INTERNATIONAL ENVIRONMENTAL AGREEMENTS WITH DEVELOPED AND DEVELOPING COUNTRIES IN A DYNAMIC APPROACH

This paper is devoted to study the stability of international environmental agreements (IEAs) in a pollution abatement model. We focus our attention on two asymmetric agents: developed countries characterized by a strong measure of environmental awareness and developing ones characterized by less attention to environmental preservation. We model a differential game in order to determine both the optimal path of the abatement levels and stock pollutant as results of open‐loop and feedback Nash equilibria. By means of the concepts of internal and external stability, we explain how the environmental awareness of two types of countries and the number of cooperators and defectors influence the size of stable coalitions. The results establish that the asymmetry assumption does not have consequences for the stability of the grand coalition, which can be obtained only with transfers.     

OPTIMAL RECOVERY OF A SHARED RESOURCE STOCK: A DIFFERENTIAL GAME MODEL WITH EFFICIENT MEMORY EQUILIBRIA

We consider an optimal two-country management of depleted transboundary renewable resources. The management problem is modelled as a differential game, in which memory strategies are used. The countries negotiate an agreement among Pareto efficient harvesting programs. They monitor the evolution of the agreement, and they memorize deviations from the agreement in the past. If the agreement is observed by the countries, they continue cooperation. If one of the countries breaches the contract, then both countries continue in a noncooperative management mode for the rest of the game. This noncooperative option is called a threat policy. The credibility of the threats is guaranteed by their equilibrium property. Transfer or side payments are studied as a particular cooperative management program. Transfer payments allow one country to buy out the other from the fishery for the purpose of eliminating the inefficiency caused by the joint access to the resources. It is shown that efficient equilibria can be reached in a class of resource management games, which allow the use of memory strategies. In particular, continuous time transfer payments (e.g., a share of the harvest) should be used instead of a once-and-for-all transfer payment.     

Weak Invariance of a Cylindrical Set with Smooth Boundary with Respect to a Control System

We consider the problem of constructing resolving sets for a differential game or an optimal control problem based on information on the dynamics of the system, control resources, and boundary conditions. The construction of largest possible sets with such properties (the maximal stable bridge in a differential game or the controllability set in a control problem) is a nontrivial problem due to their complicated geometry; in particular, the boundaries may be nonconvex and nonsmooth. In practical engineering tasks, which permit some tolerance and deviations, it is often admissible to construct a resolving set that is not maximal. The constructed set may possess certain characteristics that would make the formation of control actions easier. For example, the set may have convex sections or a smooth boundary. In this context, we study the property of stability (weak invariance) for one class of sets in the space of positions of a differential game. Using the notion of stability defect of a set introduced by V.N. Ushakov, we derive a criterion of weak invariance with respect to a conflict control dynamic system for cylindrical sets. In a particular case of a linear control system, we obtain easily verified sufficient conditions of weak invariance for cylindrical sets with ellipsoidal sections. The proof of the conditions is based on constructions and facts of subdifferential calculation. An illustrating example is given.     

An Approach to Fuzzy Noncooperative Nash Games

Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize/minimize his/her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends.In this paper, we utilize fuzzy set theory in order to incorporate the players' heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations.     

Stability,structural stability,and games: Toward a theory of differential hypergames

Differential games (DG's) are investigated from a stability point of view. Several resemblances between the theory of optimal control and that of structural stability suggest a differential game approach in which the operators have conflicting interests regarding the stability of the system only. This qualitative approach adds several interesting new features. The solution of a differential game is defined to be the equilibrium position of a dynamical system in the framework of a given stability theory: this is the differential hypergame (DHG). Three types of DHG are discussed: abstract structural DHG, Liapunov DHG, and Popov DHG. The first makes the connection between DG and the catastrophe theory of Thom; the second makes the connection between the value function approach and Liapunov theory; and the third provides invariant properties for DG's. To illustrate the fact that the theory sketched here may find interesting applications, the up-to-date problem of the world economy is outlined.This research was supported by the National Research Council of Canada.     

多重因素约束下的网格搜索对策问题研究

首次基于搜索成本及搜索资源等限制因素,构造局中人面向多重约束条件的可行策略集合,建立相应的搜索空间;在给定搜索点权值的基础上,考虑搜索成本与搜索成功概率等因素,构造相应的支付函数,建立多重因素约束下的网格搜索对策模型.为简化模型求解,将对策论问题转化为约束最优化问题,求解约束问题获得最优值,转化为模型的对策值,并给出双方最优混合策略.最后,给出军事想定实例,说明上述模型的实用性及方法的有效性.     

AN INTERNATIONAL MARINE POLLUTANT SINK IN AN ASYMMETRIC ENVIRONMENTAL TECHNOLOGY GAME

Abstract A differential game with N countries as players is developed for the analysis of a marine resource with open access used by the countries as a pollutant sink and for production of an ecosystem good. Consumption, investment, abatement, and environmental research sectors may differ across countries. Under the assumption that property rights are well defined within the sovereignty of each country although there is a lack of enforcement in the international area, the game is solved for the feedback Nash equilibrium, using the Isaacs–Bellman dynamic programming technique, identifying the nonlinear feedback Nash flows of consumption, investment, harvest effort, abatement, and environmental research effort in each country, which is then compared to the Pareto optimal global solution.     

Asymptotic properties of minimax solutions of Isaacs-Bellman equations in differential games with fast and slow motions

Sufficient conditions under which the solutions of the Cauchy problem for singularly-perturbed Hamilton-Jacobi equations will converge to a limit are established. The results are used to investigate the asymptotic behaviour of the value function of a differential game involving fast and slow motions.     

Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach

A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N -person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.     

Deployment of rural health facilities in a developing country

This study describes the problem of finding suitable sites for additional health facilities in a rural area in Bangladesh. The objective is to improve the accessibility of people to the health care system given the existing set of facilities. As is frequently the case in developing countries, activities designed to develop and improve differing sectors of the infrastructure are poorly integrated and ill-coordinated. As a result, decision-makers may make independent and individual decisions about locating new service facilities. Often, as has been the case in Bangladesh, these decisions are taken at a relatively low level, by officers of local government or by elected leaders in a region, or by a combination of these. In the absence of any formal analysis and generation of alternatives, the final decision may be made on political or pragmatic considerations. As a result the decisions are often far from optimal. Ultimately, better health care will enhance many sectors of a regional economy, and so the decision about where to invest in new or better resources is important for reasons over and above that of providing health care for the population. In this paper, the role of location-allocation modelling in developing countries is considered, and the specific Bangladeshi problem is considered as a maximal covering location problem which is solved by an efficient heuristic method.     

The problem of conflicting control with mixed constraints

The control problem for a linear dynamical system is considered at a minimax of the terminal quality index. Feasible controls are simultaneously restricted by geometrical constraints and by integrated momentum constraints, the latter being thought of as a store of control resources. The problem is formalized as a differential game [1–4] using concepts [5–8] developed at Ekaterinburg. Here, because of the geometrical constraints, the momentum formulation and its associated difficulties [2–4] do not appear. On the other hand the presence of the integral restrictions leads to the appearance of additional variables whose evolution describes the dynamics of the expenditure of the control resources. These variables are subject to phase restrictions, which is a peculiarity of the problem. A reasonably informative picture and a class of strategies for which the given game has a value and a saddle point are given. A constructive method for computing the value function of the game and constructing optimal strategies is presented. This method is conceptually related to the construction of a stochastic programming synthesis [5] and is based on the recursive construction of upper-convex envelopes for certain auxiliary functions. The possibility of exchanging the minimum and maximum operations over the resource parameters when calculating the value of the game using these procedure is established.     

基于政府支持的军民合作技术创新演化博弈研究

如何促进军民合作技术创新是军民深度融合战略背景下军民双方亟需解决的重要问题。基于演化博弈的基本理论和方法,构建了包含民企、军企与政府在内的三方博弈模型,寻找出能使整个系统处于均衡状态的稳定策略,并利用数值仿真分析了政府支持不同方式对军民合作技术创新的影响。结果表明:在政府不同支持方式下,民企和军企相互促进,双方均向合作技术创新的方向演化,并最终保持稳定;随着时间的推进,政府最终均会选择退出支持,不同支持方式下退出速度不同;政府应对不同支持方式进行优化。     

Criterion function for accessibility,uncertainty problems in regional land-use planning

One objective in regional planning is the creation of communities with great accessibility. Thus we should plan the locations of inhabitants and the activities of the region so that the total accessibility will be maximized subject to some restrictions. This is a quadratic programming problem, which can be solved by quadratic programming techniques, but we cannot then take into account the uncertainties of the problem.In this paper a new criterion function is proposed for accessibility, uncertainty problems in regional land-use planning. It is derived from Hurwicz's generalized maximin principle. Many advantages are gained, for the planning problem is separated into linear programming problems, the uncertainties are taken into consideration as in game theory and the methods of parametric programming are available.A simplified problem of the populations of three town areas is studied and the method is generalized for problems of many activities and areas.     

具有随机工资的养老金最优投资问题

在三种目标函数下, 研究了具有随机工资的养老金最优投资问题. 第一种是均值-方差准则, 第二种基于效用的随机微分博弈, 第三种基于均值-方差准则的随机微分博弈. 随机微分博弈问题中博弈的双方为养老金计划投资者和金融市场, 金融市场是博弈的虚拟手. 应用线性二次控制理论求得了三种目标函数下的最优策略和值函数的显式解.     

Complex Strategic Analysis: A Hypergame Study of the Fall of France

It is argued that a crucial element in decision-making in conflicts is the need for adequate conceptual complexity in problem formulation. This is illustrated by reference to a disastrous military failure—the fall of France in 1940. A formal model of the strategic situation is constructed using the Hypergame approach, in which the usual game-theoretic assumption that all "players" see the same "game" is discarded. Using this model, further features of the case are explored, and some general conclusions discussed. It is suggested that Hypergame analysis can be of assistance in achieving adequate levels of problem-perception in complex, conflict-prone environments, in particular by helping in the generation of multiple models.     

The composition conjecture for Abel equation

The composition conjecture for the Abel differential equation states that if all solutions in a neighborhood of the origin are periodic then the indefinite integrals of its coefficients are compositions of a periodic function. Several research articles were published in the last 20 years to prove the conjecture or a weaker version of it. The problem is related to the classical center problem of polynomial two-dimensional systems. The conjecture opens important relations with classical analysis and algebra. We give a widely accessible exposition of this conjecture and verify the conjecture for certain classes of coefficients.     

A BSDE approach to stochastic differential games with incomplete information

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our aim is to quantify the amount of information the informed player has to reveal in order to play optimally: to do so, we show that the value function of this zero-sum game can be rewritten as a minimization problem over some martingale measures with a payoff given by the solution of a backward stochastic differential equation.     

Construction of the value function in a pursuit-evasion game with three pursuers and one evader

A differential pursuit-evasion game is considered with three pursuers and one evader. It is assumed that all objects (players) have simple motions and that the game takes place in a plane. The control vectors satisfy geometrical constraints and the evader has a superiority in control resources. The game time is fixed. The value functional is the distance between the evader and the nearest pursuer at the end of the game. The problem of determining the value function of the game for any possible position is solved.

Three possible cases for the relative arrangement of the players at an arbitrary time are studied: “one-after-one”, “two-after-one”, “three-after-one-in-the-middle” and “three-after-one”. For each of the relative arrangements of the players a guaranteed result function is constructed. In the first three cases the function is expressed analytically. In the fourth case a piecewise-programmed construction is presented with one switchover, on the basis of which the value of the function is determined numerically. The guaranteed result function is shown to be identical with the game value function. When the initial pursuer positions are fixed in an arbitrary manner there are four game domains depending on their relative positions. The boundary between the “three-after-one-in-the-middle” domain and the “three-after-one” domain is found numerically, and the remaining boundaries are interior Nicomedean conchoids, lines and circles. Programs are written that construct singular manifolds and the value function level lines.     

区域合作减排策略选择及提升对策研究

跨区域合作的碳减排是实现减排目标较为有效的机制。通过构建政府间减排演化博弈模型,模拟了区域内地方政府独立减排、合作减排情形的策略选择演化过程。研究发现,(1)当区域内本地政府和外部政府经济发展水平都比较低时,无论是独立减排还是合作减排,{减排,减排}都是地方政府的稳定选择策略,但减排效果不显著;(2)独立减排情形下,经济先发地区减排意愿薄弱,后发地区有减排意愿,但减排效果并不显著;(3)合作减排时,当协同收益小于交易成本时,随着地方政府经济发展,减排系统博弈最终会向地方政府一方减排一方不减排的方向演进;当协同收益大于交易成本时,通过合作减排,实现了资源的优势互补,降低了碳排放的负外部效应,提高了减排意愿。最后提出通过搭建起区域合作交流平台,激发地方政府减排活力及推进低碳经济发展等建议,来提高协同收益或降低交易成本,有效促进区域合作减排。     

Spatial oligopolistic equilibria with arbitrage,shared resources,and price function conjectures

This paper considers equilibria among multiple firms that are competing non-cooperatively against each other to sell electric power and buy resources needed to produce that power. Examples of such resources include fuels, power plant sites, and emissions allowances. The electric power market is a spatial market on a network in which flows are constrained by Kirchhoffs current and voltage laws. Arbitragers in the power market erase spatial price differences that are non-cost based. Power producers can compete in power markets à la Cournot (game in quantities), or in a generalization of the Cournot game (termed the conjectured supply function game) in which they anticipate that rivals will respond to price changes. In input markets, producers either compete à la Bertrand (price-taking behavior) or they can conjecture that price will increase with consumption of the resource. The simultaneous competition in power and input markets presents opportunities for strategic price behavior that cannot be analyzed using models of power markets alone. Depending on whether the producers treat the arbitrager endogenously or exogenously, we derive two mixed nonlinear complementarity formulations of the oligopolistic problem. We establish the existence and uniqueness of solutions as well as connections among the solutions to the model formulations. A numerical example is provided for illustrative purposes.Support was provided by the National Science Foundation under grant ECS-0080577.This authors research was partially supported by the National Science Foundation under grants ECS-0080577 and CCR-0098013.The authors thank Chris Day, Fieke Riekers, and Adrian Wals for their collaboration. They are particularly indebted to Grant Roch for writing AMPL and MATLAB codes for solving the numerical example reported in the paper.