Non-cooperative Game Research Articles

Weight Restriction Approach in a Two-stage Network Structure: A DEA-based Approach

The standard data envelopment analysis model aimed to maximize the efficiency scores using the most favourable input/output weights. In two-stage network structures, the presence of intermediate undesirable measures leads to a distinct domain of weight restriction study. In the presence of undesirable intermediate measures and equipped with non-cooperative game theory, this study developes a joint weight restriction approach to derive a common set of weights. Concurrently, the overall efficiency of the system can be evaluated. Numerical instances of 34 OECD countries in 2012 have been presented to elucidate the details and applicability of the proposed method.

The Future of the CFA Franc: A Game Theory Approach

Aims: Based on the theory of non-cooperative games, this paper aims to determine whether the African Franc Zone (AFZ) countries should leave or remain in monetary cooperation with France. Methodology: Empirically, we implement a non-cooperative game pitting France against the AFZ countries. The strategies defined for the two players are "Maintain (M)" and "Exit (E)." The potential benefit is the preservation of the pooling of 50% of the AFZ countries' foreign exchange reserves in the French Treasury. Results: Using Nash equilibrium, the study analyzes strategic decisions in monetary cooperation. At the end of technical manipulations, we obtain two results based on two assumptions: (i) Assuming that the AFZ is the first player, and the decision being taken by political leaders without consulting the other sociological components, the optimal solution would be (M, M), reflecting the preservation of 50% of foreign exchange reserves within the French Treasury; (ii) Then, when the leaders of the AFZ countries incorporate the will of the people and the aspirations of the African Union, we arrive at two Nash equilibria, (E, E) and (E, M) respectively, giving gains of 50% for the AFZ and 0% for the French Treasury, significantly implying an exit decision for AFZ countries. These results show that, beyond the positions of technocrats and leaders, the people's will is a determining factor in the economic and monetary conditions of a country or group of countries. Conclusion: However, these equilibria could be sensitive to the order of the game (who plays first), political shocks such as coups d'état, types of threat, grouped or solitary exit strategies, but also to the bargaining power of the players, mixed-strategy equilibrium and external geopolitical influences. The countries of the AFZ need to strengthen their monetary sovereignty by reforming cooperation mechanisms with France, while also incorporating the aspirations of their populations into the decision-making process. This will promote a more legitimate and contextually relevant monetary policy that aligns with current economic and social realities.

Prescribed-time multi-coalition Nash equilibrium seeking by event-triggered communication

This article investigates the event-triggered prescribed-time Nash equilibrium seeking problem among multiple coalitions of agents in noncooperative games. Each coalition acts as a virtual player in the noncooperative game, with decisions made by its member agents. Agents lack complete information about others’ decisions and instead estimate them through a communication graph. An event-triggered prescribed-time multi-coalition Nash equilibrium seeking method is developed based on the leader-following consensus protocol, dynamic average consensus protocol, and gradient play. This method ensures the Nash equilibrium of the multi-coalition game is reached within a prescribed time, even when communication between agents only occurs under specific triggering conditions—effectively conserving communication resources. Unlike existing approaches, the proposed algorithm allows precise settling time assignment without prior knowledge of system parameters. This algorithm also prevents Zeno behavior. Lastly, the efficiency of the designed algorithm is demonstrated through simulation experiments.

The equilibrium strategy of insurance companies’ dividends and reinsurance games

We investigated the optimal risk management strategies of an insurance company within a two-player non-cooperative differential game framework. The key feature of this model is considering the company’s surplus as a strategic variable to make the insurance company more attractive to shareholders. In this setup, shareholders are participants who demand a share of the surplus, while managers are participants concerned with the risk management of the surplus. The objective of the shareholders is to maximize the expected discounted dividends. We address this asymmetric game under two different assumptions about the managers’ objectives: in the first scenario, the managers aim to minimize the probability of bankruptcy; in the second scenario, the managers aim to maximize the expected discounted utility derived from the surplus.

Incorporation of Likely Future Actions of Agents Into Pseudo-Gradient Dynamics of Noncooperative Games

Incorporation of Likely Future Actions of Agents Into Pseudo-Gradient Dynamics of Noncooperative Games

Human-like Decision Making for autonomous lane change driving: a hybrid inverse reinforcement learning with game-theoretical vehicle interaction model

The development of automated driving vehicles aims to provide safer, comfortable, and more efficient mobility options. However, the decision-making control of autonomous vehicles still embraces limitations on human performance mimicry. These limitations become particularly evident in complex and unfamiliar driving scenarios, where weak decisionmaking abilities and poor adaptation of vehicle behaviour are prominent issues. This paper proposes a game-theoretic decisionmaking algorithm for human-like driving in the vehicle lane change scenario. Firstly, an inverse reinforcement learning (IRL) model is used to quantitatively analyse the lane change trajectories of the natural driving dataset, establishing the human-like human cost function. Subsequently, joint safety, comfort to build the comprehensive decision cost function. Use the combined decision cost function to conduct a non-cooperative game of vehicle lane changing decision to solve the optimal decision of host vehicle lane changing. The host vehicle lane-changing decision problem is formulated as a Stackelberg game optimization problem. To verify the feasibility and effectiveness of the algorithm proposed in this study, a lane change test scenario has been established. Firstly, we analyse the human-like decision-making model derived by the maximum entropy inverse reinforcement learning algorithm to verify the effectiveness and robustness of the IRL algorithm. Secondly, the human-like game decisionmaking algorithm in this paper is validated by conducting an interactive lane-changing experiment with obstacle vehicles of different driving styles. The experimental results prove that the human-like driving decision-making model proposed in this study can make lane-changing behaviours in line with human driving patterns in lane-changing scenarios of expressway.

An Integrated SIMUS–Game Theory Approach for Sustainable Decision Making—An Application for Route and Transport Operator Selection

The choice of management strategy for companies operating in different sectors of the economy is of great importance for their sustainable development. In many cases, companies are in competition within the scope of the same activities, meaning that the profit of one company is at the expense of the other. The choice of strategies for each of the firms in this case can be optimized using game theory for a non-cooperative game case where the two players have antagonistic interests. The aim of this research is to develop a methodology which, in non-cooperative games, accounts for the benefits of different criteria for each of the strategies of the two participants. In this research a new integrated sequential interactive model for urban systems (SIMUS)–game theory technique for decision making in the case of non-cooperative games is proposed. The methodology includes three steps. The first step consists of a determination of the strategies of both players and the selection of criteria for their assessment. In the second step the SIMUS method for multi-criteria analysis is applied to identify the benefits of the strategies for both players according to the criteria. The model formation in game theory is drawn up in the third step. The payoff matrix of the game is formed based on the benefits obtained from the SIMUS method. The strategies of both players are solved by dual linear programming. Finally, to verify the results of the new approach we apply four criteria to make a decision—Laplace’s criterion, the minimax and maximin criteria, Savage’s criterion and Hurwitz’s criterion. The new integrated SIMUS–game theory approach is applied to a real example in the transport sector. The Bulgarian transport network is investigated regarding route and transport type selection for a carriage of containers between a starting point, Sofia, and a destination, Varna, in the case of competition between railway and road operators. Two strategies for a railway operator and three strategies for a road operator are examined. The benefits of the strategies for both operators are determined using the SIMUS method, based on seven criteria representing environmental, technological, infrastructural, economic, security and safety factors. The optimal strategies for both operators are determined using the game model and dual linear programming. It is discovered that the railway operator will apply their first strategy and that the road operator will also apply their first strategy. Both players will obtain a profit if they implement their optimal strategies. The new integrated SIMUS–game theory approach can be used in different areas of research, when the strategies for both players in non-cooperatives games need to be established.

Strategic behaviors of renewable energy generation companies participating in the electricity and carbon coupled markets based on non-cooperative game theory

Renewable energy (RE) can participate in electricity and carbon market trading in China, which can help stimulate the investment of RE. Thus, we propose a bi-level model for non-cooperative game interactions among power generation companies (GenCos), considering the electricity and carbon coupled markets. The upper-level model considers strategic behaviors driven by maximizing profits for GenCos. The lower-level model includes a two-stage electricity market: the day-ahead market and the real-time market; it implements joint clearing of energy and reserves, and continuous trading with competitive auctions in the carbon market based on the clearing results of the electricity market. Simulations are performed based on the actual data of the power system in a certain region of Guangdong Province in China. The results show that electricity and carbon coupled markets can effectively reduce market costs and carbon emissions, improve the society welfare and RE benefits. The uncertain increase in RE output and higher installed capacity reduce the total revenue of the RE in the coupled markets. The initial carbon quota decomposition optimization decision of the coal-fired GenCos and gradual reduction in the initial carbon quota will increase the revenue of the RE GenCos.

Interactive strategy of shared control vehicle and automated vehicles based on adaptive non-cooperative game

Considering the complex traffic environment in the future, an interactive strategy between human-machine shared control vehicle (HSCV) and automated vehicles (AVs) based on the adaptive non-cooperative game (NCG) theory is proposed to ensure the safety of vehicles interaction control involving drivers with different characteristics. In HSCV, first, considering the environmental risk potential field (ERPF) and the human-machine conflict coefficient, an adaptive weight distribution method is designed to realize the weight distribution between a driver and an automation system. Subsequently, the steering angle command imposed by a driver is introduced into the game solving process between HSCV and AVs, enabling adaptive dynamic game through weight adjustment. During V2V interaction, based on NCG and distributed model predictive control, a motion planning controller (MOPC) is designed to integrate the optimal solution problem of path planning and tracking control and solve the interaction problem with constraints. Two typical interactive scenarios are used to verify the feasibility of the strategy. The results demonstrate that the interaction strategy considering the different drivers’ operating commands not only realizes the interaction between a driver and an ego vehicle but also realizes the interaction between an ego vehicle and nearby vehicles to ensure the safety of vehicles.

Stochastic Differential Games of Carbon Emission Reduction in the Four-Tier Supply Chain System Based on Reference Low-Carbon Level

This paper takes corporate social responsibility goodwill and consumers’ reference low-carbon level as endogenous variables of joint carbon emission reduction in the “supplier–manufacturer–retailer–consumer” supply chain system. The joint carbon emission reduction strategies of this four-tier system are analyzed from a dynamic perspective by considering random factors that affect the endogenous variables. Three stochastic differential games are proposed to examine the mechanism between each player, namely the cooperative model, Nash non-cooperative model, and Stackelberg master–slave model. Compared to the Nash non-cooperative game, the manufacturer/supplier-led Stackelberg master–slave game leads to Pareto improvement in the profits of the entire supply chain system and each player. The cooperative game demonstrates the highest expected emission reduction and corporate social responsibility goodwill, but also the highest variance. More importantly, the reference low-carbon level embraces consumers’ subjective initiative in the dynamic of carbon emission reduction. This level is an internal benchmark used to compare against the observed low-carbon level. This paper provides a theoretical foundation for strategic decision-making in emission reduction, contributing to sustainable development. By addressing environmental, economic, and social sustainability, it promotes climate action through carbon reduction strategies and offers policy recommendations aligned with the Sustainable Development Goals.

Risk-Sharing Mechanism Design in Non-Cooperative Multi-Defender Stackelberg Defense Resources Allocation Game

Risk-Sharing Mechanism Design in Non-Cooperative Multi-Defender Stackelberg Defense Resources Allocation Game

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 %.

Coordination of Monetary and Fiscal Policies from a Game Theoretic Perspective

Under the backdrop of a highly intricate international environment and sluggish recovery of the global economy, it is crucial to delve into methods for bolstering national economic prowess and promoting economic prosperity and stability. Monetary policy and fiscal policy, as two primary macro-control tools, play a pivotal role in national progress, with their effective coordination becoming a significant issue. Game theory, a tool to mathematically model decisions made by different individuals through logical analysis, provides a solid theoretical foundation and practical framework for studying the issue. This paper utilizes game theory to model the coordination among the two policy-makers, the central banks and the governments while establishing a payoff matrix that reflects their utilities. During normal or recovery periods, this paper views it as a cooperative game, and the cooperative equilibrium will be that both policy-makers choose expansionary policies. During financial crisis, this paper views it as a non-cooperative game, and the Nash equilibrium will be that both policy-makers choose contractionary policies. Additionally, this paper selects specific examples from Brazilian history to validate the rationality of the model while confirming that the short-term equilibrium aligns with the modeling conclusions.

A two-layer stochastic game approach to reinsurance contracting and competition

We propose a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle. The reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus, and their competition is settled by a noncooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semiclosed form. Furthermore, we obtain interesting sensitivity results for the equilibrium strategies through both analytical and numerical studies.

Towards coordinating self-healing instances: Policy-based and non-cooperative game theory-based approaches with location awareness

Self-healing is an essential functionality in Self-Organizing cellular Network (SON). It aims to ensure service continuity by detecting, diagnosing, and compensating network outage after triggering appropriate Cell Outage Compensation (COC) functions according to the outage case. The role of self-healing is increasingly become indispensable, especially in high density network as in 5 G and beyond, in order to maintain the availability and retainability of mobile service and save revenues. However, the essence of COC entails modifications of different Network Control Parameters (NCP) which are under control of SON Functions (SONF) that are related to other self-x functionalities. In addition, it can request different types of compensation functions according to the outage case. Moreover, it requires to harmonize the objectives of the requested stand-alone SONFs over the involved Candidate Cells (CC) in order to re-build a consistent coverage model. Thus, the need for self-coordination is mandatory to guarantee conflict-free outage compensation procedure. In this paper, we propose a novel integrated coordination scheme in order to coordinate Antenna Tilt (AT)-based and Transmission Power (TXP)-based COC functions. Beside their primary targets of conflict avoidance and resolution, we prove that our location-aware coordination mechanisms, which are based on policies and Non-Cooperative Zero-Sum Game (NCZSG) theory, can collaboratively guide greedy stand-alone single-objective COC functions to reach a stable coverage model. The coordination is done even when there is no prior knowledge of the environment or the compensatory algorithms themselves. The choice of optimal Network Control Parameters Values (NCV) is determined according to the function after the coordinator's verification.

Security, QoS and energy aware optimization of cloud-edge data centers using game theory and homomorphic encryption: Modeling and formal verification

Privacy and efficient data processing are crucial research areas in the field of outsourcing computing. Thus, the contribution of the paper is twofold. First of all, we develop a secure offloading technique that can process data while preserving privacy. Although RSA and Paillier cryptosystems are highly beneficial for mathematical operations on basic encrypted data due to their homomorphic properties, images are processed using permutation-ordered binary (POB) and Shamir's secret sharing (SSS). Second, a non-cooperative game theory model was formulated to examine the interactions between service providers, characterizing each edge as an M/M/1 system with an infinite queue. Through formal verification using rigorous mathematical reasoning, the suggested strategies for task offloading and resource allocation are shown to be effective in terms of security, quality of service (QoS), and energy consumption. The best-response dynamics approach is used to calculate the final strategy for each participant and assess how fairly resources are allocated. Finally, the potential of our approach is demonstrated numerically, revealing a faster convergence towards attaining Nash equilibrium in a duopoly cloud-edge data center market, granted that the necessary and sufficient conditions are met.

Bipartite consensus of concatenated opinion dynamics for two antagonistic groups: A game theoretical perspective

Recent decades have witnessed a significant surge in scholarly attention towards formulating dynamic models for opinion formation on social networks. This paper considers the bipartite consensus problem over a series of issues for two antagonistic groups wherein two graphs are employed to model the interaction within groups and a noncooperative game to describe the interaction between groups. Firstly, we prove that the noncooperative game admits the unique Nash equilibrium. Secondly, we give sufficient conditions for achieving a bipartite consensus that both graphs are strongly connected. Additionally, we obtain that the game’s mechanism decides the convergence rate of bipartite consensus from one issue to the next. It is important to highlight that confrontation is key in elevating the most influential individuals to leadership positions within their groups. Thirdly, we construct the bipartite consensus state for a particular case where the networks of two groups are balanced. Finally, we present two examples to demonstrate the theoretical results.

Optimal avoidance strategy based on nonlinear approximate analytic solution of non-cooperative differential game

Abstract This study examines the pursuit-evasion game involving unmanned aerial vehicles (UAVs), with a specific focus on the scenario of N-pursuers-one-escapee. The primary objective is to develop an optimal strategy for the escapee when the pursuers possess superior capabilities. To obtain this objective, we conduct the following study. Firstly, to enhance realism, a non-cooperative differential game model is formulated, incorporating multiple motion characteristics, including aerodynamics, overloading, and imposed constraints. Secondly, the end-value performance index is subsequently converted to an integral one, simplifying the solution process of the Hamilton-Jacobi-Bellman (HJB) equation. An iterative method is utilised to determine the covariates using the Cauchy initial value problem, and its convergence and uniqueness are established. The optimal avoidance strategy is subsequently derived from the covariates. Finally, the superiority of the proposed strategy is validated through simulation experiments and compared to three advanced optimal avoidance strategies. A total of 1,000 anti-jamming simulation experiments are conducted to verify the robustness of the proposed strategy.

Coopetition strategies in a two-stage, multi-agent supply chain under hybrid carbon trading mechanisms

ABSTRACT Managing a multi-agent supply chain within a hybrid carbon trading framework, which integrates Certified Emission Reductions (CERs) and Carbon Quota Trading (CQT), presents a significant challenge. This complexity is further amplified by the interplay of competition and cooperation among agents. Motivated by this, we develop a biform game-based cooperative mechanism for a two-stage supply chain that includes a high-emission manufacturer, a negative-emission manufacture and a downstream retailer. This mechanism is designed to encapsulate both the non-cooperative and cooperative game elements. The former features a product competition game among the manufacturers and retailer, setting the stage for the cooperative game without directly yielding equilibrium solutions. The latter involves a cost-sharing agreement for the CER project's initial investment, informed by various coalitional zero-sum games. Our analytical findings, corroborated by numerical simulations, reveal that the biform game coordination mechanism significantly enhances the volume of CERs traded and consumer surplus, compared to a non-cooperative scenario. It effectively aligns the collaborative efforts of all agents within the supply chain. This research contributes substantially to the literature on coordinating multi-stage, multi-agent supply chains, and the strategic deployment of emission reduction initiatives in supply chains. It also offers valuable managerial insights for the design of government regulations in carbon markets.

Pairwise Stability in Weighted Network Formation Games: Selection and Computation

This paper is concerned with the selection and computation of pairwise stable networks when agents have differentiable and concave utility functions. We show that a pairwise stable network can be obtained by finding a Nash equilibrium of a noncooperative game played by the nodes and links in the network. Based on this observation, we introduce a logarithmic tracing procedure and a path-following algorithm for network formation games. We apply the algorithm to several models in the literature and make comparisons with two existing algorithms: a path-following algorithm based on the linear tracing procedure (LinTP) and a decompose and exhaustive search method (DaE). Numerical results indicate that the proposed method is more than four times as efficient as LinTP. Although DaE demonstrates exceptional efficiency for small-scale problems, our method outperforms it significantly for large-scale problems, where DaE may fail to find a solution. We also show that the decomposition technique of DaE can be used to further accelerate our algorithm for a special class of problems. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 12201289, 12122107, and 72394363/72394360], the Natural Science Foundation of Jiangsu Province [Grant BK20220754], the Guangdong Basic and Applied Basic Research Foundation [Grant 2021A1515110207], the Young Elite Scientists Sponsorship Program by CAST [Grant 2023QNRC001], and the Open Research Fund from the Guangdong Provincial Key Laboratory of Big Data Computing [Grant B10120210117-OF05]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0546 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0546 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .