the introduction of a method by which agents can play optimal strategies in the absence of rationality. Through the process of Darwinian selection, a population of agents can evolve to an evolutionary stable strategy (ESS). In this article, we find the ESS as a solution of MOPs using a coevolutionary algorithm based on evolutionary game theory. By applying newly designed coevolutionary algorithms to several MOPs, we can confirm that evolutionary game theory can be embodied by the coevolutionary algorithm and this coevolutionary algorithm can find optimal equilibrium points as solutions for an MOP. We also show the optimization performance of the co-evolutionary algorithm based on evolutionary game theory by applying this model to several MOPs and comparing the solutions with those of previous evolutionary optimization models. This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24#x2013;26, 2003.     

无线自组网中节点协作的纳什均衡研究

根据自私节点的特性,提出节点协作的博弈模型。针对单阶段博弈及采取礼尚往来策略、冷酷策略、单步触发策略的重复博弈,分析并比较实现节点协作的纳什均衡条件。结果表明,单阶段博弈中自私节点的纳什均衡类似于囚徒困境,重复博弈采用礼尚往来策略时,实现最佳纳什均衡的临界值最小,相比其他策略更易实现协作。     

Consensus in Noncooperative Dynamic Games: A Multiretailer Inventory Application

We focus on Nash equilibria and Pareto optimal Nash equilibria for a finite horizon noncooperative dynamic game with a special structure of the stage cost. We study the existence of these solutions by proving that the game is a potential game. For the single-stage version of the game, we characterize the aforementioned solutions and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multistage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately, not necessarily Pareto optimal. The algorithm returns a sequence of joint decisions, each one obtained from the previous one by an unilateral improvement on the part of a single player. We also specialize the game to a multiretailer inventory system.     

Distributed aggregative games for Euler–Lagrange systems with system parameter uncertainties

In this paper, an aggregative game of Euler–Lagrange (EL) systems is studied, where the parameters of the EL systems are not available. To seek the Nash equilibrium of the game, a novel distributed Nash equilibrium seeking algorithm is proposed, where the system parameters are not used in the feedback control. Moreover, a Lyapunov function is constructed such that EL players are proved to exponentially converge to the Nash equilibrium of the game. Finally, an example in the electricity market is provided to illustrate our result.     

H∞控制理论在纳什均衡动态对策问题中的应用研究

在l2范数有界不确定性扰动影响情况下,把N人线性二次纳什对策问题归结为由非合作、非零和线性二次动态对策及二人零和动态对策组成的复合对策问题;基于纳什均衡对策理论的H∞控制理论方法,给出并证明了不确定环境下纳什对策问题状态反馈解存在的条件及其求解方法;通过一个政府债务稳定问题简例,说明了算法的有效性。     

Properties of Nash solutions of a two-stage nonzero-sum game

This paper contains exact expressions for the complete class of uncountably many globally optimal affine Nasb equilibrium strategies for a two-stage two-person nonzero-sum game problem with quadratic objective functionals and with dynamic information for beth players. Existence conditions for each of these Nash equilibrium solutions are derived and it is shown that a recursive Nash solution is not necessarily globally optimal. Cost-uniqueness property of the derived Nash strategies is investigated and it is proven that the game problem under consideration admits a unique Nash cost pair if and only if it can be made equivalent to either a team problem or a zero-sum game. It is also shown that existence conditions of a globally optimal Nash solution will be independent of the parameters characterizing the nonuniques of the Nash strategies only if the game problem can be made equivalent to a team problem.     

基于Nash均衡的自适应遗传算法

文章针对遗传算法中存在算法“搜索能力”和“收敛能力”的矛盾问题,提出了在遗传算法中引入博弈理论,将“搜索能力”和“收敛能力”看成博弈中的两个参与者,利用Nash均衡理论协调处理这一对矛盾,达到“双赢”目的,即在保证全局最优的同时提高收敛速度。通过理论分析和实例表明该算法的优越性。     

基于Stackbelberg博弈的认知无线网络速率控制模型

提出了基于Stackelberg博弈的认知无线单跳网络流量速率控制模型。应用反向归纳法对提出的流量速率Stackelberg博弈模型纳什均衡进行了分析,证明了提出的模型纳什均衡存在性及唯一性,并给出了Stackelberg博弈模型纳什均衡解的具体形式。仿真验证了提出的模型正确性,仿真结果表明在模型的纳什均衡处网络总体效用是最优的,且网络效用最大时认知结点可获得最优数据传输速率。     

Nash equilibrium in differential games and the quasi-strategy formalism

We consider a two-player nonzero-sum differential game in the case where players use nonanticipative strategies. We define the Nash equilibrium in this case and obtain a characterization of Nash equilibrium strategies. We show that a Nash equilibrium solution can be approximately realized by control-with-guide strategies.     

Ad Hoc网络中基于重复博弈的攻击预测模型

大多数入侵检测系统预测攻击行为能力较弱,不能实时主动地响应攻击。针对该问题,提出一种基于重复博弈的攻击预测模型。通过建立入侵者和入侵检测系统之间的阶段博弈模型,给出阶段博弈的纳什均衡,并求出重复博弈情况下的子博弈精炼纳什均衡。使用QRE模型预测攻击者和防御者在博弈阶段1~t中选择各种策略的概率,利用Gambit分析得出预测结果。基于GloMoSim的仿真结果表明,相比纳什均衡模型,QRE均衡模型的预测效果更好。     

一类n×n矩阵博弈的Nash均衡的近似计算

给出了一种求解某类n×n矩阵博弈Nash均衡的近似解的算法。通过剖分单纯形,将混合策略空间离散化,利用初始的单纯形根据标号函数和替换规则求出此类矩阵博弈Nash均衡的近似解。并分析了其最优解与近似解的计算误差。     

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium.     

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.     

A partial information non-zero sum differential game of backward stochastic differential equations with applications

This paper is concerned with a new kind of non-zero sum differential game of backward stochastic differential equations (BSDEs). It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motion. We establish a necessary condition in the form of maximum principle with Pontryagin’s type for open-loop Nash equilibrium point of this type of partial information game, and then give a verification theorem which is a sufficient condition for Nash equilibrium point. The theoretical results are applied to study a partial information linear-quadratic (LQ) game and a partial information financial problem.     

一种新的多目标优化策略机制及其应用

在博弈问题中很多学习机制只能使Agent收敛到Nash均衡解，不能很好地满足实际需要。将博弈问题转化为多目标优化问题，提出了一种新的多目标优化策略机制——保留受控策略机制，并将其应用到囚徒困境问题中得到比Nash均衡更有意义的Pareto最优解，在自博弈实验中取得了较高的满意度。实验结果表明,该策略机制求解Pareto最优解的有效性。     

Equilibrium Trajectories in Dynamical Bimatrix Games with Average Integral Payoff Functionals

This paper considers models of evolutionary non-zero-sum games on the infinite time interval. Methods of differential game theory are used for the analysis of game interactions between two groups of participants. We assume that participants in these groups are controlled by signals for the behavior change. The payoffs of coalitions are defined as average integral functionals on the infinite horizon. We pose the design problem of a dynamical Nash equilibrium for the evolutionary game under consideration. The ideas and approaches of non-zero-sum differential games are employed for the determination of the Nash equilibrium solutions. The results derived in this paper involve the dynamic constructions and methods of evolutionary games. Much attention is focused on the formation of the dynamical Nash equilibrium with players strategies that maximize the corresponding payoff functions and have the guaranteed properties according to the minimax approach. An application of the minimax approach for constructing optimal control strategies generates dynamical Nash equilibrium trajectories yielding better results in comparison to static solutions and evolutionary models with the replicator dynamics. Finally, we make a comparison of the dynamical Nash equilibrium trajectories for evolutionary games with the average integral payoff functionals and the trajectories for evolutionary games with the global terminal payoff functionals on the infinite horizon.     

Bounded budget betweenness centrality game for strategic network formations

In computer networks and social networks, the betweenness centrality of a node measures the amount of information passing through the node when all pairs are conducting shortest path exchanges. In this paper, we introduce a strategic network formation game in which nodes build connections subject to a budget constraint in order to maximize their betweenness in the network. To reflect real world scenarios where short paths are more important in information exchange in the network, we generalize the betweenness definition to only count shortest paths with a length limit ? in betweenness calculation. We refer to this game as the bounded budget betweenness centrality game and denote it as ?- B³C game, where ? is the path length constraint parameter.We present both complexity and constructive existence results about Nash equilibria of the game. For the nonuniform version of the game where node budgets, link costs, and pairwise communication weights may vary, we show that Nash equilibria may not exist and it is NP-hard to decide whether Nash equilibria exist in a game instance. For the uniform version of the game where link costs and pairwise communication weights are one and each node can build k links, we construct two families of Nash equilibria based on shift graphs, and study the properties of Nash equilibria. Moreover, we study the complexity of computing best responses and show that the task is polynomial for uniform 2- B³C games and NP-hard for other games (i.e. uniform ?- B³C games with ?≥3 and nonuniform ?- B³C games with ?≥2).