Hierarchical Game Theory Research Articles

Individual and cluster demand response in retail electricity trading with end-users in differentiated oligopoly market: A game-theoretical approach

The characterization of the competitive interdependence among power consumers in power trading system contributes to pursuing efficient power supply and suppressing peak–valley load differences. Even though Stackelberg–Nash game approach has been applied to retail electricity trading with a single utility company and a group of end-users under competitive interdependence, the extension to multi-cluster retail electricity markets is not focused yet and the best strategies of end-users are still decoupled to each other. To bridge this gap this paper investigates the price-based demand response problem in multi-cluster retail electricity markets to coordinate the energy consumption behavior of the end-users and the retail price behavior of the utility companies. Adopting the structure of hierarchical game theory, the cluster retail price is controlled by the utility company to affect the energy consumption demand of end-users within the corresponding cluster and hence increase the income of both the utility companies and the end-users. In order to describe the coupled competition relationship among the bottom end-users in the system, the Cournot competition model of the differentiated oligopoly market is constructed by taking energy consumption as the individual strategy of end-users. The existence and uniqueness of Nash equilibrium and Stackelberg Nash equilibrium in such a hierarchical game system are proved, and a seeking algorithm is proposed to seek the Stackelberg Nash equilibrium, which is regarded as the extension from the existing algorithm for multi-cluster setup. This work gives an insight to theoretically check whether the utility companies need to redesign the contract with the power generator to ask for larger maximum supply.

Designing Fairness in Autonomous Peer-to-peer Energy Trading

Several autonomous energy management and peer-to-peer trading mechanisms for future energy markets have been recently proposed based on optimization and game theory. In this paper, we study the impact of trading prices on the outcome of these market designs for energy-hub networks. We prove that, for a generic choice of trading prices, autonomous peer-to-peer trading is always network-wide beneficial but not necessarily individually beneficial for each hub. Therefore, we leverage hierarchical game theory to formalize the problem of designing locally-beneficial and network-wide fair peer-to-peer trading prices. Then, we propose a scalable and privacy-preserving price-mediation algorithm that provably converges to a profile of such prices. Numerical simulations on a 3-hub network show that the proposed algorithm can indeed incentivize active participation of energy hubs in autonomous peer-to-peer trading schemes.

A Hierarchical Game Theory Based Demand Optimization Method for Grid-Interaction of Energy Flexible Buildings

Building demand-side management is an effective solution for relieving the peak and imbalance problems of electrical grids. How to explore the energy flexibility of buildings and to coordinate a variety of buildings with different energy flexibilities for effective interactions with smart grids are a great challenge. This paper proposes a game theory–based hierarchical demand optimization method for energy flexible buildings for achieving better grid interactions. This method consists of two optimization strategies at the grid and building levels. At the grid level, a demand-price interaction model for buildings and the grid is established to identify the Nash equilibrium solutions based on game theory; these solutions are used to determine the optimized energy demand of buildings and the associated electricity prices by accommodating the interests of all participants involved. At the building level, three types of buildings with different energy flexibilities are investigated to analyze the influence of building management strategies on grid interactions. The effectiveness of the proposed method is verified in a simulated case study. The results show that the optimization method can reduce building operational cost by 3–18%, reduce the fluctuation of the power grid by 30–50%, and ensure that the power grid increases income by 8–20%.

Driver Modeling Through Deep Reinforcement Learning and Behavioral Game Theory

In this work, a synergistic combination of deep reinforcement learning and hierarchical game theory is proposed as a modeling framework for behavioral predictions of drivers in highway driving scenarios. The modeling framework presented in this work can be used in a high-fidelity traffic simulator consisting of multiple human decision-makers. This simulator can reduce the time and effort spent for testing autonomous vehicles by allowing safe and quick assessment of self-driving control algorithms. To demonstrate the fidelity of the proposed modeling framework, game-theoretical driver models are compared with real human driver behavior patterns extracted from two different sets of traffic data.

Построение комплексных расписаний обработки пакетов данных в конвейерной системе при задании ограничений на длительность интервалов времени ее функционирования

The problem of planning data packet processing in a pipeline system with a time limit on the duration of its operation intervals is considered. The solution of the problem involves determining the composition of data packets, the composition of groups of data packets processed during these time intervals, and the schedules for processing packets of each group. To optimize solutions, the hierarchical game theory is applied. Conditions have been introduced that allow you to determine packages that are processed or readjusted to processing, which causes maximum downtime of pipeline segments. A method for constructing effective group compositions is proposed, which involves excluding packages that are determined in accordance with these conditions and placing packages that are not included in them in groups.

Selfish node detection based on hierarchical game theory in IoT

Cooperation between nodes is an effective technology for network throughput in the Internet of Things. The nodes that do not cooperate with other nodes in the network are called selfish and malicious nodes. Selfish nodes use the facilities of other nodes of the network for raising their interests. But malicious nodes tend to damage the facilities of the network and abuse it. According to reviews of the previous studies, in this paper, a mechanism is proposed for detecting the selfish and malicious nodes based on reputation and game theory. The proposed method includes three phases of setup and clustering, sending data and playing the multi-person game, and update and detecting the selfish and malicious nodes. The process of setup and clustering algorithm are run in the first phase. In the second phase, the nodes of each cluster cooperate with each other in order to execute an infinite repeated game while forwarding their own or neighbor nodes’ data packets. In the third phase, each node monitors the operation of its neighbor nodes for sending the data packets, and the process of cooperation is analyzed for determining the selfish or malicious nodes which forwarded the data packets with delay or even not sent them. The other nodes reduce the reputation of the nodes which does not cooperate with them, and they do not cooperate with the selfish and malicious nodes, as punishment. So, selfish and malicious nodes are stimulated to cooperate. The results of simulation suggest that the detection accuracy of the selfish and malicious nodes has been increased by an average of 12% compared with the existing methods, and the false-positive rate has been decreased by 8%.

Selection of Optimal Variant of Hybrid System under Conditions of Uncertainty

The aim of the study is to select an optimal variant of a hybrid system under conditions of uncertainty according to selected criteria. The problems of the study are the different options for building the hybrid system and choosing an adequate criterion for choosing the optimal variant. The study covers analysis of three variants of building up a hybrid system for supplying of autonomous electric load. The three variants are: introduction of an active user for equalizing the load schedule; introduction of additional generating source for covering the peak portion of the load schedule; covering the peak portion of the load by using an additional generating source and diesel generator. An optimal variant is selected under the conditions of uncertainty according to two criteria: minimum discounted expenses and loss of power. To this effect, the method of Mathematical hierarchical game theory analysis is applied. As a result of the study, the appropriate criteria for choosing an optimal variant for building a hybrid system are obtained. The results obtained allow to set a different degree of significance of the formulated basic criteria in the computational algorithm for decision making for the construction of the hybrid system.

Joint Spectrum Allocation and Pricing for Cognitive Multi-Homing Networks

In this paper, a spectrum pricing and allocation problem, based on hierarchical game theory framework, is studied for cognitive multi-homing networks. The spectrum pricing and allocation are subject to constraints in the required transmission rate for heterogeneous constant bit rate and variable bit rate services. A hierarchical game theory framework is designed based on a Stackelberg game. In the two-level game framework, primary network operators are leaders and determine the spectrum price, while cognitive mobile terminals (MTs) are followers and allocate the spectrum resource. Then, the spectrum allocation among secondary MTs is solved by a Bargaining game, and the spectrum price is set by a Bertrand game. To obtain the Nash equilibrium of hierarchical game theory framework, a joint spectrum pricing and allocation (JSPA) scheme is proposed in an iterative manner. Simulation results demonstrate that the proposed JSPA not only raises the payoff for primary network operators, but also improves the quality of service for secondary MTs.

Hierarchical Game Theory for System-Optimal Control: Applications of Reverse Stackelberg Games in Regulating Marketing Channels and Traffic Routing

Complex decision-making problems have two common features: 1) they involve agents (firms, drivers, countries) with interdependent payoffs, that is, the action of one agent affects the others' rewards, and 2) they are inherently dynamic, that is, the agents compete or cooperate repeatedly over time, and their actions have an impact on the evolution of the state of the system [1]-[3]. An example can be found in road-traffic networks, where a driver affects the other drivers' travel time by selecting a particular route and a particular speed profile. When too many drivers opt for a popular connection at the same time, congestion results [4], [5]. Fisheries provide another, similar example. Overfishing means fewer fish are available for others in the short run, and the long-term sustainability of the fishery is put at risk [6]. These situations illustrate how the lack of coordination between parties in a system may result in a highly suboptimal use of scarce resources. While it is in the parties' common interest that some players act in an individually suboptimal manner, for instance, by taking unpopular routes that are not the shortest in distance, there is no mechanism that guarantees the behavior of the other parties. As a result, all parties act selfishly and face the suboptimal result of a severe traffic jam or a shortage of fish. For an illustration of this dilemma, see The Wardrop Equilibrium Principles and the Braess Paradox.

On Systematic Computation of Optimal Nonlinear Solutions for the Reverse Stackelberg Game

In control of large-scale intelligent infrastructures, multilevel optimization can serve as a useful framework to deal with overall complex problems, especially in networks that already exhibit a natural hierarchy of decision makers with different objectives. In particular, solution methods from the hierarchical game theory can be adopted. Here, we focus on solving problems that belong to the specific class of reverse Stackelberg games. In this game, a follower player acts subsequent to the leader's revelation of her so-called leader function, which maps the leader decision space to the follower decision space. In general, the problem of finding a leader function such that the leader's objective function is optimized while taking into account a follower decision that is optimal for the follower, is difficult to solve. We provide a structured solution approach for the class of nonlinear leader functions and make a comparison with the evolutionary approaches proposed in the literature. In particular, a continuous multilevel optimization approach and a gridding approach are proposed to compute an optimal leader function based on basis functions. Also, leader functions derived by interpolation are discussed. All approaches are illustrated and compared in a worked example, in which the required computation times and deviation from the desired solution are considered.