Dynamic Game Research Articles

An online interactive physics-informed adversarial network for solving mean field games

We propose an online interactive physics-informed adversarial network (IPIAN) to address mean field games (MFGs) from the perspective of physics-informed interaction. In this study, we model the interaction between agents as a physics-informed exchange process, quantifying the evolution and distribution of individual strategy choices. We utilize the variational dyadic structure of MFGs to transform the dynamic game problem into a static optimization problem, subsequently employing the adversarial network to solve the mean field games. Based on the generative adversarial framework, two online physics-informed networks solve the value and density functions. These networks are trained to approximate the solution of MFGs through adversarial means. Additionally, a self-attention mechanism is introduced to enhance the focus on strategic physics-informed, thereby improving the expressiveness of IPIAN. Numerical experiments validate the effectiveness of IPIAN in solving high-dimensional mean field game models, as demonstrated by obstacle avoidance experiments with a quadrotor in various scenarios.

Demerit of the information concerning decision-making methodology: A dynamic Cournot game with adaptive expectation

It is not uncommon for firms to gain access to the information concerning not only the previous decisions of others but also their decision-making methodologies. However, few literatures study the information concerning decision-making methodologies in dynamic Cournot games. This paper considers a dynamic Cournot game with adaptive expectation. It is assumed that each firm extra acquires the information regarding the other competitors' decision-making methodologies, and the information will be employed to estimate the outputs of other firms in the next period. The information leads to a decline in the stability of the original Cournot-Nash equilibrium, as demonstrated by both theoretical analysis and numerical simulation. It implies that boundedly rational firms need be vigilant for the information concerning decision-making methodologies in certain cases.

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.

Integrated Pricing and Inventory Decisions for Product Quality-Driven Extended Warranty Services

Extended warranty services have become increasingly important for both manufacturers and retailers, offering avenues for new profit sources and growth opportunities. Focusing on the multiple effects of product quality, this study develops a two-period supply chain decision model to analyze the effects of product quality, pricing, and inventory management in the context of extended warranty services. Using a Stackelberg dynamic game model, this study examines the interaction between a manufacturer and a dominant retailer who provides extended warranties. The results indicate significant differences in optimal decisions between centralized and decentralized supply chains, especially concerning pricing and inventory control. Introducing a “quality cost-sharing” contract enhances product quality and improves coordination, leading to increased profits for both the manufacturer and the retailer. Numerical simulations confirm that the cost-sharing contract effectively balances product quality improvements with supply chain profitability.

Understanding Customer Readiness for Digital Gamification

ABSTRACT Digital gamification has been studied extensively in different contexts across information systems and digital marketing. Interestingly, scholarly studies in information systems/marketing regarding the benefits of digital gamification are mixed, with several research works reporting negative outcomes. Our study attempts to resolve these contradictions and explain why digital gamification failed in certain instances—the target customers were not ready. The present study, done in the USA covering 446 usable responses, adds to the extant literature in many ways. First, we throw light on gamified engagement programs and the mediating role of customer readiness and consequent outcomes. Our results reveal that simplicity and information quality are other important dimensions of gamified engagement programs, in addition to intrinsic and extrinsic game dynamics, for achieving adequate customer readiness. Additionally, customer participation makes the greatest contribution to company engagement, followed by program loyalty and program satisfaction. We conclude with the study’s implications on different fronts.

A game-based power system planning approach considering real options and coordination of all types of participants

With the ongoing advancement of global power marketization, the increasing diversity of stakeholders in the power market and their interactions have a significant impact on power system planning and operation. Traditional methods employ game theory to describe the interactions among market participants. However, these approaches fail to include all relevant participant types and overlook the long-term uncertainty value of planning schemes. Therefore, this paper proposes a game theory-based power system planning approach considering real options (RO) and coordination of all types of participants. First, the dynamic gaming interaction among supply-transmission-demand is studied, and the independent system operator is integrated into the game planning framework based on the overall perspective of power market operation. Moreover, the new power supply, grid planning, and operation of distributed generation (DG) are taken as decision variables based on the RO theory, and a game decision model of all participants in the power system planning considering the investment uncertainty is constructed. Finally, the iterative search algorithm is employed to solve the model, and the framework is validated based on the IEEE 30-bus system. The results indicate that through collaborative planning involving various market participants, Generation Companies and Transmission Companies expand their investments to maximize profits, while large power consumers reduce their investment in DG and instead increase their direct power purchases to lower costs. Moreover, these participants are inclined to pursue projects with higher asset value volatility, which further enhances their profit. By integrating RO theory with game theory, the proposed approach establishes a comprehensive planning framework that effectively addresses investment uncertainty. This integration enables market participants to make more optimal decisions, ultimately leading to an enhancement in the long-term economic performance of the power system.

Talking to Machado de Assis: Generative Artificial Intelligence to Simulate Dialogues with Prominent Figures

Generative artificial intelligence encompasses techniques for automatically generating content such as image, music, and text. A common application of these techniques, especially involving text generation, is the construction of conversational agents. In education, generative artificial intelligence has the potential to transform the learning process and enable new forms of teaching, such as the practical application of concepts studied in class and the acquisition of new knowledge through the interaction with computational tools. In Brazil, literature teachers often complain about students' resistance to the content and insufficient reading practice. To address these challenges, this work presents a serious game in which students can chat with Machado de Assis, an important writer of the Brazilian literature. The game was developed by integrating with ChatGPT. The validation was conducted with 15 high school students for them to interpret the book "Dom Casmurro". The MEEGA+ instrument was used to evaluate the usability and the experience with the game. The main findings were that students better understood the book, found the game easy to use, and felt immersed in the conversation with Machado de Assis, although they assessed the texts as long and tiring. In a world dominated by faster and visually stimulating forms of entertainment, such as video games and social networks, students may have different expectations regarding the reading experience. If they are not used to reading denser and more introspective texts, they may find it difficult to maintain interest when chatting with Machado de Assis. Finally, another implicit point in the game dynamics is observed: the (re)signification of the methodology to be adopted by the teacher, who will perceive the need to complement interactions with the writer in class according to what he can or should answer, tending to responses that stimulate students to study more about what is within the realm of knowledge about Machado de Assis.

A virtual 3D Chemistry Escape Room for Exam Preparations

Chemistry can be incredibly captivating. However, learning the theory can often be challenging and less appealing for students. Providing them with hands-on methods in their learning process is beneficial and also helps to lower the barrier for understanding theory. In a gamified approach, the "ChemScape" virtual 3D chemistry escape room, designed as a realistic laboratory with various equipment and hidden chemical tasks, can help solidify chemical knowledge and prepare students for chemistry exams. In 2023, as part of an e-learning project, the foundation of such a chemistry escape room was established, and several chemical questions were incorporated as escape room tasks. The objective is to discover hidden questions within the laboratory, utilize different instruments (such as scales), conduct virtual chemistry experiments, and solve various chemistry questions using theoretical knowledge (such as nomenclature and understanding of pH) in a game-based setting (utilizing multiple-choice, drag and drop, connecting cables, solving color codes, etc.). Typically, a code (comprising numbers, letters, signs, etc.) needs to be obtained for progression. To solve the chemistry tasks, approximately 10 different door-openers have been developed. Initial user tests have been conducted, and adjustments were made based on the feedback received, which was satisfactory and positive. In 2024, the "ChemScape" escape room will evolve from a game with a fixed set of tasks to a dynamic escape room game with a dynamic database that allows for the creation of new questions at the same stations, significantly expanding learning opportunities. A virtual chemistry laboratory rat provides hints if a participant gets stuck and requires assistance. Furthermore, "ChemScape" will be trialed in chemistry lectures and potentially utilized as an additional attraction at events held at the University of Applied Sciences.

Multiplayer game dynamics and their applications into simplicial complexes with memory effect

Abstract We investigate the evolutionary dynamics of the multiplayer, snowdrift-like game based on memory effects, in which cooperators and defectors interact with another type of player named as exiter. To avoid being exploited by defectors, the conservative exiters tend to drop out of a game and merely share quite minor returns. Results on the well-mixed populations indicate that the existence of exiters is less conducive to cooperation. Whereas, in networks with simplicial complexes, the memory effect can effectively inhibit evolution of defection and promote cooperation. Other outcomes with respect to the evolution of exiters and defectors, including the co-existence of all three types of players in the network and the favor of exiter, can be obtained by tuning the payoff to exit and the proportion of 1-simplices and 2-simplices. The current results provide insight into how mutual cooperation emerges in real networked populations, influenced by the memory-based exit options.

Demand cannibalization during product rollovers in the presence of strategic customers

This paper studies how different types of demand cannibalization take place during product rollovers and their effects on a firm’s profitability. Due to continuous product upgrades, demand cannibalization among various generations of products has become a common practice, raising interesting investigations from professionals and academics. Within this context, we model firms’ and customers’ decision-making as a two-period sequential game and derive equilibrium results under a dual rollover strategy, with and without a trade-in program. We find that demand cannibalization is essentially caused by customers’ strategic comparison of available purchase options. Our analysis further reveals that both the cannibalization effect and the postponement effect resulting from customers’ waiting for upgraded products are necessary for firms to improve profits. On the contrary, the postponement effect due to waiting for a discount is entirely detrimental to the firm. We propose effective launch strategies to avoid unfavorable demand cannibalization under different conditions. In addition, offering trade-in programs helps not only suppress strategic waiting, but also foster demand for an upgraded product. These strategies are particularly effective when the firm holds a greater quantity of inventory or when the degree of incremental innovation is high.

A maneuvering strategy based on motion camouflage in three-player differential game

In this paper, we consider a three-player differential game in which the defender provides coverage for the evader by maneuvering toward the line of sight between the pursuer and the evader. The TAD game is divided into two pursuit-evasion games to obtain the saddle point strategy for each player. Different from the general solution, the defender uses motion camouflage conditions as its payoff function and gives the real-time maneuvering strategy. This approach ensures that the constraint in the gaming process is met by providing the saddle point solution for each time interval. Additionally, interception strategies are created for each player to get the required heading angle. These strategies and game dynamics can be predicted by examining the current state of the game. Consequently, we establish the advantage region for the pursuer and the defender based on these predictions. Based on the given initial conditions, the advantage region for the defender is presented in its initial velocity vector. Finally, the simulations validate the effectiveness of the proposed strategy and the capture region analysis.

Firms’ location decisions, supply chain disruptions and government subsidies: A dynamic game

This paper develops a dynamic game to study the interaction between firms’ production location decisions and a government subsidy policy. On the one hand, firms consider the cost of shielding their production capacity from (potential) supply chain disruptions. On the other hand, the government is interested in curbing production offshoring to increase domestic tax revenues. The location decision of each firm is affected by the government subsidy policy and the location choices of other firms, while the share of firms producing domestically influences the government’s decision on whether and to what extent to provide subsidies to firms. We show that government subsidy policy must target a sufficiently large number of firms to encourage production reshoring and achieve the Pareto-efficient equilibrium. However, a subsidy policy providing a high number of low subsidies is likely to be ineffective in increasing domestic production, highlighting the importance of careful fine-tuning of the policy. Finally, in some scenarios, industrial policy becomes crucial to increase the resilience of domestic supply chains and foster reshoring.

Requester mobility for mobile crowdsensing system: A dynamic alliance-based incentive mechanism

In the Mobile Crowdsensing (MCS) system, due to the heterogeneity of requesters, they are in mobile which means requesters will join or leave the MCS system at different times and their data demands are time-varying. The uncertainty of requesters caused by requester mobility will generate the instability of the match between requesters and participants which means the established matching algorithm cannot be completed due to the dissatisfaction of requesters and participants caused by the changes in the intensity of competition. For requester mobility, we design a dynamic alliance-based incentive mechanism where requesters can leave, join the MCS system separately, and change their data needs. To the instability, we divide the dynamic mechanism into different stages and will update the matching rules in each stage. A unique algorithm based on the dynamic Stackelberg game and the corresponding updated algorithm is proposed to analyze the matching strategies of requesters and participants to make an optimal match. By proving the stability of the updated rules, we guarantee the stability of the match with requester mobility. Through numerical analysis, alliance formation can significantly reduce weak requesters’ costs by at most 90%. Besides, in our mechanism any requester participates in the game at most twice, the chosen rate can be up to 100%.

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 dynamic evolutionary game to discourage enterprise “greenwashing”

To meet the increasing consumer demand for green products and services, governments have increased their regulation of enterprise production behaviors so that enterprises may choose “greenwashing” to obtain the premium of green products at the lowest cost under government regulation. The increase of greenwashing hinders green innovation by enterprises. To quantify this problem and seek solutions to promote enterprises cleaner production and sustainable development, we established a tripartite evolutionary game model for enterprises, consumers, and governments. Using the model, we analyzed the stability of their strategy combinations through simulations and explored the impact of some parameters on the strategy selection. We found that (1) the combination of enterprises adopting true green, consumers buying green products, and weak government regulation was the most environmentally friendly and low-cost strategy solution in the tripartite game system. (2) An increase in government penalties or subsidies to enterprises, as well as a reduction of the extra cost of producing green products, can improve the probability that enterprises will adopt cleaner production. Based on the results, the government should define reasonable subsidies and penalties, guide enterprises to assume their social responsibility, and stimulate consumer green demand. Enterprises should improve their moral qualities, actively engage in green innovation, and increase investment in green product research to guide the game system towards the ideal state.

Decoding futsal offensive game moments: an in-depth qualitative study with expert coaches

ABSTRACT Purpose In futsal, coaches must make decisions in unpredictable contexts by continuously selecting the most relevant information to understand the game dynamics. This study aims to characterise and interpret what elite futsal coaches perceive as critical information. Specifically, per each game moment, it was intended to explore the coaches’ perceptions about what is the critical information presented. Methods Ten expert futsal coaches (48.30 ± 5.85 years; experience 18.10 ± 4.12 years) that currently coach elite futsal teams were selected. A total of 37 video clips were selected and exhibited. Qualitative data was obtained through semi-structured interviews and analysed by content analysis. Results The findings portrayed expert coaches identified and interpreted different informational constraints as critical according to the environment of play. In detail, to explain the attack, coaches perceived the information related with the defensive system. Also, most of the information highlighted was related with individual actions that sustains team’s behaviour in relation to the opponent. Conclusion The informational constraints that support coaches’ perception about each game moment were specific to each play circumstances. Thus, we emphasised the need for coach education courses to master the interplay between knowledge about and knowledge of the environment, in developing novice coaches.

Joint Planning Method of Shared Energy Storage and Multi-Energy Microgrids Based on Dynamic Game with Perfect Information

Under the background of the Energy Internet and the shared economy, it is of great significance to explore the collaborative planning strategies of multi-energy microgrids (MEMGs) and a shared energy storage operator (SESO) supported by shared energy storage resources. In this context, a joint planning method of SESO and MEMG alliances based on a dynamic game with perfect information is proposed in this paper. First, an upper-level model for energy storage capacity configuration and pricing strategy planning of SESO is proposed to maximize the total planning and operational income of SESO. Then, a lower-level model for the optimal configuration of MEMGs’ alliance considering SES is proposed to minimize the total planning and operational costs of the MEMG alliance. On this basis, a solving algorithm based on the dynamic game theory with perfect information and the backward induction method is proposed to obtain the Nash equilibrium solution of the proposed bi-level optimization models. Finally, a case study with one SESO and an alliance consisting of five MEMGs is conducted, and the simulation results show that the proposed bi-level optimization method can increase SESO’s net income by 1.47%, reduce the average planning costs for each MEMG at least by 1.7%, and reduce model solving time by 62.9% compared with other counterpart planning methods.

An analysis of optimal equilibrium in the carbon trading market - From a tripartite evolutionary game perspective

As the climate crisis intensifies, achieving the global consensus of carbon peaking and carbon neutrality has become imperative. Carbon trading is an important financial measure to address the environmental crisis, and the realization of the dual‑carbon goals requires the cooperation and joint efforts of all parties involved in the carbon emissions trading market. This study constructs a dynamic evolutionary game model involving enterprises, government, and financial institutions while considering consumers' influence. By solving for equilibrium points and conducting numerical simulations, we explore optimal strategy choices for each stakeholder. Our findings reveal that the success of enterprise low-carbon transition is contingent upon market dynamics and requires active cooperation from government, financial institutions, and the public. Furthermore, factors such as financial market efficiency and internal governance capacity significantly impact enterprises' transformation decisions by influencing low-carbon transition costs. Public feedback indirectly affects enterprise decisions through its influence on financial institutions' provision of green services. Additionally, gradual reduction of carbon quotas by government entities facilitates progress toward low-carbon transformation objectives.

Tripartite evolutionary game analysis of government reward and punishment mechanisms and agricultural resilience under a dual carbon context

PurposeUnder the “dual carbon” framework, the article explores the equilibrium points among the government, agricultural enterprises and village committees, and uses sensitivity analysis to reveal the dynamic factors affecting these stakeholders, thereby proposing methods to enhance agricultural disaster resilience.Design/methodology/approachThe article uses MATLAB to construct a game model for the three parties with interests: agribusiness, government and village council. It examines the stability of strategies among these entities. Through graphical simulation, the paper analyzes the sensitivity of agricultural enterprises carbon emissions and village committees’ rent-seeking behaviors in the decision-making process, focusing on significant factors such as government carbon tax and regulatory policies.FindingsA single government reward and punishment mechanism is insufficient to influence the strategic choices of enterprises and village committees. The cost of rent-seeking does not affect the strategic choices of enterprises and village committees. A key factor influencing whether the village committee engages in rent-seeking is the level of labor income of the village committee as an “intermediary”.Originality/valueThis paper focuses on the dynamic game between three stakeholders (the government, agricultural enterprises and village committees), seeking dynamic equilibrium and conducting sensitivity analysis through visualization to provide the government with optimal policy recommendations.

Blockchain Technology Adoption by Critical Stakeholders in Prefabricated Construction Supply Chain Based on Evolutionary Game and System Dynamics

Blockchain technology (BT) is a promising solution to address information asymmetry and trust issues in the prefabricated construction supply chain (PCSC). However, its practical application in PCSC remains limited under the influence of stakeholders’ adoption strategies. While previous studies have analyzed drivers and barriers to BT adoption, they often take a static view, neglecting the long-term dynamic decision-making interactions between stakeholders. This study addresses this gap by examining the interests of owners, general contractors, and subcontractors, and by developing a tripartite evolutionary game model to analyze the interaction mechanism of the strategy of adopting BT in PCSC. Additionally, a system dynamics simulation validates the evolution of stabilization strategies and examines the impact of key parameters. The results indicate that successful BT adoption requires technology maturity to surpass a threshold between 0.5 and 0.7, along with a fair revenue and cost-sharing coefficient between general contractors and subcontractors, ranging from 0.3 to 0.5 at the lower limit and 0.7 to 0.9 at the upper limit. Notably, general contractors play a pivotal role in driving BT adoption, acting as potential leaders. Furthermore, appropriate incentives, default compensation, and government subsidies can promote optimal adoption strategies, although overly high incentives may reduce owners’ willingness to mandate BT adoption. This study provides practical insights and policy recommendations for critical stakeholders to facilitate the widespread adoption of BT in PCSC.