Non-cooperative Game Research Articles

Measuring decentralized network efficiency: A pre-mortem Stackelberg game approach

In this paper, we present the ‘pre-mortem Stackelberg game approach’ as a non-cooperative game model that can serve as a viable alternative to the conventional decentralized network DEA model, which suffers from the infeasibility problem. We identified the circumstances that give rise to the issue and recommended the use of non-radial slacks as a remedy. The rationale behind this method is provided in relation to relevant game theories as a modeling justification. To validate the effectiveness of the proposed model, we conducted an empirical study on the performance evaluation of local agents of a Korean life insurance company. Our findings show that the proposed model not only provides an alternative efficiency measure for the follower but also enables an optimal adjustment of intermediate products, for which feasible solutions do not exist under the conventional decentralized network DEA model. Moreover, the proposed model delivers efficiency measures that are equivalent to those of the conventional model when feasible solutions do exist. The proposed model is expected to facilitate the use of non-cooperative game in network DEA, particularly when the VRS assumption is appropriate for performance evaluation.

Measuring the evolutionary game process among three functional space types at the county scale in Henan Province, China

Conflicts among various spatial planning policies have created a spatial game over land function and utilization due to the limitation of land resources. We quantitatively assess the evolutionary game process among three functional space types (agricultural production, urban–rural living, and blue–green ecological) using the concept of game theory during the period of 1980–2020 in Henan Province, China, as a case study. A research framework for assessing the spatial game process was established, and a measurement method based on spatial game type (SGT) and spatial game intensity (SGI) is proposed. The results demonstrate that the evolutionary game process among three functional space types exhibited significant spatiotemporal variation and spatial agglomeration. SGI increased from low to high values and then decreased again, and exhibited spatial autocorrelation. SGT supported classification into positive-sum and zero-sum games. The period of 1990–2000 had the largest SGI and the most counties with high-intensity zero-sum games. A highly urbanized urban center showed a high-intensity zero-sum game at the expense of agricultural production spaces. Balancing the areas devoted to various uses, enhancing spatial connectivity and improving functional mixing degree of land use may be effective ways to alleviate noncooperative games and spatial conflicts among these three functional space types.

A Game Analysis on International Emissions Trading under Climate Change

Carbon emissions and climate are intricately related. People's activities are growing as a result of advances in science and technology, which raises carbon dioxide emissions. As a result of these greenhouse gases, the atmosphere's ability to dissipate heat will decline, raising global temperatures and making climate change a more serious issue. To achieve sustainable development, people must begin to pay attention to these challenges and strike a balance between the environment and economic progress. This paper introduces the mechanism of emissions trading and the benefits of its operation. In order to discuss the possibility of enabling countries to use emissions trading, this paper uses a non-cooperative game theory model to analyze the choices made by developing and developed countries under the background of the Kyoto Protocol. Combined with the equilibrium obtained by the hypothesized model, some methods and reasons for improving the results are proposed. This paper concludes that both developed and developing countries are more inclined to use emissions trading to achieve emission reduction targets or obtain certain benefits.

Data-Driven games in computational mechanics

We resort to game theory in order to formulate Data-Driven methods for solid mechanics in which stress and strain players pursue different objectives. The objective of the stress player is to minimize the discrepancy to a material data set, whereas the objective of the strain player is to ensure the admissibility of the mechanical state, in the sense of compatibility and equilibrium. We show that, unlike the cooperative Data-Driven games proposed in the past, the new non-cooperative Data-Driven games identify an effective material law from the data and reduce to conventional displacement boundary-value problems, which facilitates their practical implementation. However, unlike supervised machine learning methods, the proposed non-cooperative Data-Driven games are unsupervised, ansatz–free and parameter–free. In particular, the effective material law is learned from the data directly, without recourse to regression to a parameterized class of functions such as neural networks. We present analysis that elucidates sufficient conditions for convergence of the Data-Driven solutions with respect to the data. We also present selected examples of implementation and application that demonstrate the range and versatility of the approach.

Research on energy sharing between distribution network and multiple systems based on the mixed game strategy and water-electric-gas integrated energy complementation

Introduction: It is significant for energy sharing to study the complementary utilization of multiple energy sources, such as water, electricity and gas, and the interaction among multiple stakeholders.Methods: We propose a research on energy sharing between distribution network and multiple systems based on the mixed game strategy and water-electric-gas integrated energy complementation. Firstly, this paper describes the relationship and functions of all stakeholders under the research framework, and establishes the mathematical model of each unit in the water-electric-gas complementary IES. Secondly, the internal roles are layered based on the relationship between stakeholders in the system. Then a non-cooperative game model for the distribution network operator and multiple subsystems is established according to the theory of Stackelberg game, and a cooperative game model for multiple subsystems is further established based on the theory of Nash bargaining. In the next step, the complexity of the problem is analyzed, followed by the description of the specific algorithm and process of solving the model.Results: Finally, the results of example analysis show that the model proposed in this paper not only balances the interests of stakeholders at the upper and lower layers of the system, but also allocates the interests of multiple subsystems at the lower layer.Discussion: Thus effectively improving the energy utilization of the system.

Service-Aware Resource Orchestration in Ultra-Dense LEO Satellite-Terrestrial Integrated 6G: A Service Function Chain Approach

With the rapid expansion of the scale of deployed low earth orbit (LEO) satellites, the ultra-dense LEO satellite-terrestrial integrated network (LTIN) is envisioned as a promising architecture in the sixth-generation (6G) system to implement seamless connectivity and high-speed data rate service. Especially for ultra-remote real-time services with long transmission distance and high delay requirements, the integrated network can guarantee its end-to-end service continuity. However, many challenges have been posed to the efficient resource orchestration for the service delivery, owing to the large scale, heterogeneity and high mobility of the integrated network. For each service, its data needs to go through a series of on-board processing, before being downloaded to the terrestrial network for further applications. To this end, service function chain (SFC), an ordered concatenation of network functions (NFs), is introduced to support service provision. By allocating the constituent NFs over the LTIN, we propose an efficient multiple service delivery scheme to minimize the overall delivery completion latency, while taking into account resource sharing and competition among multiple SFCs. First, we formulate the multiple SFC embedding problem as a noncooperative game that is further proved as the weighted potential game with at least one Nash equilibrium (NE). With the help of the proposed global coordination mechanism, we design two algorithms to obtain the NE. One is the best response (BR) algorithm with faster convergence, while the other is adaptive play (AP) algorithm with more capacity for best solutions. Then, the stochastic learning (SL) algorithm is proposed to adapt to network dynamics and reduce global information exchange. Finally, extensive simulations validate the convergence and effectiveness of the proposed algorithms.

Byzantine Agents’ Detection in Distributed Nash Equilibrium Seeking Algorithms Using an Adaptive Event-Triggered Scheme

In this article, a resilient, adaptive event-triggered distributed Nash equilibrium seeking algorithm is investigated for a class of multimicrogrid systems. Since the strategy of each microgrid affects others’ costs through total generation cost, such interaction among microgrids is modeled as a noncooperative game. To reduce unnecessary signal transmission among the aggregators, an adaptive algorithm, where threshold parameters are adjusted based on the behavior of the estimated signals in the last two iterations, is proposed. It is observed that when false data is injected into an agent, its estimated signals begin to diverge from the equilibrium point, and as a result, the threshold value becomes increasing. Furthermore, the misbehaving agents are identified and isolated using a reputation-based mechanism and are allowed to rejoin the network when they behave normally again. To deal with arbitrary behavior of users, receding horizon scheme of predictive control is used. Finally, a set of simulation results is presented to evaluate the effectiveness of the suggested algorithm.

Behavioral Decision-Making Approach for Vehicle Platoon Control: Two Noncooperative Game Models

Game theory has been extensively studied in recent years for its potential benefits on solving interactions between autonomous vehicles in platoon control. In this paper, we propose two behavioral decision-making approach based on non-cooperative game theory with both the complete information and incomplete information for cooperative vehicle platoon systems. The non-cooperative game payoff function takes the platooning performances of economy, comfort, safety, and further achieving self-driving functions into consideration. For the driving situations with incomplete information, a belief pool is constructed to represent the action probability for different behavioral types of vehicles, which will be updated by combining the driving intention identification with a Bayesian probability formula. With this, the stable strategies can be obtained for the two potentially conflicting parties, ensuring that neither of them has a motivation to change their driving behavior. Finally, the simulation results demonstrate that with the proposed behavioral decision-making approaches with complete information, the cooperative platoon performance can be markedly improved; with incomplete information, the platoon can determine the behavioral types of conflicting vehicles and complete collaborative decision-making approaches for solving not only the simple road-rights conflicting problems, but also for the extended vehicle platoon driving scenarios in a more complex transportation system.

A Multi-Period Charging Service Pricing Game for Public Charging Network Operators Considering the Dynamics of Coupled Traffic-Power Systems

The proliferation of electric vehicles (EVs) couples the operations of traffic systems and power systems, necessitating the interdependent traffic-power modeling to optimize the on-road EV charging decisions. In this paper, the multi-period charging service pricing interactions between multiple charging network operators (CNOs) are discussed considering the dynamics of traffic-power systems. A multi-period user equilibrium model considering mixed vehicle types is formulated to describe the possible vehicle trip transitions between different periods in urban transportation network. For the power distribution network, a convexified multi-period AC optimal power flow model is adopted for local electricity market clearing. With the dynamics of traffic-power systems, the pricing interaction between multiple CNOs is a non-cooperative game. We analyze the existence of Nash Equilibrium with fixed-point theory, and propose an iterative method based on the best response strategy to find <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -Nash Equilibrium. Numerical studies based on an interdependent power-traffic system consisting of two 18-node power distribution networks and one revised Nguyen-Dupuis transportation network demonstrate that with the proposed CNOs’ charging pricing strategy, the CNOs’ service profits can increase by 1%-3% while the PDNs’ operation costs decrease about 1%-2% for the interdependent traffic-power system.

Predefined-Time Distributed Nash Equilibrium Seeking for Noncooperative Games With Event-Triggered Communication

In this paper, we investigate a predefined-time distributed Nash equilibrium seeking problem for a class of noncooperative games under an event-triggered scenario. To achieve fast convergence while reducing the communication and computation costs, a novel distributed Nash equilibrium seeking approach is proposed by applying the gradient play, a consensus-based estimator, and a time base generator (TBG). Different from existing works on Nash equilibrium computation under a bounded convergence time, the design of distributed algorithm in this paper is based on a newly developed TBG. The new TBG is more efficient and convenient than the traditional TBG. By virtue of an adaptive event-triggered rule, the distributed estimators are designed to estimate other players’ actions over strongly connected directed graphs. Moreover, the predefined-time convergence analysis of the players’ actions to the Nash equilibrium is given based on the Lyapunov stability method. Finally, simulation studies are provided to demonstrate the effectiveness of the constructed TBG and the advantages of the derived strategy.

Decentralized, Privacy-Preserving Routing of Cellular-Connected Unmanned Aerial Vehicles for Joint Goods Delivery and Sensing

Unmanned aerial vehicles (UAVs) have been extensively applied to goods delivery and in-situ sensing. It becomes increasingly probable that multiple UAVs are delivering goods and carrying out sensing tasks at the same time. The destinations of the UAVs are usually required to jointly design their trajectories and sensing selections, leading to privacy concerns for the UAVs. This paper presents a new game-theoretic routing framework for joint goods delivery and sensing of multiple cellular-connected UAVs, where the UAVs minimize their energy consumption and connectivity outage, maximize their sensing reward, and ensure timely goods delivery and trajectory privacy by optimizing their trajectories and sensing task selections in a decentralized manner. The key idea is that we unify routing and sensing in a single task selection process, which is further transformed into routing on a task-time graph. Another important aspect is that we design a non-cooperative potential game for the routing on the task-time graph. A distributed strategy is developed, where each UAV only reports its sensing task selections and withholds its destination information and its best response produced by the Bellman-Ford algorithm. By this means, the destination and trajectory privacy of the UAVs are protected. Simulations show that the new game-theoretic approach can ensure timely delivery and achieve close-to-optimal solutions with significantly lower complexity compared to a centralized brute-force approach.

Games in a foreign exchange market and solutions

Abstract Exchange rate and its related risk management are too important for main participants in foreign exchange markets. There are many approaches developed in the literature for studying risk management say arbitrage detection, say finding replication portfolio. However, in the current paper, arbitrage opportunities are studied using the game theory perspective. This paper proposes different types of games played in a specified foreign exchange market in the presence of three exchange rates. Proposed games are exchange rate games in two cases of no arbitrage and existence of arbitrage, optimal stopping game, the arbitrage game, threshold strategies used in global game and Non-cooperative exchange rate game. Most of cases, the bang-bang rule of optimal control is used for finding the Nash equilibriums (NE). However, simulated and stochastic approximation (SA) solutions are also given. Most highlights of the current paper are: (I) considering two types of arbitrage opportunities, simultaneously, (II) translating arbitrage detection as game theory concepts, (III) solving the problem using techniques of optimal control theory. Finally concluding remarks are proposed.

Identifying and assessing risk of cascading failure sequence in AC/DC hybrid power grid based on non-cooperative game theory

Identifying and assessing risk of cascading failure sequence in AC/DC hybrid power grid based on non-cooperative game theory

System Dynamics-Based Game Theoretical Analysis for Watershed Eco-Compensation Design: A Case Study in Tuojiang River, Sichuan Province, China

Eco-compensation is an important policy tool to trade off economic development and environmental protection in a watershed. This study introduced the gross ecosystem product (GEP) accounting system to identify the eco-compensation provider (ECP) and eco-compensation receiver (ECR) of a river basin. Then, a cooperative game model and a non-cooperative game model between the ECP and the ECR were established, in which system dynamics was incorporated into the game theoretical analysis to aid selection of the optimal compensation scheme. The study further demonstrated the model applications by taking the Tuojiang River Basin as a case. The results showed that the accounted GEP increased from CNY 32.2 billion in 2018 to CNY 35.5 billion in 2020, with a growth rate of 10.2%. Deyang City, as an ECP, had a cumulative difference of CNY 11.759 billion between its accounted GEP and actual GEP output over the three years. Neijiang City, Zigong City, and Luzhou City were taken as the ECR, receiving the GEP revenues as CNY 11.289 billion, 7.661 billion, and 1.497 billion, respectively. Chengdu City changed from the ECP to the ECR and ultimately to the ECP. However, Ziyang City and Meishan City changed from the ECP to the ECR. The eco-compensations increased to varying degrees during 2018–2020 in both game scenarios, with ECP payments and ECR revenues increasing by 16.5% and 4.6% in the non-cooperative game and by 5.0% and 50.8% in the cooperative game. Particularly, the eco-compensation obtained by the cooperative game had better environmental and economic performance, as there was a total of CNY 7.049 billion being saved. However, there was no savings of compensation by the non-cooperative game. It is expected that the results may provide insight into the design of the eco-compensation standard for a river basin.

Examining B2B channel decision-making within differential quality-level zone: a supply chain design using a non-cooperative strategic game theoretic approach (“Stackelberg Supply Chain for B2B”)

Purpose The consumers want to purchase the target products in the right place, whereas the manufacturers want to allocate their possible products to optimal distribution channels. The manufacturer must know how to handle itself in this business. The study aims to examine the B2B channel decision-making with different product qualities in a non-cooperative supply chain. Design/methodology/approach The authors develop a B2B Manufacturer-Stackelberg game as an analytical framework, combining asymmetric preference of purchase channels choice by the consumers, a continuous quality setting of the manufacturer and differential channel structure to study the manufacturer’s product strategy and channel optimisation. By horizontal comparisons across four channel structures, product variety can be classified into the differential quality-level zone through exogenous quality intervention, and the preference of manufacturers in each quality-level zone within the structures can be ranked. Findings Theoretically and practically, the hybrid-channel structure should be completely neglected when the direct channel dominates the retail channel. In contrast, dual-channel structures dominate single channels irrespective of the channel power, and channel preferences between high-quality and low-quality zones are stable, whereas the preference in medium-quality zone is unstable. In addition, the supply chain system cannot achieve global Pareto improvement without any additional coordination mechanism between the manufacturer and the retailer. Originality/value The extended results by numerical examples suggest that the bigger the area of the medium-quality zone, the more significant the product variety of the manufacturer.

Participation of strategic district heating networks in electricity markets: An arbitrage mechanism and its equilibrium analysis

Combined electricity-heat operation improves social welfare compared with the traditional heat-driven operation. However, it is left open how to achieve such an improvement in the current electricity market. Therefore, an arbitrage mechanism enabling strategic district heating networks (DHNs) to participate in electricity markets is designed, which settles the payment concerning the power deviation and the locational marginal price (LMP). Individual interests of both energy sectors are addressed via a bi-level model, while analytical results of the arbitrage equilibrium are proved theoretically. Although the mechanism intends to allow DHNs to profit selfishly from utilizing energy storage, it is strikingly guaranteed that electric power networks also benefit from this. A Pareto improvement is thus achieved by the mechanism with enhanced social welfare efficiency at the arbitrage equilibrium. The proposed mechanism is numerically compared with the traditional heat-driven operation, combined operation and existing cooperative and non-cooperative game approaches, while the merits are verified in two integrated electricity and heat systems with different scales.

Contributing with private bundles to public goods

We extend to multiple private commodities the seminal model by Bergstrom et al. (J Public Econ 29:25–49, 1986) on the private provision of public goods. Considering the relative value of the aggregate donations, we define a notion of equilibrium and show its existence. We analyze the effects of resource redistributions on the equilibrium outcome, identifying conditions that guarantee neutrality. We study some further properties of the contribution equilibrium, and provide a strategic market game approach, defining a sequence of non-cooperative games whose equilibria converge to an equilibrium of the economy.

On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals

This paper considers a callback single-server system with an orbit and a First-Come First-Served (FCFS) service discipline. Customers (users, clients) that encounter a busy server are sent into orbit and then have the option to retry service after an exponential period of time. In addition, each customer entering the system uses a strategy and must independently decide when to arrive in the system within a fixed admission period of time so that the expected sojourn time is minimal. We interpret the arrival process as a Nash equilibrium solution of a noncooperative game when the arrival intensity is completely described by an unknown distribution function, and then we propose a way to find an equilibrium for the case when the client’s waiting time for service is obviously limited. The analytical solution for the equilibrium is illustrated numerically for two-person and three-person games.

Robust optimal energy management with dynamic price response: A non-cooperative multi-community aggregative game perspective

Energy management system gradually becomes an effective means in smart grid for paving the way to low carbon economy. However, information privacy, a large population of users, and the uncertainties of renewable energy sources and consumers’ behaviors have led to significant challenges for energy management system operation in terms of security and robustness. To conquer such difficulties, a bilevel energy management scheme for the day-ahead optimal scheduling of multi-community system combined with distributed energy sources is first proposed. Meanwhile, uncertainties induced by renewable energy sources generation and load consumption are handled through adjustable robust optimization. Secondly, a non-cooperative multi-community aggregative game is formulated to describe the interaction of numerous residential users which are coupled through the dynamic electricity price. Then, to seek the ɛ-Nash Equilibrium of the proposed game, an improved decentralized iterative algorithm based on Mean-Field control and consensus is presented which is benchmarked with centralized algorithm and a decentralized optimization method based on quadratic programming. Since each player in the proposed algorithm does not need to exchange information directly with other players, the information privacy is fully preserved. Also, the convergence of the proposed algorithm is provided. Case studies of a five-community system are conducted and the comparison results show that our proposed approach has better performance in terms of computational time and electricity cost.

How to Choose the Refueling of New Energy Vehicles under Swapping vs. Charging Mode: From the Consumers’ Perspective

Battery charging mode (CM) is a prevalent method of trans-shipping power to new energy vehicles (NEVs). Unfortunately, due to the limited capacity of batteries, typical NEVs can only travel for approximately 350 miles on a single charge and require hours to be recharged. Battery swapping mode (SM), as a novel alternative, can offer an ideal solution by exchanging depleted batteries for recharged ones at swapping stations in the middle of long trips, inevitably influencing potential consumers’ purchase behaviors. To examine the impact of SM and CM on consumers’ purchase intention, this paper examines a duopolistic market consisting of two new energy vehicle manufacturers (i.e., a NEV-SM manufacturer and a NEV-CM manufacturer), who adopt SM and CM to service consumers, respectively. Considering SM is characterized by low initial investment and ease of use for consumers, NEV-CM manufacturers capitalize on extended battery warranty services in response to rivals’ utilization of SM. Thereby, non-cooperative game models are formulated, in which government subsidies are taken into account. The optimal production decision for both the NEV-SM manufacturer and the NEV-CM manufacturer are analyzed under three scenarios: without extended warranty service, with extended warranty service, and with extended warranty service and subsidy. The results show that the two manufacturers’ market dominance relies on the ratio of the swapping station’s convenience to the extended warranty service and the valuation incremental rate. Additionally, we also find that the government subsidy can dramatically improve the NEV-SM manufacturer’s performance at the initial stage, but if the subsidy is insufficient in size at the subsequent stage, this will lead to policy failure and inefficiency in propelling the diffusion of swapping mode.