A Dynamic Multi-Objective Duopoly Game with Capital Accumulation and Pollution

This paper studies a discrete-time dynamic duopoly game with homogenous goods. Both firms have to decide on investment where investment increases production capacity so that they are able to put a larger quantity on the market. The downside, however, is that a larger quantity raises pollution. The firms have multiple objectives in the sense that each one maximizes the discounted profit stream and appreciates a clean environment as well. We obtain some surprising results. First, where it is known from the continuous-time differential game literature that firms invest more under a feedback information structure compared to an open-loop one, we detect scenarios where the opposite holds. Second, in a feedback Nash equilibrium, capital stock is more sensitive to environmental appreciation than in the open-loop case.

Feedback Nash Equilibrium of N Agents Fishery Problem

This paper is built on the fundamental of Jorgensen and Sorge considering a differential game about fishery problem. In reality, the exploiters can be many because of the non-excludability of common resource. Thus, we expand the former two players model to N players model and we find more different equilibriums in N players scenario. Through this, we want to find some guidance for the changing of common resource stock. Further to control overexploitation.

Analytical and experimental nonzero-sum differential game-based control of a 7-DOF robotic manipulator

We formulate a Nash-based feedback control law for an Euler–Lagrange system to yield a solution to noncooperative differential game. The robot manipulators are broadly used in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler–Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

A Differential Game of Industrial Pollution Management considering Public Participation

In recent years, with the rapid development of economy, industrial pollution problems have become more and more serious. In this paper, a differential game model is proposed for industrial pollution management, in which public participation is taken into consideration. Then, a feedback Nash equilibrium (FBNE) solution is obtained among the government, enterprises, and the public. Finally, a numerical example is given to illustrate the results. The results show that the public participation will take a positive part in forcing enterprises to reduce emissions. Furthermore, with the increase of the probability of the public reporting the illegal discharge of pollutants by enterprises, the probability of enterprises' active emission reduction will also greatly increase

Experimental and Analytical Nonzero-Sum Differential Game-Based Control of a 7-DOF Robotic Manipulator

We formulate a Nash-based feedback control law for an Euler-Lagrange system to yield a solution to non-cooperative differential game. The robot manipulators are broadly utilized in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler-Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution in order to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

Cooperative Dynamic Game-Based Optimal Power Control in Wireless Sensor Network Powered by RF Energy

This paper focuses on optimal power control in wireless sensor networks powered by RF energy, under the simultaneous wireless information and power transfer (SWIFT) protocol, where the information and power can be transmitted at the same time. We aim to maximize the utility for each sensor through the optimal power control, considering the influences of both the SINR and the harvested energy. The utility maximization problem is formulated as a cooperative dynamic game of a given time duration. All the sensors cooperate together to control their transmission power to maximize the utility and agree to act cooperatively so that a team optimum can be achieved. As a result, a feedback Nash equilibrium solution for each sensor is given based on the dynamic programming theory. Simulation results verify the effectiveness of the proposed approach, by comparing the grand coalition solutions with the non-cooperative solutions.