A cooperative stochastic differential game of transboundary industrial pollution

Though cooperation in environmental control holds out the best promise of effective actions, limited success has been observed because existing multinational joint initiatives fail to satisfy the property of subgame consistency. A cooperative solution is subgame consistent if the solution optimality principle is maintained in any subgame which starts at a later time with any feasible state brought about by prior optimal behaviors. This paper presents a cooperative stochastic differential game of transboundary industrial pollution with two novel features. The first feature is that industrial production creates short-term local impacts and long-term global impacts on the environment. Secondly, a subgame consistent cooperative solution is derived in this stochastic differential game together with a payment distribution mechanism that supports the subgame consistent solution. This is the first time that pollution management is analyzed in a cooperative stochastic differential game framework under these novel features.     

A differential game of retailer promotions

The paper identifies equilibrium marketing strategies over time in a marketing channel of distribution. A number of retailers promote locally a manufacturer's brand in order to increase their sales. However, sustained and substantial retailer promotions will damage the image of the manufacturer's brand. The manufacturer advertises nationally to improve the brand image. Demand at the retail outlets increase both by the local promotions and by the strength of brand image. First, we identify a noncooperative equilibrium of a differential game played with Markovian strategies. Next, we study a cooperative game where the players make coordinated marketing decisions and address the question whether the manufacturer can design an incentive strategy such that the retailers will stick to their parts of the agreed solution.     

A differential game of joint implementation of environmental projects

This paper proposes a two-player, finite-horizon differential game model to analyze joint implementation in environmental projects, one of the flexible mechanisms considered in the Kyoto Protocol. Our results show that allowing for foreign investments could in some cases increase the welfares of both parties involved in the project. Further, imposing an environmental target constraint does not necessarily deteriorate the payoffs of both players.     

Slowing deforestation pace through subsidies: a differential game

This paper deals with the issue of deforestation, one of the main global environmental problems. We consider two players having different utilities for forest conservation. The first one (call it North) represents a set of countries having as an objective to maximize the size of tropical forest at a certain time horizon. The (South) second player's revenue function involves a trade-off between forest exploitation and agricultural activities. We study two scenarios. In the first one, the assumption is a laisser-faire policy, where the South solves an optimal control problem over a finite horizon. Revenue and optimal forest exploitation obtained represent a benchmark for the second scenario, where the North offers subsidies to the South to reduce the deforestation rate. The two scenarios are analyzed and compared in terms of strategies, outcomes and forest conservation.     

Deforestation and foreign transfers: a Stackelberg differential game approach

In this paper, our concern is with deforestation as a global environmental issue. Foreign transfers from developed or Northern countries to developing or Southern countries have been proposed to deal with that issue. We use a Stackelberg differential game approach where the two players are: a donor community (the leader) and a recipient country (the follower). We study the impact of different specifications for the transfer function, related to the different information structures the players can consider when playing the Stackelberg game. The different scenarios are compared both from the environmental and economic points of view.     

A differential control method for the proportional directional valve

For the proportional directional valve controlled by two proportional solenoids, the normal control method （NCM） energizes only one solenoid at a time. The performance of the valve is greatly influenced by the nonlinearity of the proportional solenoid, such as dead zone and low force gain with a small current, and this effect cannot be eliminated by a simple dead-zone current compensation. To avoid this disadvantage, we propose the differential control method （DCM）. By employing DCM, the controller outputs differential signals to simultaneously energize both solenoids of the proportional valve, and the operating point is found by analyzing the force output of the two solenoids to make a minimum variation of the current force gain. The comparisons of the valve response characteristics are made between NCM and DCM by nonlinear dynamic simulation and experiments. Simulation and experimental results show that by using DCM, the frequency response of the valve is greatly enhanced, especially when the input is small, which means that the dynamic characteristics of the proportional valve are improved.     

The singular zero-sum differential game with stability usingH ∞ control theory

In this paper we consider the zero-sum, infinite-horizon, linear quadratic differential game. We derive sufficient conditions for the existence of (almost) equilibria as well as necessary conditions. Contrary to all classical references we allow for singular weighting on the minimizing player in the cost criterion. It turns out that this problem has a strong relation with the singularH _∞ problem with state feedback, i.e., theH _∞ problem where the direct feedthrough matrix from control input to output is not necessarily injective.     

A result on output feedback linear quadratic control

In this note we consider the static output feedback linear quadratic control problem. We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depends only on the output and control variables.This result is used to present both necessary and sufficient conditions under which the corresponding linear quadratic differential game has a Nash equilibrium in case the players use static output feedback control.Another consequence of this result is that the conditions also provide sufficient conditions for the static output stabilizability problem. Of course, in case these conditions are not met this does not mean that the system is not stabilizable via static output feedback.     

A linear differential game with a fixed termination time and restrictions on resources

A linear game with a fixed termination time and integral restrictions on player controls is considered. The pursuer constructs his control with knowledge of the control of the evader, and the evader uses information on all previous actions of his opponent at each instant of time. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 178–183, July–August, 2000.     

认知无线电中基于非合作博弈的功率控制算法

针对认知无线电中的功率控制问题,基于非合作博弈模型,提出了一种新的效用函数,证明了该博弈中纳什均衡的存在性和唯一性。设计了一种分布式功率控制算法并证明了其收敛性。讨论了几个参数对系统性能的影响。仿真表明,该算法可实现对认知用户发射功率的有效控制。与SINR平衡算法和Koskie-Gajic算法相比,本算法既保障了每个认知用户的QoS需求,又增加了系统吞吐量。     

Robust control and differential games on a finite time horizon

It is well known that theH control problem has a state space formulation in terms of differential games. For a finite time horizon control problem, the analogous differential game is considered. The disturbance is the control for the maximizing player. In order to allow forL ² disturbances, the controls for at least one player must be allowed to be unbounded. It is shown that the value of the game is the viscosity solution of the corresponding Isaacs equation under rather general conditions.     

一种基于非合作博弈的无线传感器网络功率控制算法

提出了一种无线传感器网络中以容量最大化为目标的非合作博弈功率控制算法。通过效益函数来选择合适的发射功率,以保证网络连通性并缓解分组碰撞状况。而后给出了对该算法纳什均衡存在性和唯一性的证明。仿真结果表明:该算法可有效提高能量效率和网络容量。     

Asymptotic analysis of nonlinear stochastic risk-sensitive control and differential games

In this paper we consider a finite horizon, nonlinear, stochastic, risk-sensitive optimal control problem with complete state information, and show that it is equivalent to a stochastic differential game. Risk-sensitivity and small noise parameters are introduced, and the limits are analyzed as these parameters tend to zero. First-order expansions are obtained which show that the risk-sensitive controller consists of a standard deterministic controller, plus terms due to stochastic and game-theoretic methods of controller design. The results of this paper relate to the design of robust controllers for nonlinear systems.Research supported in part by the 1990 Summer Faculty Research Fellowship, University of Kentucky.     

A concept of cooperative equilibrium for dynamic games

The paper proposes an equilibrium solution concept for dynamic games where players can communicate with one another, but cannot make contractual agreements. In such games, unlike the static problems without contracting possibilities, the cooperation between players is possible due to the fact that the realization of negotiated agreements can be enforced by suitably-defined strategies. The definition presented combines dynamic programming, the theory of bargaining and the notion of enforceable agreements to produce a class of cooperative solutions defined in the form of memory Nash equilibria satisfying the principle of optimality along the equilibrium trajectory. The choice of a particular solution in this class depends on players' expected actions in case of disagreement, and on an adopted negotiation scheme formalized in the form of a bargaining model. Possible formulations of disagreement policies and bargaining models are discussed in some detail.     

环境污染博弈问题的系统动力学模型*

用系统动力学建立环境污染管理问题中政府管理部门与生产排污企业之间的一个混合战略重复博弈模型,考虑信息延迟和环境的污染量净化问题进行模型的仿真。结果表明,环境污染问题中政府管理部门与生产排污企业之间博弈的Nash均衡实际上很难达到稳定,尤其是在考虑信息延迟的情况下。最后提出一种简单可行的双重惩罚策略,既可以促使博弈双方尽快达到Nash均衡,也能有效地改善环境污染问题。     

基于SD的环境污染多人演化博弈问题研究*

主要对政府与竞争关系条件下两企业之间的监督博弈演化过程进行动态性分析,利用系统动力学建立一个环境监管部门与两个竞争关系企业的多人演化博弈模型,分析不同惩罚策略对博弈均衡和过程的影响。结果表明：罚款额度的惩罚系数k的大小与博弈过程的动态性密切相关;一般惩罚策略能有效抑制环境污染,而动态惩罚策略则在博弈过程波动性控制方面具有明显效果。     

Families of semipermeable curves in differential games with the homicidal chauffeur dynamics

Families of semipermeable curves in differential games with the homicidal chauffeur dynamics are studied both from theoretical and computational points of view. The knowledge of such families is very useful because semipermeable curves bound capture sets in games of kind. They can also appear as barrier lines on which value functions of time-optimal differential games are discontinuous. Two examples of differential games with the homicidal chauffeur dynamics are considered. Capture sets are constructed using semipermeable curves. The results are verified through computation of level sets of the value functions in the related time-optimal games.     

A cooperative game of a pair of learning automata

A cooperative game played in a sequential manner by a pair of learning automata is investigated in this paper. The automata operate in an unknown random environment which gives a common pay-off to the automata. Necessary and sufficient conditions on the functions in the reinforcement scheme are given for absolute monotonicity which enables the expected pay-off to be monotonically increasing in any arbitrary environment. As each participating automaton operates with no information regarding the other partner, the results of the paper are relevant to decentralized control.     

A differential evolution algorithm with self-adapting strategy and control parameters

This paper presents a Differential Evolution algorithm with self-adaptive trial vector generation strategy and control parameters (SspDE) for global numerical optimization over continuous space. In the SspDE algorithm, each target individual has an associated strategy list (SL), a mutation scaling factor F list (FL), and a crossover rate CR list (CRL). During the evolution, a trial individual is generated by using a strategy, F, and CR taken from the lists associated with the target vector. If the obtained trial individual is better than the target vector, the used strategy, F, and CR will enter a winning strategy list (wSL), a winning F list (wFL), and a winning CR list (wCRL), respectively. After a given number of iterations, the FL, CRL or SL will be refilled at a high probability by selecting elements from wFL, wCRL and wSL or randomly generated values. In this way, both the trial vector generation strategy and its associated parameters can be gradually self-adapted to match different phases of evolution by learning from their previous successful experience. Extensive computational simulations and comparisons are carried out by employing a set of 19 benchmark problems from the literature. The computational results show that overall the SspDE algorithm performs better than the state-of-the-art differential evolution variants.