非合作博弈的轻微利他平衡点的存在性

在Marco和Morgan提出博弈论中一种新的解——轻微利他平衡的基础上,讨论了一类不连续博弈的轻微利他平衡点的存在性,进一步讨论了支付函数更弱情况(拟凹)的轻微利他平衡点的存在性.     

轻微利他弱Pareto-Nash均衡

2008年,Marco和Morgan在正规型博弈中引入轻微利他均衡和友好均衡的概念.利用轻微利他的思想,研究多目标博弈.证明轻微利他弱Pareto-Nash均衡的存在性定理,进一步地讨论轻微利他弱Pareto-Nash均衡和本质均衡的关系.     

主从博弈的轻微利他平衡点

针对一个领导者的主从博弈问题,研究轻微利他平衡点的存在性问题.首先,基于非合作博弈Nash均衡的概念,给出了主从博弈轻微利他Nash均衡的定义;然后,应用非线性问题稳定性理论,证明了平衡点的存在性.     

多主从博弈的轻微利他平衡点问题

基于经典非合作博弈的Nash平衡点问题,结合利他主义的思想,研究了多主从博弈的轻微利他平衡点问题.通过利用Fan-Glicksberg不动点定理,对两个领导者的多主从博弈在轻微利他情况下的平衡点存在性进行了讨论和研究.     

利他扰动与Nash均衡点集的利他稳定性

引入了一个新的利他扰动.定义了KyFan点集的利他本质集,进一步证明在此扰动下,KyFan点集的利他本质连通区的存在性.证明了满足一定条件的n人非合作博弈中,Nash均衡点集至少存在一个利他本质连通区,而且Nash均衡点集的每一个本质集必是利他稳定集,Nash均衡点集的本质连通区也是利他本质集连通区.     

生产经济平衡点的极小本质集与本质连通区

进上步研究了生产经济平衡的稳定性,讨论了生产经济平衡“集合值”的稳定性,证明了生产经济平衡点集至少存在一个极小本质集且每一极小本质集是连通的,从而能够给出本质连通分支的存在性。     

非合作对策的随机Nash平衡点存在性定理

利用Ｌｅｅｓｅ的可逆选择定理，得到非合作对策的随机Ｎａｓｈ平衡点的存在性定理。     

n维环型Lotka-Volterra系统平衡点全局稳定的充分条件

本文讨论 n维环型 Lotka- Volterra系统平衡点全局稳定的充分条件 .它包括种群间和一种群与多种群间的环型 Lotka- Volterra系统 ,得到的条件简单 ,易验证     

多目标博弈平衡点存在性定理的推广

以向量值KyFan不等式的推广为基础,讨论支付函数为向量形式的n人非合作多目标博弈弱Pareto-Nash平衡点存在性条件,将多目标博弈平衡点存在性定理中策略空间的紧性,支付函数的凸性等条件减弱.     

一类竞争——合作生态模型平衡点的渐近稳定性

研究一类竞争-合作生态数学模型平衡点的渐近稳定性,得到了一组保证平衡点渐近稳定的充分条件.     

Nash平衡的存在性与稳定性

本文对Nash平衡的存在性与稳定性作了较为详细的研究和综述.     

THE EFFECTS OF DIFFERENT STRATEGIC VARIABLES IN NONCOOPERATIVE FISHERIES GAMES

Abstract In this paper, we use stock size, harvest quantity, and fishing effort as strategic variables. We model a two‐agent noncooperative fishery game, where the agents (nations) harvest a common fish stock. The planning horizon is infinite. The model is solved successively using one instrument at a time as the strategic variable in the game. The net present values of fishing and the escapement stock level from the three different models are compared to show how the choice of variables affects the results. The choice of strategic variable is not a trivial one, as the results are shown to be sensitive to the discounting, the stock's rate of growth, and the assumptions about the distribution of the fish in response to harvesting.     

COMPUTING THE EQUILIBRIA OF DYNAMIC COMMON PROPERTY GAMES

In this paper we discuss techniques for rapidly computing the equilibria of a class of dynamic linear-quadratic games involving the extraction of a common property resource. Though this class of games has been much studied, the search for equilibria of these games has only been attempted in special cases, and analysis of the game has tended to focus on its steady-state properties. We construct a pseudo-planning problem, the optimal of which correspond to the Markov perfect equilibria of the class of games we explore. We show how the optima (equilibria) of this pseudo-planning problem (game) can be rapidly computed via a Riccati-like equation. Finally, we illustrate the use of these techniques with several examples involving the extraction of a common property resource.     

STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer concentration b is below a critical value b*(6.7314863965), the only equilibrium state is isotropic and it is stable; when b*< b < 15/2, two anisotropic (prolate) equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b > 15/2, there are three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable oblate state.     

单主多从博弈中中级社会Nash均衡的存在性与应用

对单主多从博弈进行分析,给出跟随者反应函数的相关性质.进一步,针对跟随者反应函数是集值映射的情形,定义出中级社会Nash均衡,讨论该均衡的存在性,并把该均衡应用到非线性反需求函数的单主多从寡头竞争,得出该模型的中级社会Nash均衡解.     

关于无限对策Nash平衡点集的本质连通区

证明了任意纯策略集是紧度量空间和支付函数连续的n人无限非合作对策存在 Nash平衡点集的本质连通区．     

Ky Fan点集的本质连通区

本文首先引入了Ｋｙ Ｆａｎ点集本质连能区的概念,证明了对任一满足一定凸性和连续性条件的函数,其Ｋｙ Ｆａｎ点集至少存在一个本质连能区．作为应用,我们推出地任何一般ｎ人非合伯对策（其支付函数满足一些凸性和连续性条件）,其Ｎａｓｈ平衡点集至少存在一个本质连通区．     

NONCOOPERATIVE MANAGEMENT OF THE NORTHEAST ATLANTIC COD FISHERY: A FIRST MOVER ADVANTAGE

The point of departure for this analysis is Bjørndal and Lindroos [2012], who developed an empirical bioeconomic model to analyze cooperative and noncooperative management of Northeast Atlantic cod. In their analysis, only constant strategies were analyzed for noncooperative games. In this paper, nonconstant strategies are considered. Moreover, the fishery in question is characterized by cooperative management. What may happen in the real world is that one nation breaks the cooperative agreement by fishing in excess of its quota. Often, it takes time for the other agent to detect this and respond. In this paper, we allow this kind of delayed response into a two‐agent noncooperative game so that, if country 2 exceeds its quota, there will be a time lag before this is detected by country 1; moreover, there may also be a delay until country 1 is able to respond. Results show that the outcome critically depends on the length of these two lags as well as initial conditions.     

多重积分Nash平衡点的Lipschitz估计

设F（p，q）和G（p，q）在无穷远点的邻域内是分别关于p和q的近似凸函数，且具有二次增长．考虑由F和G构成的一对定义在Soblev空间中的泛函．本文利用blowup技巧，证明了这样一对泛函的Nash平衡点实际上是Lipschitz连续的．