Blockchain-enabled governance of greenwashing in the building material supply chain: A differential game approach

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We present an analysis of advertising activities in a dynamic oligopoly with differentiated goods using a differential game approach under general demand and cost functions. The main conclusion is that the memoryless closed‐loop solution and the feedback solution are equivalent when there is no spillover effect of advertising activities. We also show that the comparison of the open‐loop solution and the memoryless closed‐loop solution depends on whether the firms’ outputs are strategic substitutes or strategic complements.

This paper presents Multi-robot co-operative hunting behavior using Differential game approach. Two robots were used as pursuers while another robot is used as evader, the two robots (pursuers) try to search and surround the prey (evader) robot. The aim of the game is for the two robots to detect the evader at the minimum possible time while at the same time the evader dodged the pursuer to the maximum possible time. Differential game approach was used to construct the problem using system of ordinary differential equation. We give the required conditions for the two pursuers to catch the evader. It was also shown that the evader maximize the capture time, while the pursuers minimize the capture time.

This paper proposes an efficient fast-optimal balanced differential game (DG) approach to address the formation control problem in dynamic environments for networked multi-agent systems (MASs). Compared to existing receding horizon distributed differential game (RH-DDG) approaches, the proposed approach employs a two-layer game structure to balance optimality and real-time performance, with a focus on formation control, collision avoidance and obstacle avoidance. In the offline layer, the problem is converted into a distributed differential game (DDG) where each agent computes strategies using distributed information from locally neighboring agents. The strategy of each agent self-enforces a unique global Nash equilibrium (G-NE) with a strongly connected communication topology, providing an optimal reference trajectory for the online game. In the online layer, a receding horizon differential game with an event-trigger mechanism (RH-DGET) is presented to track the G-NE trajectory. Ego players are triggered to update online Nash strategies only when the event-triggering condition is satisfied, ensuring the real-time safety certificate. Rigorous proofs demonstrate that the online Nash strategies converge to the offline G-NE until the trigger ends, and a certain dwell time condition is given to prevent the Zeno behavior. Simulation results validate the effectiveness of the proposed approach.

It is well known that non-cooperative behaviour of different policy-makers, either central bank and government on a national level or governments of different countries on an international level, may result in severe overall losses and inefficiencies. On the other hand, policy coordination is difficult to achieve, given the mechanisms of negotiations between several policy-making institutions. A solution to this “trade-off” would be a mechanism inducing individual behaviour that ensures efficient (Pareto-optimal) outcomes equivalent to those achieved by cooperation, but without the need of explicit agreements.

This paper studies the navigation strategy of intelligent vehicles crossing through unsignalized intersections. Each vehicle can make decisions independently or act in a cooperative manner. The problem is described as a dynamic differential game in which two vehicles make decisions according to the expected behavior of the other vehicle. Both non-cooperative game (a vehicle only optimizes its own cost) and cooperative game (a vehicle coordinates its decision to optimize a joint cost) are considered. Unlike traditional discrete game theoretical methods that divide the acceleration of vehicles into several pieces, the proposed differential game generates continuous-time acceleration signals that are flexible to vary during the entire intersection crossing period. The efficacy of the differential game approach is verified by simulations, and results show that the method make vehicles pass through the unsignalized intersection more quickly than traditional discrete game theoretical methods, and satisfies safety and comfort requirements at the same time.

Considering personalized driving preferences, a new decision-making framework is developed using a differential game approach to resolve the driving conflicts of autonomous vehicles (AVs) at unsignalized intersections. To realize human-like driving and personalized decision-making, driving aggressiveness is first defined for AVs. To improve driving safety, a Gaussian potential field model is built for collision risk assessment. Besides, in the proposed decision-making framework, the collision risk assessment model is further used to reduce the computational complexity based on an event-triggered mechanism. In the construction of payoff function, both driving safety and passing efficiency are comprehensively considered, and the driving aggressiveness is also reflected. Two kinds of equilibrium solution to the differential game, i.e., the Nash equilibrium and Stackelberg equilibrium, are discussed and solved. Finally, the proposed decision-making algorithm is tested through a hardware-in-the-loop testing platform, and its feasibility, effectiveness, and real-time implementation performance are validated.

Time varying Formation Control Using Differential Game Approach

In this study, the leader's behavior learning problem is investigated for a class of leader-follower systems, where the leader's behavior is assumed not a priori known to all followers that are autonomous. A multi-player nonzero-sum differential game is introduced to indicate the control interaction between agents, where the leader's behavior is modelled by an unknown cost function. The autonomous followers aim to retrieve the weighting matrix in the leader's cost function collaboratively. A distributed online adaptive inverse differential game (IDG) approach to the leader's behavior learning is proposed for the autonomous followers. Specifically, a concurrent learning (CL) based adaptive law and an interactive game controller are first developed for each autonomous follower to learn the leader's feedback gain matrix online, while the feedback Nash equilibrium of the game can be achieved. Then, a linear matrix inequality (LMI) optimization problem is formulated to determine the weighting matrix of the leader's cost function for each autonomous follower. The proposed method simply requires that all followers share their interactive feedback gain matrices, not their private intents, and use only the system state data, not both the system state data and the leader's control input data. The main advantages of the proposed method are that it can be implemented online without requiring the persistent excitation condition and needs less computational power for all followers. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the developed method.

It is well-known that coordination within a supply chain reduces an inefficiency due to double marginalization in a decentralized chain. We study the effect of coordination in a three-tier supply chain consisting of a supplier, a manufacturer, and a retailer. A manufacturer invests in quality improvement. In this supply chain, coordination may occur between a supplier and a manufacturer (upstream coordination), or between a manufacturer and a retailer (downstream coordination). Using differential games approach, we characterize the equilibrium strategies and profits in three models, i.e., a decentralized supply chain, upstream coordination, and downstream coordination, for a finite planning horizon. We show that, although either type of coordination improves supply chain efficiency, upstream coordination and downstream coordination have different impacts on the equilibrium pricing and quality strategies and the consequent profits.

In contrast, the differential game approach Air-to-air missile guidance laws are derived makes no assumption on future target maneuvers, using optimal control and differential game theory but instead takes into consideration the target's with final miss distance as the optimization cri- maneuver capabilities. The guidance law then terion. A perfect target airframe /autopilot re - guides the missile so as to minimize the potential sponse is assumed, while both perfect and first effects of the target's intelligent use of hie maorder missile responses are considered. With a neuver capabilities. first order missile response the target is always able to force a non zero final miss distance in the differential game formulation. For all other formulaticjns considered there are states from which the missile can force zero terminal miss. In these cases, an auxiliary performance index (e. g., control energy) can be used to specify unique controls. Two simulation scenarios were used to evaluate the guidance laws: one with missile launch near the inner launch boundary and the other near the outer launch boundary. The differential game guidance laws are less sensitive to errors i,: rstimates of current target acceleration than the optimal control laws. The laws based on a perfect missile response performed better for the outer launch boundary scenario, whereas for the inner launch boundary scenario the laws based on a first order missile response achieved srnaller miss distances. The purpose of this paper

Hackers evaluate potential targets to identify poorly defended firms to attack, creating competition in IT security between firms that possess similar information assets. We utilize a differential game framework to analyze the continuous time IT security investment decisions of firms in such a target group. We derive the steady state equilibrium of the duopolistic differential game, show how implicit competition induces overspending in IT defense, and then demonstrate how such overinvestment can be combated by innovatively managing the otherwise misaligned incentives for coordination. We show that in order to achieve cooperation, the firm with the higher asset value must take the lead and provide appropriate incentives to elicit participation of the other firm. Our analysis indicates that IT security planning should not remain an internal, firm-level decision, but also incorporate the actions of those firms that hackers consider as alternative targets.

Despite its advantages of flexility and low-cost networking, unmanned aerial vehicle (UAV) communications face various attacks such as eavesdropping. Existing studies on secure UAV communications assume fixed-location eavesdroppers and rarely consider interactions between legitimate nodes and eavesdroppers. In this paper, we investigate eavesdropping and anti-eavesdropping interaction between a UAV-enabled eavesdropper (UAV-E) and a UAV-enabled base station (UAV-BS) in a downlink wiretap system. The UAV-E aims to wiretap downlink signals by adaptively adjusting its trajectory while the UAV-BS aims to maximize secrecy-sum-rate with minimum power consumption by jointly optimizing user scheduling, power control, and trajectory. Dynamic differential equations are formulated to characterize motions of UAVs, following which a zero-sum differential game is formulated to model the “pursuit-evasion” interaction between the UAV-BS and the UAV-E. Definition and existence of Nash equilibrium (NE) are provided. To obtain the NE, Pontryagins minimum principle is leveraged to solve the trajectory design problem. Further, Gauss-Seidel-like implicit finite-difference method is leveraged to obtain saddle-point strategies at NE. Finally, numerical results are provided to verify the effectiveness of the proposed game model. It is revealed that the differential game can well-characterize the strategy interactions between UAVs. Moreover, results show that the initial positions and weights of UAVs, the energy consumption factor, and the user scheduling have key impacts on motion interactions between the UAV-BS and the UAV-E and further on UAV-BS’s power control.

Obstacle circumvention strategies can be shaped by the dynamic interaction of an individual (evader) and an obstacle (pursuer). We have developed a mathematical model with predictive and emergent components, using experimental data from seven healthy young adults walking toward a target while avoiding collision with a stationary or moving obstacle (approaching head-on, or diagonally 30° left or right) in a virtual environment. Two linear properties from the predictive component enable the evader to predict the minimum distance between itself and the obstacle at all times, including the future intersection of trajectories. The emergent component uses the classical differential games model to solve for an optimal circumvention while reaching the target, wherein the locomotor strategy is influenced by the obstacle, target, and the evader velocity. Both model components were fitted to a different set of experimental data obtained from five poststroke and healthy participants to derive the minimum predicted distance (predictive component) and obstacle influence dimensions (emergent component) during circumvention. Minimum predicted distance between evader and pursuer was kept constant when the evader was closest to the obstacle in all participants. Obstacle influence dimensions varied depending on obstacle approach condition and preferred side of circumvention, reflecting differences in locomotor strategies between poststroke and healthy individuals. Additionally, important associations between model outputs and observed experimental outcomes were found. The model, supported by experimental data, suggests that both predictive and emergent processes can shape obstacle circumvention strategies in healthy and poststroke individuals. NEW & NOTEWORTHY Obstacle circumvention during goal-directed locomotion is modeled with a new mathematical approach comprising both predictive and emergent elements. The major novelty is using differential games solutions to illustrate the dynamic interactions between the individual as an evader and the approaching obstacle as a pursuer. The model is supported by experimental evidence that explains the behavior along the continuum of locomotor adaptation displayed by healthy subjects and individuals with stroke.

This paper studies the optimal extraction and taxation of nonrenewable natural resources. It is well known that the market values of the main strategic resources such as oil, natural gas, uranium, copper,..., etc, fluctuate randomly following global and seasonal macroeconomic parameters, these values are modeled using Markov switching L\'evy processes. We formulate this problem as a differential game. The two players of this differential game are the mining company whose aim is to maximize the revenues generated from its extracting activities and the government agency in charge of regulating and taxing natural resources. We prove the existence of a Nash equilibrium. The corresponding Hamilton Jacobi Isaacs equations are completely solved and the value functions as well as the optimal extraction and taxation rates are derived in closed-form. A Numerical example is presented to illustrate our findings.