基于微分博弈, 研究由一个供应商与一个制造商组成的低碳供应链中纵向合作减排的动态优化问题. 构建了以制造商占主导、供应商跟随的Stackelberg 微分博弈模型, 分别得到了制造商和供应商的最优反馈均衡策略及各自的利润最优值函数, 推导出产品碳排放量随时间变化的最优轨迹. 通过数值算例分析了制造商和供应商的长期合作减排策略对产品碳排放量的影响, 为供应链上下游企业开展长期减排合作提供了理论依据.
相似文献为解决多个承包商间的项目合作伙伴选择问题, 采用多目标规划构建工程系统进度优化的协同决策模型. 以合作博弈理论为基础, 运用主要目标法设计一种基于期望收益约束选择的模型求解方法. 算例结果表明, 所提出的方法可以在保障参与协同的承包商收益需求前提下实现工程系统进度最优, 所获得的协同方案更容易为各方接受.
相似文献This paper suggests a new approach for repeated Stackelberg security games (SSGs) based on manipulation. Manipulation is a strategy interpreted by the Machiavellianism social behavior theory, which consists on three main concepts: view, tactics, and immorality. The world is conceptualized by manipulators and manipulated (view). Players employ Machiavelli’s tactics and Machiavellian intelligence in order to manipulate attacker/defender situations. The immorality plays a fundamental role in these games, defenders are able to not be attached to a conventional moral in order to achieve their goals. We consider a security game model involving manipulating defenders and manipulated attackers engaged cooperatively in a Nash game and at the same time restricted by a Stackelberg game. The resulting game is non-cooperative bargaining game. The cooperation is represented by the Nash bargaining solution. We propose an analytical formula for solving the manipulation game, which arises as the maximum of the quotient of two Nash products. The role of the players in the Stackelberg security game are determined by the weights of the players for the Nash bargaining approach. We consider only a subgame perfect equilibrium where the solution of the manipulation game is a Strong Stackelberg Equilibrium (SSE). We employ a reinforcement learning (RL) approach for the implementation of the immorality. A numerical example related to developing a strategic schedule for the efficient use of resources for patrolling in a smart city is handled using a class of homogeneous, ergodic, controllable, and finite Markov chains for showing the usefulness of the method for security resource allocation.
相似文献Repeated quantum game theory addresses long-term relations among players who choose quantum strategies. In the conventional quantum game theory, single-round quantum games or at most finitely repeated games have been widely studied; however, less is known for infinitely repeated quantum games. Investigating infinitely repeated games is crucial since finitely repeated games do not much differ from single-round games. In this work, we establish the concept of general repeated quantum games and show the Quantum Folk Theorem, which claims that by iterating a game one can find an equilibrium strategy of the game and receive reward that is not obtained by a Nash equilibrium of the corresponding single-round quantum game. A significant difference between repeated quantum prisoner’s dilemma and repeated classical prisoner’s dilemma is that the classical Pareto optimal solution is not always an equilibrium of the repeated quantum game when entanglement is sufficiently strong. When entanglement is sufficiently strong and reward is small, mutual cooperation cannot be an equilibrium of the repeated quantum game. In addition, we present several concrete equilibrium strategies of the repeated quantum prisoner’s dilemma.
相似文献We deal with the location-quantity problem for competing firms when they locate multiple facilities and offer the same type of product. Competition is performed under delivered quantities that are sent from the facilities to the customers. This problem is reduced to a location game when the competing firms deliver the Cournot equilibrium quantities. While existence conditions for a Nash equilibrium of the location game have been discussed in many contributions in the literature, computing an equilibrium on a network when multiple facilities are to be located by each firm is a problem not previously addressed. We propose an integer linear programming formulation to fill this gap. The formulation solves the profit maximization problem for a firm, assuming that the other firms have fixed their facility locations. This allows us to compute location Nash equilibria by the best response procedure. A study with data of Spanish municipalities under different scenarios is presented and conclusions are drawn from a sensitivity analysis.
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