Dynamic Game Research Articles

Manufacturing resource outsourcing and matching: service mode selection and equilibrium evolution

Manufacturing resource outsourcing platforms facilitate the meeting and matching of manufacturing service seekers and providers. The platform’s service mode, the willingness of seekers to match, and providers’ carbon emission reduction (CER) directly affect entities’ decisions. Therefore, this paper employs an evolutionary game approach to analyse the manufacturing resource matching (MRM) between the providers and seekers and a sequential game model to analyse the pricing and CER strategies between the platform and providers. First, this study reveals that the service mode does not influence the evolutionary path and stability of MRM. However, matching in the cooperative mode becomes easier due to higher resource quantities. Second, we find that the cooperative mode can enhance the system’s profits, and an appropriate revenue-sharing ratio is crucial for the platform and providers. Third, the analysis indicates that while the cooperative model can generate higher profits, it may also result in increased total carbon emissions.

Optimal investment of distribution energy resources via energy performance contracts: An evolutionary game approach

Investment in distributed energy resources (DERs) is crucial for the expansion of distribution networks. However, traditional methods often lack comprehensive project management throughout their entire lifecycle and precise matching between distribution network operator (DNO) and energy consumer (EC) at the investment level. To address these issues, this paper proposes a novel investment model based on energy performance contracts (EPCs). Three EPC mechanisms are introduced: energy shared savings model (ESSM), energy guaranteed saving model (EGSM), and energy cost trust model (ECTM). Additionally, DERs investment strategies under EPC mechanisms are proposed to satisfy full-process management of project and precise matching between EC and DNO. The investment and operation problem is solved by an evolutionary game theory that ensures bounded rational agent to achieve satisfactory expected returns through repeated dynamic games. Results from the case study of an actual urban 37-bus system demonstrate that different EPC mechanisms are suitable for various scenarios depending on the EC's profit demand and project scale. The proposed model provides a comprehensive framework for DERs investment, considering the interests of both DNO and EC, and promotes the optimal expansion of distribution networks in a more practical and effective manner.

ε-Nash Equilibrium of Pursuer–Evader–Defender Missile Navigation Dynamic Games

This research is dedicated to developing a min–max robust control strategy for a dynamic game involving pursuers, evaders, and defenders in a multiple-missile scenario. The approach employs neural dynamic programming, utilizing multiple continuous differential neural networks (DNNs). The competitive controller devised addresses the robust optimization of a joint cost function that relies on the trajectories of the pursuer–evader–defender system, accommodating an uncertain mathematical model while adhering to control restrictions. The dynamic programming min–max formulation facilitates robust control by accounting for bounded modeling uncertainties and external disturbances for each game component. The value function of the Hamilton–Jacobi–Bellman (HJB) equation is approximated by a DNN, enabling the estimation of the closed-loop formulation for the joint dynamic game with state restrictions. The controller’s design is grounded in estimating the state trajectory under the worst possible uncertainties and perturbations, providing a robustness factor through the robust neural controller. The learning law class for the time-varying weights in the DNN is generated by studying the HJB partial differential equation for the missile motion for each player in the dynamic game. The controller incorporates the solution of the obtained learning laws and a time-varying Riccati equation, offering an online solution to the control implementation. A recurrent algorithm, based on the Kiefer–Wolfowitz method, adjusts the initial conditions for the weights to satisfy the final condition of the given cost function for the dynamic game. A numerical example is presented to validate the proposed robust control methodology, confirming the optimization solution based on the DNN approximation for Bellman’s value function.

Experience is all you need: a large language model application of fine-tuned GPT-3.5 and RoBERTa for aspect-based sentiment analysis of college football stadium reviews

ABSTRACT Despite extensive research in service industries, fine-grained explorations of customer experience within spectator sports remain limited. This study pioneers a transfer learning approach grounded in a post-positivism paradigm, underpinned by an integrative customer experience framework for aspect-based sentiment analysis of user-generated content, shedding light on the complexity of the college football game day experience. Three fine-tuned large language models were employed to qualitatively identify and quantitatively analyze customer experience from Tripadvisor reviews on college football stadiums. Our findings indicated that fans’ positive reactions to stimuli related to core (game dynamics), functional (facilities/services), emotional (intense feelings), and socialization (fan interactions/bonding) significantly increased the likelihood of them giving a five-star rating. Mitigating negative experiences across functional, emotional, socialization, safety, and monetary experience was crucial for achieving a top rating, with reducing negative functional issues and safety concerns having the greatest positive impact. Our study contributes to the sport management literature by establishing a unified view of customer experience, enabling a holistic conceptualization and operationalization of customer experience in spectator sports. Empirically, our research proposes targeted strategies to manage customer experience in college football and offers sport management professionals ready-to-use large language models along with detailed deployment guidelines tailored for distinct use cases.

Complexity Analysis of the Interaction between Government Carbon Quota Mechanism and Manufacturers’ Emission Reduction Strategies under Carbon Cap-and-Trade Mechanism

Based on different carbon quota trading mechanisms, the price and emission reduction strategies of oligopoly manufacturers in the low-carbon market and the government carbon quota mechanism are considered. A dynamic game evolution model of the two oligopoly manufacturers with competitive relations is established. The stability of the equilibrium point of the game model, the price adjustment speed of the decision variable, the impact of carbon emission reduction investment, and the government carbon quota on the system are discussed. Through nonlinear dynamics research, it is found that the advantage of the grandfathering method is that it is conducive to maintaining market stability when the government’s carbon quota decision changes; the advantage of the benchmarking method is that when manufacturers formulate price adjustment strategies, the benchmarking method carbon quota mechanism has a stronger stability range for the market, the manufacturer’s profit price adjustment speed is positively correlated, and the government carbon quota decision and emission reduction investment are also positively correlated. Decision makers need to choose appropriate carbon quota mechanisms and manufacturers’ emission reduction strategies according to actual market changes to maintain supply chain stability.

Dynamic delay-based game approach in car and petrol supply chains under government intervention

Effective decision-making in a temporal context is challenged by the enduring impacts of delays, where decisions made in a certain period are influenced by choices made in preceding periods. This paper delves into the analysis of decision-making in a dynamic game system characterized by delay impact on decisions. Notably, it pioneers the application of a game approach to detect the intricate relationship between car and petrol supply chains operating under conditions of dynamism and uncertainty. The marginal profit method is applied to deal with the dynamic game model. Furthermore, this article investigates the improvement of green car levels, on member profits. In the car supply chain, the car manufacturer sells two distinct product types: green and regular. In this paper, green cars refer to cars with low petrol consumption, and as gas consumption decreases, the green level of the car ascends. This study marks the first instance where optimal production capacity allocation is examined within the framework of delay and uncertainty. Considering the government's initiative to curtail petrol consumption in automobiles, the effects of the government's supporting role are also analyzed in this paper. As a result, the greenness level witnessed a 4.1-fold increase, leading to an 81.7% surge in the demand for green cars, consequently boosting the profit of the entire car supply chain. Several numerical experiments of a real case were examined to evaluate the performance of the proposed models. Finally, some sensitivity analyses were applied to the principal parameters of the model to extract managerial insights.

Differentiated health insurance policy for coordinating healthcare referral in hierarchical healthcare systems with an internet diagnosis platform

The integration of the Internet with traditional medical services is poised to transform health insurance policies. This study aims to explore the coordinating role of differentiated health insurance policies within the context of Internet healthcare. A four-stage sequential game decision-making model is developed within a queuing framework to address scenarios involving online patient referrals and misdiagnoses. The model begins by analyzing the equilibrium arrival strategy of patients, followed by the determination of optimal service capacity strategies for a nonprofit community health center (CHC) and optimal pricing strategies for a for-profit general hospital (GH). Additionally, the model describes an optimal differentiated subsidy strategy for the government aimed at minimizing total social costs. Analysis reveals that under certain conditions, an increase in the service price at GH relative to CHC can lead to a higher influx of online patients visiting GH in person. Furthermore, when the number of online patients exceeds a specific threshold, it not only prompts the government to increase the disparity in health insurance subsidies between the two hospital tiers but also encourages GH to reduce its service prices and offer free services to online patients. Numerical experiments explore the effects of government budgets, sharing ratios, and other variables on the system's equilibrium state, providing several managerial insights. Notably, when patients' misdiagnosis costs are partially covered, increasing GH's misdiagnosis cost-sharing ratio not only enhances the patient arrival rate but also enhances GH's profitability.

Game Dynamics in Professional Padel: Shots Per Point, Point Pace and Technical Actions.

This study aimed to determine the distributions of number of shots per point, point duration, point pace and technical actions during the match in professional men and women padel players. A total of 35,145 hits (3239 points; men = 1602 and women = 1637) were analyzed in 20 matches corresponding to quarterfinal, semifinal and final matches of the World Padel Tour 2020 season. The observations were conducted through systematic observation and involved a total of 32 players (16 men and 16 women). Men's points lasted 13.5-14.8 s, comprising 10-11 hits, resulting in a ratio of 0.80 shots per second, with no differences between sets. Women's points lasted longer than men's (14.4 to 16.2 s, p = 0.011) but included a similar number of shots per point, resulting in a lower rhythm of play (0.73-0.75 shots per second, p < 0.001), particularly in the third set (p = 0.004). Volleys, lobs and directs were used in >60% of the points, with a frequency of one to three times per point. Bandejas were used in 50-60% of the points, with a frequency of one to two times per point. Backwalls and flat smashes were used at least once in 30-48% of the points. Selective actions had a greater frequency of use in the third set (i.e., flat smash and smash x3 in women; forehand/backhand volleys and side-wall forehand in men), suggesting occasional changes in the style of play, but likely explained by the onset of fatigue. In conclusion, game volumes, intensity and actions remained broadly similar throughout professional padel matches.

A dynamic analysis of the firms in oligopoly market structure: a case study

Purpose Over the last years, powerful advances in the area of dynamic games have enriched game theory and made it more applicable to the modeling of real-world competitive strategies. The study of strategic behaviors of firms in an oligopoly market has received little attention, even though real firms have been shown to compete in output and in price in a single industry. The purpose of this study is to propose a game-theoretic approach to studying strategic behaviors of firms in an oligopoly market structure. Design/methodology/approach This approach was developed to study market dynamics and pricing strategic behavior of firms that have the possibility of deciding to be one of the two types (price-maker or price-taker) and reconsider the choice overtime on the basis of their current insights and knowledge and their experience. Firms try to improve their performance in the competitive market in a strategic way, by considering their steady-state profits and choosing the best type given the other firms’ types, actions and interactions. Findings The results of the present study confirm the previous study that the Cournot market is a stable market, where each firm can be a price-maker and enjoy individual learning as well as social learning. On the contrary, the market with price-takers only is never stable, and, therefore, the Walrasian equilibrium may not be supported in some instances. The Cournot market loses its stability as the number of firms in the market increases due to the fact that it will be more profitable for a firm to switch to price-taking when the number of firms is high enough. In such a situation, when the number of price-takers increases, there are no stable markets and price dynamics are destabilized. Originality/value The study and modeling of real-world competitive strategies would enhance the understanding of oligopoly markets. The study of strategic behaviors of firms in an oligopoly market has received little attention, even though real firms have been shown to compete in output and in price in a single industry as price-takers and price-makers.

Three-player autonomous racing by Stackelberg game methods

This paper considers the autonomous racing of three cars, including a team of two cars and an opponent car. To handle it, the competition is modeled as a two-leader one-follower Stackelberg game to obtain the optimal strategies for each car. In the sequential game, all the cars maximise their progress while avoiding collisions. In the blocking game, blocking behaviours are taken into account by adding a reward to the payoff function. Through successful collaboration, actions are more aggressive in the second game. Given that the Stackelberg equilibrium is not unique in both games, the cost functions are designed for the players to cope with multiple strategies that have the same progress. The competitions are performed in a receding horizon fashion, and the aim of the research is to study the effects of cooperation and make the team have successful blocking behaviours under constraints as well as speed disadvantages.

Optimal Bidding Strategies for Wind-Thermal Power Generation Rights Trading: A Game-Theoretic Approach Integrating Carbon Trading and Green Certificate Trading

In response to the challenges of low wind power consumption and high pollution emissions from thermal power, the implementation of wind-thermal power generation rights trading is a proactive attempt to reduce wind power curtailment and promote its consumption. This study first regards the alternating bidding process between the two parties as a dynamic game, using the Rubinstein bargaining game model to determine the incremental profit allocation and optimal bidding for both parties in power generation rights trading. Secondly, an energy conservation and emission reduction model is constructed to analyze the benefits from the perspectives of standard coal consumption saving and the carbon emission reduction caused by power generation rights trading. Finally, a combined trading revenue model is established to analyze the final profit of both parties involved in the trading. The results show that the combined trading of wind-thermal power generation rights, incorporating carbon trading and green certificate trading, can effectively promote coal consumption savings in thermal power units and reduce the carbon emissions of the power industry. Moreover, it significantly increases the final profit for both parties, stimulating the enthusiasm of generators for participating in power generation rights trading, and ultimately promoting wind power consumption.

Leveraging gamification for tourism marketing activities: Toward a comprehensive conceptual model

Gamification has become one of the most effective ways to generate customer engagement. However, there needs to be more structured research on the drivers of the adoption and sustained use of gamification in travel and tourism research. Drawing upon the uses and gratifications theory and the technology acceptance model, this research examines the individual motivational drivers for adopting gamification in the context of tourism services. We employed a combination of partial least squares—structural equation modeling and fuzzy set qualitative comparative analysis on the data gathered from 680 users of various online travel agencies. Our findings show that individual motivational dimensions of uses and gratifications significantly influence perceived usefulness and ease of use in gamified marketing activities. Our analysis demonstrates five configurations leading to a high level of adoption of gamified marketing activities. This study extends the use of gamification in the tourism industry, offering insights into enhancing customer motivations for adopting and effectively utilizing game mechanics and dynamics in marketing activities. Furthermore, through a novel framework, this study advances the uses and gratification theory at the intersection of gamification research and tourism literature.

Complex dynamics of a quantum Cournot duopoly game with two different objectives

Complex dynamics of a quantum Cournot duopoly game with two different objectives

A model predictive Stackelberg solution to orbital pursuit-evasion game

In this paper, we investigate analytical numerical iterative strategies for the pursuit-evasion game involving spacecraft with leader–follower information. In the proposed problem, the interplay between two spacecraft gives rise to a dynamic and real-time game, complicated further by the presence of J2 perturbation. The primary challenge lies in crafting control strategies that are both efficient and applicable to real-time game problems within a nonlinear system. To overcome this challenge, we introduce the model prediction and iterative correction technique proposed in model predictive static programming, enabling the generation of strategies in analytical iterative form for nonlinear systems. Subsequently, we proceed by integrating this model predictive framework into a simplified Stackelberg equilibrium formulation, tailored to address the practical complexities of leader–follower pursuit-evasion scenarios. Simulation results validate the effectiveness and exceptional efficiency of the proposed solution within a receding horizon framework.

The Efficacy of Joyful Learning on Exercise in Older Adults: The GAME Strategy

Exercise can effectively slow aging and prevent the onset and reduce the complications of chronic diseases in the elderly. However, roughly one-third of older adults are inactive. Joyful learning is an effective method for promoting physical activity, while using games is a feasible strategy for achieving joyful learning that enables individuals to fully immerse themselves in and enjoy an activity. Therefore, exploring gaming strategies to enhance physical activity among the elderly is worthwhile. In this paper, a set of gaming strategies based on the literature and practical experience is proposed. The name of this strategy, GAME, is an acronym of the following: goal setting and educational content development (G), activity design and game content creation (A), mechanics and dynamics implementation (M), and evaluation of qualitative and quantitative health outcomes (E). This systematic descriptive approach helps clearly demonstrate how gamification strategies can promote physical activity and health in older adults. The aim of this paper is to provide a reference and guide for education, research, and clinical practice in health promotion programs targeting older adults.

Independence or cooperation? Evaluating emission reduction strategies in non-competitive and competitive environments

This study combines a dynamic game and the Nash bargaining model to discuss the choice of manufacturers’ emission reduction strategies independently or in cooperation with cleantech firms under the cap-and-trade mechanism. The models comprise one manufacturer and one cleantech firm in a non-competitive environment, and two manufacturers with different emission reduction capacities in a competitive environment. The results show that competition will produce significant substitution effects, and some sensitivity analyses of the disadvantaged manufacturer tend to be opposite to those under a non-competitive environment. On the contrary, cooperation will bring significant positive impacts, carbon reduction rates will be improved after cooperating with cleantech firms. However, when profits are concerned, the Nash equilibrium model (C, C) may fall into a prisoner’s dilemma choice, while cleantech firms with low technical improvement capacities can drive it to become a Pareto optimality strategy, which will cause false prosperity in the cleantech industry. Given this, the objective of carbon neutrality and the cooperation model with the same cleantech firm is further extended, showing effective cooperation and improvement to provide new perspectives into emission reduction strategies.

Corrections to “Opinion Dynamic Games Under One Step Ahead Optimal Control”

Corrections to “Opinion Dynamic Games Under One Step Ahead Optimal Control”

Does cooperative intervention affect pricing decisions in the agricultural supply chain?

In global agricultural markets, farmers often face profit squeezes due to low bargaining power, which affects the sustainability of agriculture and the livelihoods of farmers. Cooperative intervention is seen as a key solution to improve bargaining power and optimize profit distribution in the agricultural supply chain. In this study, a two-stage dynamic game model is adopted to focus on bargaining power and compare the effects of linear pricing versus a double charging system under cooperative intervention. It is found that the cooperative is better when it has full bargaining power or when it faces downstream sellers with comparable bargaining power, and the dual-charging system is more favorable. When cooperatives bargain with sellers, the degree of differentiation of agricultural products affects the cooperatives’ profitability and cooperatives tend to maintain the two-part tariff when the bargaining power is less than a threshold condition containing the degree of differentiation of agricultural products; when discounts exceed the threshold, cooperatives shift to linear pricing to safeguard their profitability. Numerical analysis validates the theory and reveals the changing pattern of cooperative profits under market forces. This study not only provides theoretical support for the study of supply chain pricing strategies under the condition of considering the bargaining power of producers (farmers) but also provides management insights for the stability and sustainable development of agricultural supply chains. Its novel dynamic game framework is cross-culturally applicable to help farmers’ cooperatives cope with the challenge of profit distribution in a global context and emphasizes the importance of differentiation strategies to enhance bargaining power and promote fairness and efficiency in global agricultural supply chains.

Research on stability strategy based on the dynamic evolution game of promoting low-carbon building green building materials market

Research on stability strategy based on the dynamic evolution game of promoting low-carbon building green building materials market

Integration of Sales and Operations: A Dynamic Mixed-Integer Programming Game

Integration of Sales and Operations: A Dynamic Mixed-Integer Programming Game