Nash Equilibrium Approach Research Articles

A fully decentralized demand response and prosumer peer-to-peer trading for secure and efficient energy management of community microgrid

A novel demand response program combines the advantages of price-based demand response under the time-of-use pricing and the incentive-driven demand reduction bidding strategy to manage energy demand, and maximize the net present value of both participants and the community-microgrid. It also facilitates the seller prosumers to optimally sell the surplus power in a fully decentralized peer-to-peer power trading manner. A novel mathematical demand reduction bidding model is proposed to minimize the community-microgrid cost by the prioritized selection of participants for demand reduction. This study proposed a novel decentralized three non-cooperative dynamic games strategy, incorporating Nash equilibrium approaches to achieve the optimum schedules of appliance, buying, and power trading agents to maximize the net present value of both prosumers and the community-microgrid while preserving participants’ privacy and control network congestion. The priority-based optimal selection of seller and buyer prosumers according to their utility and pricing function in the peer-to-peer power trading scheme is accomplished using a proposed color-based segmented decentralized bilateral power trading to maximize the net present value. The numerical and simulation results demonstrate the feasibility and effectiveness of the proposed strategies and increase the net present value of prosumers up to 42.4 % and community-microgrid up to 34.79 %.

A peer‐to‐peer joint energy and reserve market considering renewable generation uncertainty: A generalized Nash equilibrium approach

AbstractPeer‐to‐peer (P2P) energy trading enhances distribution network resilience by reducing energy demand from central power plants and enabling distributed energy resources to support critical loads after extreme events. However, adequate reserves from main grids are still required to ensure real‐time energy balance in distribution networks due to the uncertainty in renewable generation. This paper introduces a novel two‐stage joint energy and reserve market for prosumers, wherein local flexible resources are fully utilized to manage renewable generation uncertainty. In contrast to cooperative optimization methods, the interactions between prosumers are modelled as a generalized Nash game (GNG), considering that prosumers are self‐interested and should follow distribution network constraints. Then, linear decision rules are employed to ensure a feasible market equilibrium and develop a privacy‐preserving algorithm to guide prosumers toward the market equilibrium with a proven convergence. Finally, the numerical study on a modified IEEE 33‐power system demonstrates that the designed market effectively manages renewable generation uncertainty, and that the algorithm converges to the market equilibrium.

Impact of information disclosure on global supply chain greenwashing: Is more information transparency always better?

As supply chains become more globalized, retailers outsource the manufacturing of their products to foreign suppliers. Supply chain greenwashing is an immoral practice employed by retailers whereby they selectively disclose information regarding upstream suppliers after exaggerating the environmental benefits of their fake green products to consumers. Using a perfect Bayesian Nash equilibrium approach, this paper examines the conditions under which a retailer who engages in greenwashing will disclose the information of an unethical foreign supplier under pressure from enhanced scrutiny by a non-governmental organization (NGO). The results show that when the increase in the NGO’s utility from targeting the unrevealed upstream supplier is sufficiently large, the greenwashing retailer prefers to disclose the unethical foreign supplier’s information, whereas when the increased utility is low, the greenwashing retailer prefers to hide the unethical foreign supplier. Different from common belief that increased information transparency may be beneficial, we find that it does not necessarily lead to reduced social damage and that it depends on the unethical foreign supplier’s capability for compliance. In particular, when the unethical foreign supplier has a low capacity for compliance, the supply chain’s transparency advantage will lead to more fake green goods being sold, thus causing greater social damage.

A robust multiple Unmanned Aerial Vehicles 3D path planning strategy via improved particle swarm optimization

Path planning algorithms for Unmanned Aerial Vehicles (UAVs) are essential in various domains, such as search and rescue operations, agriculture, and delivery services. Nonetheless, finding optimal flight paths in complex environments with obstacles remains challenging. This paper proposes a novel path planning algorithm that uses a Nash equilibrium approach based on game theory to strike a balance between the exploitation and exploration capabilities of UAVs. The algorithm is designed in a simulated flight environment with obstacles, utilizing the self-awareness and group awareness coefficients from particle swarm optimization(PSO) as participants in the game theory model. The proposed path planning algorithm significantly improves the navigation of multiple UAVs in complex scenarios with obstacles by achieving a balance between their exploitation and exploration capabilities. Simulation experiments demonstrate that the proposed method surpasses traditional approaches, exhibiting an average improvement of 32.57%, 32.17%, and 29.33% in the algorithm convergence time, average flight distance, and average flight time, respectively. The significance of this research lies in its contribution to advancing UAV path planning algorithms. By integrating game theory and PSO, the proposed method optimizes the exploration and exploitation capabilities of UAVs, leading to improved navigation and resource utilization.

Optimal Choice between Defined Contribution and Cash Balance Pension Schemes: Balancing Interests of Employers and Workers

In the context of pension plans, the employer and the worker have distinct interests and face different risks. The worker seeks higher retirement benefits, while the employer aims to minimize the cost of fulfilling his obligations. To address these diverse needs, the defined contribution plan managed with participating life insurance (DC-PL) and the cash balance plan managed with unit-linked insurance (CB-UL) serve as suitable choices. The multi-criteria analysis is conducted using the cumulative prospect theory model to measure the utility of the parties involved toward a mixed product combining these two pension plans. By assigning weights to risk measures and maximizing utilities, the paper employs both additive utility and Nash equilibrium approaches. The results reveal that the CB-UL plan aligns with employers’ interests, offering potential financial gains, while the DC-PL plan attracts workers due to its profit-sharing aspect. Significantly, when equal importance is given to both parties, the CB-UL plan emerges as the prevailing choice. This study contributes to the understanding of pension plan design and decision-making dynamics between employers and workers, providing valuable insights for achieving a balance between retirement benefits and cost management.

A study on behavior of producers, retailers and speculators in futures and day-ahead markets: A Nash equilibrium model

Uncertainties in different parameters such as the output power of renewable energy sources, available capacity of generators, or the condition of grid lines in the future, face market players with financial risks in the power system. Futures contracts are used in parallel with the day-ahead electricity markets to protect market players against financial risks of undesirable price fluctuations. Supplying a demand by both futures and day-ahead markets leads to mutual impacts between these two markets. In this paper, a Nash equilibrium approach is introduced to model the interactions between the futures and day-ahead markets. The proposed model includes producers, retailers, and speculators as market players, the uncertainty in the output power of wind farms (WFs), the possibility of the financial settlement of contracts, market players' risk preferences, and transmission system limitations. Using this approach, the optimal strategy of market players in futures and day-ahead markets, the effects of transmission system congestion on the Nash equilibrium of the system, and the role of the financial settlement of contracts in dealing with the uncertainty of WFs' output power and transmission lines capacity are discussed. Eventually, the behavior of speculators and their impacts on the gaming of other market players are evaluated. Simulation results highlight the role of the financial delivery feature in the effective utilization of futures contracts and the behavior of market players.

Nash Equilibrium and Stackelberg Approach for Traffic Flow Optimization in Road Transportation Networks—A Case Study of Warsaw

The article discusses the issue of modelling traffic flows and the transport network. Faced with an increase in the number of vehicles in road networks, the problem of congestion and the need to optimise traffic and adapt the transport infrastructure to changing demand are growing, especially in large cities. With this in mind, the authors of this publication developed a model of the road network in the north-eastern part of the Warsaw agglomeration based on the proposed algorithm. Two methods were used to optimise the distribution of traffic flows: the Nash equilibrium and the Stackelberg approach. The Nash equilibrium assumes the aim of achieving equal average times on all roads for each origin–destination (O-D) pair. This describes the state pursued by a decentralised system guided by the individual benefits of the traffic users. On the contrary, the Stackelberg approach aims to achieve optimal travel times for the entire system. The study was carried out for three scenarios that differed in the assumed traffic demand on the road network. The basic scenario assumed the average hourly traffic demand during the morning peak hour based on traffic measurements. On the other hand, the two alternative scenarios were developed as a 10% variation in traffic volumes from the baseline scenario. On the basis of the results, it was concluded that an increase in traffic volumes for all O-D pairs could result in a decrease in traffic volumes on some links of the road network. This means that the transport network is a complex system and any change in parameters can cause significant and difficult to predict changes. Therefore, the proposed approach is useful in terms of traffic forecasting for road networks under conditions of changing traffic flow volumes. Additionally, the total travel time for the entire system differed for each scenario by a percentage difference of 0.67–1.07% between the optimal solution according to the Nash equilibrium and the Stackelberg approach.

Nonlinear Distributed Model Predictive Control for multi-zone building energy systems

This paper presents a distributed Model Predictive Control (MPC) approach for multi-zone building energy systems based on nonlinear Modelica controller models. The method considers both thermal and hydraulic coupling among different building zones. The iterative and parallel distributed optimization approach builds upon an uncooperative approach for thermal coupling using the Nash equilibrium approach and a cooperative approach for the hydraulic coupling using the Alternating Direction Method of Multipliers (ADMM). Apart from thermal coupling through walls, the modeling takes thermal coupling through doors into account using a data-driven approach, which calculates the inter-zone air exchanges based on temperature differences between door-coupled zones. The hydraulic coupling enables consideration of interactions between the zones introduced by a shared, central Heating, Ventilation and Air Conditioning (HVAC) system. The distributed MPC framework is structured in an easy-scalable, plug-and-play composition, where local systems are automatically assigned to the global coordination scheme. The distributed MPC method is applied to a simulative nonlinear case study, consisting of a six-room-building Modelica model considering both thermal and hydraulic interactions. The benefits of the proposed approach are demonstrated and compared against centralized and decentralized control concepts in terms of energy consumption, discomfort and computation time.

A Nash Equilibrium Approach to the Brazilian Seasonalization of Energy Certificates

This paper presents a Nash equilibrium approach to model a non-cooperative game that takes place among Brazilian hydro-generating companies in the annual process called “seasonalization”. We have “remade” the seasonalizations that occurred in the period of 2013–2020 by using our model and comparing the financial outcomes with the current ones that resulted from the seasonalizations the generators made each year, with financial improvements in almost every year. By using the Nash equilibrium approach, it is possible to achieve optimal decisions concerning the seasonalization process that were not evident by using traditional methods. This approach is useful for companies willing to enhance their income and to improve their risk management by making better choices in seasonalization.

Modeling energy depletion in rat livers using Nash equilibrium metabolic pathway analysis

The current gold standard of Static Cold Storage (SCS), which is static cold storage on ice (about + 4 °C) in a specialized media such as the University of Wisconsin solution (UW), limits storage to few hours for vascular and metabolically active tissues such as the liver and the heart. The liver is arguably the pinnacle of metabolism in human body and therefore metabolic pathway analysis immediately becomes very relevant. In this article, a Nash Equilibrium (NE) approach, which is a first principles approach, is used to model and simulate the static cold storage and warm ischemia of a proposed model of liver cells. Simulations of energy depletion in the liver in static cold storage measured by ATP content and energy charge are presented along with comparisons to experimental data. In addition, conversion of Nash Equilibrium iterations to time are described along with an uncertainty analysis for the parameters in the model. Results in this work show that the Nash Equilibrium approach provides a good match to experimental data for energy depletion and that the uncertainty in model parameters is very small with percent variances less than 0.1%.

Lane-changing decision modelling in congested traffic with a game theory-based decomposition algorithm

This study presents a cellular lane-changing model where the traffic lanes are discretized into cells and formulates the lane-changing process as a multi-player non-zero-sum non-cooperative game in a connected environment where the real-time surrounding traffic data is shared. In a congested traffic scenario where a large quantity of mandatory lane-changing maneuvers are required simultaneously, the size of the game is extended dynamically (i.e., 2–5 players in this case, and it can be extended more if necessary) based on the traffic situation. Discretionary lane-changing maneuvers are also considered in the decision-making process to maximize the use of the capacity of each traffic lane, i.e., distributing the vehicles to each traffic lane as uniform as possible. Moreover, the competing vehicle on the target lane has more flexible actions (i.e., changing to other lanes) except for accelerating and decelerating actions. Thus, its temporary benefit is sometimes sacrificed by taking these actions to pursue the global benefit so that other vehicles could complete mandatory lane-changing maneuvers. It is a known fact that the space complexity expands exponentially as the game size increases, so a novel decomposition algorithm based on game theory is proposed to reduce the complexity and improve computational efficiency. Finally, a rule-based approach, a classic Nash equilibrium approach and the proposed decomposition algorithm are compared by the critical indicators such as the number of lane-changing vehicles, the maximum incoming queues during the process, the mean of computational time per iteration, etc. The performance shows no significant difference in the efficacy of lane-changing maneuvers among these approaches under the uncongested traffic condition. At the same time, the decomposition algorithm is more efficient in computing time than the classic Nash equilibrium approach. As the traffic gets congested, the game theory-based approaches prove more effective in lane-changing behaviours than the rule-based approach. Meanwhile, the decomposition algorithm outperforms the classic Nash equilibrium approach more significantly in terms of computational time.

Parametrized Inexact-ADMM based coordination games: A normalized Nash equilibrium approach

Generalized Nash equilibrium problems are single-shot Nash equilibrium problems, whereby the decisions of all agents are coupled through a shared constraint. Such games are generally challenging to solve as they might give rise to a very large number of solutions. In this context, spanning many equilibria can be interesting to provide meaningful interpretations. In the literature, to compute equilibria, equilibrium problems are classically reformulated as optimization problems, potential games, relaxed and extended games. Applications of these reformulations to an economic dispatch problem under perfect and imperfect competition are provided. Unfortunately, these approaches only enable to describe a very limited part of the equilibrium set. To fill that gap, relying on normalized Nash equilibrium as solution concept, we provide a parametrized decomposition algorithm inspired by the Inexact-ADMM to span many more equilibrium points. Complexifying the setting, we consider an information structure in which the agents can withhold some local information from sensitive data, resulting in private coupling constraints. The convergence of the algorithm and deviations in the players’ strategies at equilibrium are formally analyzed. In addition, the algorithm can be used to coordinate the agents on one specific equilibrium with desirable properties at the system level. The coordination game is formulated as a principal-agent problem, and a procedure is detailed to compute the equilibrium that minimizes a secondary cost function capturing system-level properties. Finally, the Inexact-ADMM is applied to a cellular resource allocation problem, exhibiting better convergence rate than vanilla ADMM, and to compute equilibria that achieve both system-level efficiency and maximum fairness.

Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.

Generalized Nash Equilibrium approach for radio resource sharing and power allocation in vehicular networks

The enabling technology of vehicular networks for Intelligent Transportation Systems (ITS), smart cities and autonomous driving, offers promising on-board services such as road-safety, easy navigation, comfort driving and infotainment. These services can co-exist simultaneously in the system. One challenging issue is to provide the different quality of service (QoS) requirements adequate to each service. This may not be an easy task because of the constrained factors characterizing these networks (e.g., growing number of connected vehicular devices, wireless communications, etc.). In this paper, we investigate the radio resources allocation problem to match different QoS requirements in terms of data rate whilst reducing the interference ratio. We first proposed a radio allocation model that aims to maximize the data rate and minimize the transmission power for all users. However, since not all vehicles use services that require high data rates, it will be more efficient to consider different required data rate for each user. Hence, we develop an efficient model for transmission power allocation that aims to reduce the interference ratio while providing the data rate required by each user. The proposed model is based on Generalized Nash Equilibrium (GNE) game where the users compete to acquire the radio resources. We proposed also two water-filling algorithms to solve the spectrum allocation game during Vehicle-to-Vehicle (V2V) communication over multiple channels. The extensive simulations have shown that our model can satisfy the users regarding different.

Feature selection schema based on game theory and biology migration algorithm for regression problems

Many real-world datasets nowadays are of regression type, while only a few dimensionality reduction methods have been developed for regression problems. On the other hand, most existing regression methods are based on the computation of the covariance matrix, rendering them inefficient in the reduction process. Therefore, a BMA-based multi-objective feature selection method, GBMA, is introduced by incorporating the Nash equilibrium approach. GBMA is intended to maximize model accuracy and minimize the number of features through a less complex procedure. The proposed method is composed of four steps. The first step involves defining three players, each of which is trying to improve its objective function (i.e., model error, number of features, and precision adjustment). The second step includes clustering features based on the correlation therebetween and detecting the most appropriate ordering of features to enhance cluster efficiency. The third step comprises extracting a new feature from each cluster based on various weighting methods (i.e., moderate, strict, and hybrid). Finally, the fourth step encompasses updating players based on stochastic search operators. The proposed GBMA strategy explores the search space and finds optimal solutions in an acceptable amount of time without examining every possible solution. The experimental results and statistical tests based on ten well-known datasets from the UCI repository proved the high performance of GBMA in selecting features for solving regression problems.

Mean-variance dynamic optimality for DC pension schemes

In this paper we deal with the mean-variance portfolio selection for a defined contribution (DC) pension fund. Since this problem is time-inconsistent, a number of papers have proposed to tackle it through either a Nash equilibrium approach or a precommitment strategy. Here, we adopt the dynamically optimal approach introduced by Pedersen and Peskir (Math Financ Econ 11:137–160, 2017), and we compare the dynamically optimal strategy with the precommitment one. While it is well known that the precommitment strategy is the solution to a target-based problem, we show that the same holds for the dynamically optimal strategy. In particular, the precommitment strategy has a constant target, while the dynamically optimal strategy has a time-varying target whose expectation coincides with the constant target of the previous case. We also show that the expected wealth is the same under the two approaches. Numerical applications show that (i) the median of the risky asset’s share is lower for the precommitment than the dynamically optimal strategy; (ii) the amount of money invested in the precommitment risky portfolio is highly more volatile than in the dynamically optimal case; (iii) the variance of wealth is lower with the precommitment strategy than with the dynamically optimal one; (iv) under scenarios of extreme market returns (either good or bad), the dynamically optimal strategy allows a more effective reaction because of the continuous adjustment of the final target.

A Generalized Nash Equilibrium Approach for Autonomous Energy Management of Residential Energy Hubs

The development of the cutting-edge technologies in cogeneration and trigeneration has led to a rapid transition toward integrated energy systems and the mushrooming of energy hubs, calling for effective energy management schemes. This paper proposes a distributed algorithm for autonomous energy management (AEM) of a cluster of residential energy hubs. Given the interactive behaviors of energy purchasing at the supply side, we treat each hub as a self-interested agent, and formulate the AEM problem of these hubs as a monotone generalized Nash game (MON-GNG). On one hand, there are global coupling constraints representing the supply limits of the input energy systems, which are imposed by the limited capacities of electrical feeders and natural gas pipelines, thus making it a GNG. On the other hand, the cost function of each hub is merely convex in its actions considering the input-to-output energy transformation inside and the impacts of the energy storage devices, which leads to an MON game. The existence of the generalized Nash equilibria (GNEs) of this MON-GNG can be theoretically guaranteed. Then, by reformulating the MON-GNG as a variational inequality problem with special decomposition structure, an efficient and single-loop distributed algorithm is then proposed for computing a GNE with clear economic interpretation based on an improved Tikhonov regularization technique. Principles of parameter selection that will guarantee convergence are suggested. Numeric simulations validate the convergence performance and effectiveness of the proposed algorithm.

An Energy Sharing Game With Generalized Demand Bidding: Model and Properties

This paper proposes a novel energy sharing mechanism for prosumers who can produce and consume. Different from most existing works, the role of individual prosumer as a seller or buyer in our model is endogenously determined. Several desirable properties of the proposed mechanism are proved based on a generalized game-theoretic model. We show that the Nash equilibrium exists and is the unique solution of an equivalent convex optimization problem. The sharing price at the Nash equilibrium equals to the average marginal disutility of all prosumers. We also prove that every prosumer has the incentive to participate in the sharing market, and prosumers' total cost decreases with increasing absolute value of price sensitivity. Furthermore, the Nash equilibrium approaches the social optimal as the number of prosumers grows, and competition can improve social welfare.

Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy

This article is concerned with a multi-item inventory model for deteriorating items. The model is formed on the basis of a two-level supply chain policy, i.e., based on manufacturer's and retailer's perspective. The deterioration rate is considered as constant. The demand factor of any items suffer from a large amount of stock level; so, we consider stock-dependent demand function. The demand of any item is also dependent on its selling price; thus, a price-dependent demand function is introduced here. The retailer adopts the trade-credit policy for his customers in order to promote market competitiveness. He can earn revenue and interest after the customer pays the amount of purchasing cost to the retailer until the end of the trade-credit period, offered by the supplier. Shortages are allowed in the retailer's model as it is a very realistic item, too. A price discount on backordered commodities is offered for those customers who are willing to backorder their demand. Thereafter, we present an easy analytical solution procedure to find the total profit for both manufacturer and retailer. We also use the classical game theory and Nash equilibrium approach to find an optimal solution of the joint profit. The results are discussed with several numerical examples to illustrate our model and to provide some managerial insights related to the model. Furthermore, a parametric sensitivity analysis of the optimal solutions is provided and a concavity figure of our profit function is supplied to stabilize our model. The paper ends with a conclusion and an outlook to future research projects.

Optimizing pricing and ordering strategies in a three-level supply chain under return policy

This paper develops an economic production quantity model in a three-echelon supply chain composing of a supplier, a manufacturer and a wholesaler under two scenarios. As the first scenario, we consider a return contract between the outside supplier and the supplier and also between the manufacturer and the wholesaler, but in the second one, the return policy between the manufacturer and the wholesaler is not applied. Here, it is assumed that shortage is permitted and demand is price-sensitive. The principal goal of the research is to maximize the total profit of the chain by optimizing the order quantity of the supplier and the selling prices of the manufacturer and the wholesaler. Nash-equilibrium approach is considered between the chain members. In the end, a numerical example is presented to clarify the applicability of the introduced model and compare the profit of the chain under two scenarios.