Generalized Nash Equilibrium Problems

The Generalized Nash Equilibrium Problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields. In this survey paper we aim at discussing its main properties and solution algorithms, pointing out what could be useful topics for future research in the field.     

Time-Dependent Generalized Nash Equilibrium Problem

We prove an existence result for the time-dependent generalized Nash equilibrium problem under generalized convexity without neither a quasi-variational inequality reformulation nor a quasi-equilibrium problem reformulation. Furthermore, an application to the time-dependent abstract economy is considered.     

Local Nash Equilibrium in Multiparty Politics

We present a model of multi-party, spatial competition under proportional rule with both electoral and coalitional risk. Each party consists of a set of delegates with heterogeneous policy preferences. These delegates choose one delegate as leader or agent. This agent announces the policy declaration (or manifesto) to the electorate prior to the election. The choice of the agent by each party elite is assumed to be a local Nash equilibrium to a game form . This game form encapsulates beliefs of the party elite about the nature of both electoral risk and the post-election coalition bargaining game. It is demonstrated, under the assumption that is smooth, that, for almost all parameter values, a locally isolated, local Nash equilibrium exists.In the final section of the paper some empirical work is reviewed in order to obtain some insights into why parties do not simply converge to an electoral center in order to maximize expected vote shares.     

α-Well-posedness for Nash Equilibria and For Optimization Problems with Nash Equilibrium Constraints

We present the concepts of α-well-posedness for parametric noncooperative games and for optimization problems with constraints defined by parametric Nash equilibria. We investigate some classes of functions that ensure these types of well-posedness and the connections with α-well-posedness for variational inequalities and optimization problems with variational inequality constraints.     

Nash Equilibrium and Subgame Perfection in Observable Queues

A subgame perfection refinement of Nash equilibrium is suggested for games of the following type: each of an infinite number of identical players selects an action using his private information on the system's state; any symmetric strategy results in a discrete Markov chain over such states; the player's payoff is a function of the state, the selected action, and the common strategy selected by the other players. The distinction between equilibria which are subgame perfect and those which are not, is made apparent due to the possibility that some states are transient. We illustrate the concept by considering several queueing models in which the number of customers in the system constitutes the state of the system.     

管理中的Nash平衡与Braess悖论现象

本给出了交通规划、经济贸易以及其它管理中的一些Nash平衡和Braess悖论实例，分析了Nash平衡和Braess悖论现象及其本质特征，指出它们在管理工作中具有普遗性和潜在应用性。     

指派问题的纳什均衡解

为弥补传统指派问题解不符合个体理性的不足,提出指派问题的纳什均衡解,并证明有限指派问题有且仅有纯纳什均衡解。相比传统的指派问题解,纯纳什均衡符合Pareto最优,是个体理性视角下的最优解。在此基础上,给出一个综合考虑个体理性与集体理性的求解方法。     

求解一类广义Nash均衡问题

Generalized Nash equilibrium problem (GNEP) is an important model that has many applications in practice. However, a GNEP usually has multiple or even infinitely many Nash equilibrium points and it is not easy to choose a favorable solution from those equilibria. This paper considers a class of GNEP with some kind of separability. We first extend the so-called normalized equilibrium concept to the stationarity sense and then, we propose an approach to solve the normalized stationary points by reformulating the GNEP as a single optimization problem. We further demonstrate the proposed approach on a GNEP model in similar product markets.     

A Penalty Approach for Generalized Nash Equilibrium Problem

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP),in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players.This problem has been used to model various problems in applications.However,the convergent solution algorithms are extremely scare in the literature.In this paper,we present an incremental penalty method for the GNEP,and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs.We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.     

竞争条件下公司最优投资策略纳什均衡分析

大多数实物期权文献都只是研究一个公司在没有竞争条件下的最优决策,然而实际上竞争者的行为经常影响到公司的投资机会.通过建立投资概率是临界值的函数模型,根据期权博弈理论研究了在不确定条件和不同信息结构下,一个或多个公司的最优投资策略纳什均衡解,并用MATLAB语言对案例进行了仿真分析,画图说明了参数变化对投资策略的影响.