Dynamic Game Research Articles

Payment schemes for resource reallocation in hierarchical medical system: Fee-for-capacity versus performance payment

This study explores resource reallocation, or capacity sinking, in a hierarchical medical system that includes a healthcare funder, a comprehensive hospital, a community hospital, and patients with varying perceptions of different hospital levels. To help the funder better coordinate the process and induce a comprehensive hospital to willingly sink its high-quality medical resources to a community hospital, we design and evaluate two payment schemes: Fee-For-Capacity (FFC) scheme and Performance Payment (PP) scheme. In the FFC scheme, the funder pays a unit capacity sinking price to the comprehensive hospital. In the PP scheme, the sinking price is paid only if the community hospital increases the rate of patient visits. By considering different parties’ decision-making behaviors, we develop a sequential game model within a queuing framework to determine equilibrium results in terms of the patient arrival rate at each hospital, the community hospital’s capacity planning, the comprehensive hospital’s capacity sinking rate, and the funder’s capacity sinking price. Our study indicates that the FFC scheme outperforms the PP scheme in terms of social welfare, patient utility, and waiting time when the budget is low or the funder’s concern about patient utility is relatively high or low. However, both schemes are suboptimal when the budget and the funder’s concern degree are medium. We find that a hybrid payment scheme can alleviate the drawbacks of FFC and PP and help achieve system optimum.

A study on supply chain information sharing strategy for emission reduction investment in electronic products based on game theory

By analyzing the competition between electronic product manufacturers and retailers in pricing, a dynamic game model is constructed. Using backward induction, the optimal choices and maximum profits under equilibrium conditions are determined. Finally, the constructed model is subjected to data simulation by setting numerical values for relevant parameters to analyze the effects of environmental emission reduction value on the supply chain and the information sharing value of each member. The following conclusions are drawn: when the emission reduction efficiency of manufacturers or the sensitivity of the market to environmental protection is high, the improvement effect of information sharing will outweigh its bilateral marginal effect. Retailers will voluntarily share all demand information and achieve a win-win situation in the supply chain.

Guaranteed cost solution for discrete-time uncertain/nonlinear dynamic games

Motivated by an example of fiscal and monetary policy interaction of a national economy, the problem of uncertain/nonlinear two players discrete-time noncooperative games is investigated. Since the models of the systems are uncertain, the notion of Nash equilibrium solution is not suitable, instead, new Nash guaranteeing strategies and Nash guaranteed costs are defined. The system’s uncertainties and/or nonlinearities are assumed to be of quadratically bounded type. First, conditions of the Nash guaranteeing strategies are derived for general uncertain nonlinear systems. These results are specified for systems that have linear nominal part and quadratic cost functions. Approximate solutions are obtained by tractable quadratic matrix inequalities. To illustrate the application of the proposed method, two numerical examples are given.

Gamification as a panacea to workplace cyberloafing: an application of self-determination and social bonding theories

PurposeGamification has been constantly demonstrated as an effective mechanism for employee engagement. However, little is known about how gamification reduces cyberloafing and the mechanism by which it affects cyberloafing in the workplace. This study draws inspiration from self-determination and social bonding theories to explain how game dynamics, namely, personalised challenges, social interactivity and progression status, enhance tacit knowledge sharing behaviour, which, in turn, reduces cyberloafing. In addition, the study also examines the negative moderating effect of fear of failure on the positive relationship between game dynamics and tacit knowledge sharing.Design/methodology/approachUsing a sample of 250 employees from information technology organisations, the study employed a 3-wave study to examine the conditional indirect effects.FindingsThe results ascertain that tacit knowledge sharing plays a central role in the relationship between gamification and cyberloafing. Further, game dynamics positively influenced tacit knowledge sharing, which in turn reduced cyberloafing. Especially, social interactivity and progression status greatly reduced cyberloafing behaviour when the fear of failure was low.Originality/valueThis study is one of the initial studies that suggest gamification as a progressive tool to reduce workplace cyberloafing behaviours. It utilises a problematisation approach to analyse and criticise the in-house assumptions regarding cyberloafing prevention measures. Further, the study proposes a conceptual model explaining the link between gamification and cyberloafing through alternate assumptions.

Evaluating Stakeholders’ Decisions in A Blockchain-Based Recycling Construction Waste Project: A Hybrid Evolutionary Game and System Dynamics Approach

To promote efficient construction waste recycling and reuse, a novel waste management approach based on blockchain technology was introduced to the industry. However, adopting blockchain platforms in construction waste recycling and reuse may impact the behavioral strategies of stakeholders and impede the prediction of the specific impacts of stakeholders’ decisions. Accordingly, this study addresses two primary questions: (1) What are the collaborative framework and the behavioral evolution trends of multiple stakeholders within the context of blockchain? (2) How can the behavioral strategies of multiple stakeholders be systematically coordinated to achieve efficient construction waste recycling and reuse driven by blockchain? To answer these questions, a tripartite game model combined with system dynamics was constructed. In this model, we aimed to elucidate the internal organizational framework, analyze the dynamic evolution process, and assess the influence of decisions made by multiple stakeholders at the individual level. It also offers corresponding policy recommendations for efficient construction waste recycling and reuse driven by blockchain at the system level. This study offers three innovations. First, it considers the decision-making of multiple stakeholders as an interdependent and coevolutionary process to overcome the defects of analyzing only one type of participant. Second, in contrast to the static analysis method, it employs a dynamic system approach to deeply analyze the evolving structures of blockchain-based projects. Third, it provides a theoretical framework for the practical implementation of blockchain-driven platforms in managing construction waste recycling and reuse, thus fostering effective policy development and management practices. This framework aims to promote sustainable development in construction waste recycling and reuse projects in China as well as globally.

ϵ$$ \epsilon $$‐Nash equilibrium of non‐cooperative Lagrangian dynamic games based on the average sub‐gradient robust integral sliding mode control

SummaryIn non‐cooperative multi‐player games, an average sub‐gradient (ASG) strategy for finding an ‐Nash equilibrium. For convex (but not necessarily strictly convex) individual cost functions, the function convergence of the multi‐player game is demonstrated. Applying Tanaka's formula that characterizes the Nash equilibrium leads to finding the strategy for each player. A min‐max formulation defines the corresponding solution for each player. The main result is proving the reachability of the desired regime, obtaining an explicit upper bound for Tanaka's function decrement. Detailed analyses for two‐player and multi‐player games are developed. For a class of two‐player games with a convex performance function, a set of numerical studies shows the applicability of the proposed method. So, the tracking of the arm in 3‐links robot is considered as an illustrative example.

The Impact of Data Federation Technology on Supply Chain Financing Based on Dynamic Evolutionary Game Analysis

Digital technology has been applied in supply chain financing(SCF), which ensures small and medium-sized enterprises (SMEs) have significantly better access to get loans. Digital SCF is established on the basis that financing companies need to provide global data to the financial service providers. However, some enterprises may be unwilling to share information for financing suppliers due to data security which affects the development of such new SCF pattern. In this paper, we propose a solution scheme based on data federation technology and evaluate the feasibility of data federation technology in SCF by dynamic evolutionary game analysis. A trustworthy financing service model is established based on data federation technology and the model highlights the characteristic of data availability but invisibility. Evolutionary simulation analysis was conducted on factors that affect data federation technology applied in SCF. The findings indicate that SMEs can get effective financial services if we use data federation technology to enhance the mutual data trust between the two parties.

An empirical Bayes approach for estimating skill models for professional darts players

Abstract We perform an exploratory data analysis on a data-set for the top 16 professional darts players from the 2019 season. We use this data-set to fit player skill models which can then be used in dynamic zero-sum games (ZSGs) that model real-world matches between players. We propose an empirical Bayesian approach based on the Dirichlet-Multinomial (DM) model that overcomes limitations in the data. Specifically we introduce two DM-based skill models where the first model borrows strength from other darts players and the second model borrows strength from other regions of the dartboard. We find these DM-based models outperform simpler benchmark models with respect to Brier and Spherical scores, both of which are proper scoring rules. We also show in ZSGs settings that the difference between DM-based skill models and the simpler benchmark models is practically significant. Finally, we use our DM-based model to analyze specific situations that arose in real-world darts matches during the 2019 season.

Sophisticated reasoning, learning, and equilibrium in repeated games with imperfect feedback

AbstractWe analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated—but impatient—expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning—that is, the ability, in the limit, to exactly forecast the sequence of future observations—thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game.

On the optimal game control in the DC microgrid systems

AbstractThis paper introduces static and dynamic competitive optimal control of DC/DC converters in DC microgrids based on game theory considering mutual effects. Using static and dynamic game theories, the conditions for competitive optimal control of DC/DC converters in Nash equilibrium with static and dynamic states are determined. Also, to reduce the complexity in the design of competitive optimal control of DC/DC converters due to the bilinear dynamic model of the system, generalized objective functions are considered. The competitive optimal controls using the Lyapunov and Riccati equations are determined to track the system trajectory to Nash equilibrium. Also, the numerical and experimental results are presented and compared in several cases. The results show that the competitive optimal control of the DC/DC converters in the DC microgrids can effectively improve the performance of the system.

Research on dynamic game operation behavior of multi‐oligopoly car‐sharing operators considering off‐peak pricing factors

AbstractIn the practical evolution of shared vehicle systems, numerous societal factors come into play, such as inadequate parking infrastructure, battery capacity, and the budget for technological improvement. This study integrates the operational realities of shared vehicle systems with governmental carbon emission reduction policies and “double control” initiatives. Considering various perturbations, the paper constructs a Stackelberg short‐term model among diverse oligopolistic shared vehicle operators with technique sharing. It also develops a long‐term repeated game framework to scrutinize the impact of pertinent parameters on operators' decision variables and profits, along with system stability and complexity. The findings, elucidated through numerical analyses, reveal that the burgeoning sensitivity of users to energy conservation augments the overall shared vehicle market. The technique sharing mechanism boosts the benefit of the whole group of shared vehicle operators while diminishing the start‐up operators' revenue. In the long term, however, excessive price adjustments by SEV operators may lead to market chaos and profit erosion. Conversely, enhancing the adjustment coefficient of technological level levels by start‐up SEV2 operators may result solely in their own decision‐making becoming unmanageable. Finally, we found that both the methods of external force feedback control and parameter control are effective in restoring the chaotic market to stability.

In-depth Review: Analysis of Soccer Players' Physical Condition in Game Dynamics

In-depth Review: Analysis of Soccer Players' Physical Condition in Game Dynamics

Research on dynamic pricing and coordination model of fresh produce supply chain based on differential game considering traceability goodwill

This study aims to solve the current pricing and coordination problems in the fresh produce supply chain by proposing a dynamic pricing and coordination differential game model based on traceability goodwill to optimize the operational efficiency and profitability of the supply chain. Freshness and traceability are critical consumer trust and brand value factors incorporated into the dynamic pricing and coordination model in the agricultural supply chain. The research methodology of this paper integrates critical factors such as supply chain cost and market demand to construct a comprehensive differential game model. It also highlights the motivation of dynamic pricing strategy and coordination mechanism based on traceability goodwill. Through traceability goodwill, operating companies can better assess and manage product quality and improve consumer trust in agricultural products, thus enhancing brand value. The dynamic pricing strategy based on traceability goodwill can flexibly adjust prices according to changes in the quality characteristics of agricultural products and market demand, realizing a dynamic balance between supply and demand. On the other hand, the mutual cost-sharing and coordination mechanism promotes the synergy between the various links of the supply chain. It improves overall efficiency through cooperation coo, coordination, and other means. The validity and reliability of the model are verified through numerical simulation experiments. The numerical simulation results show that the dynamic pricing and coordination model based on traceability will significantly improve supply chain efficiency and profitability compared with the traditional model. Specifically, the interests of supply chain participants are balanced, and the overall supply chain operational efficiency is improved. The main contribution of this study is to propose a dynamic pricing and coordination model based on traceability goodwill and verify its superiority through numerical simulation experiments. This study provides a valuable reference for fresh agricultural products supply chain management and offers new ideas for improving supply chain efficiency and profitability.

Evolutionary game selection creates cooperative environments.

The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how strategic decisions coevolve with the environment has so far mostly been overlooked. Here, we consider a game selection model where not only the strategies but also the game can change over time following evolutionary principles. Our results show that coevolutionary dynamics of games and strategies can induce novel collective phenomena, fostering the emergence of cooperative environments. When the model is taken on structured populations the architecture of the interaction network can significantly amplify pro-social behavior, with a critical role played by network heterogeneity and the presence of clustered groups of similar players, distinctive features observed in real-world populations. By unveiling the link between the evolution of strategies and games for different structured populations, our model sheds new light on the origin of social dilemmas ubiquitously observed in real-world social systems.

Position Matters: Play a Sequential Game to Detect Significant Communities

Position Matters: Play a Sequential Game to Detect Significant Communities

High-stakes failures of backward induction

We examine high-stakes strategic choice using more than 40 years of data from the American TV game show The Price Is Right. In every episode, contestants play the Showcase Showdown, a sequential game of perfect information for which the optimal strategy can be found through backward induction. We find that contestants systematically deviate from the subgame perfect Nash equilibrium. These departures from optimality are well explained by a modified agent quantal response model that allows for limited foresight. The results suggest that many contestants simplify the decision problem by adopting a myopic representation, and optimize their chances of beating the next contestant only. In line with learning, contestants' choices improve over the course of our sample period.

Orbital Impulsive Pursuit–Evasion Game Formulation and Stackelberg Equilibrium Solutions

The spacecraft pursuit–evasion game in orbit with impulsive maneuvers is investigated based on dynamic game theory. First, the game models are developed progressively from the single-impulse game to the multi-impulse game. In the models, the two-sided optimal strategies of both players form a Stackelberg equilibrium in single-impulse games and constitute a multistage Stackelberg equilibrium in multi-impulse games. Then, the optimality necessary conditions for the two equilibriums are derived and simplified as two multipoint boundary value problems (MPBVPs). To handle the complicated MPBVPs, a rolling backward induction based on the Lambert algorithm accompanied by a homotopy shooting method is proposed to solve the equilibrium solutions. Simulations showed the effectiveness of the proposed methods and verified that the obtained solutions are the (multistage) Stackelberg equilibrium. Meanwhile, the differences between the Stackelberg equilibrium and the Nash equilibrium are illustrated in detail. Finally, an analysis of the influence of the observation delay on the game results is provided.

Video game characters and transmedia storytelling: The dynamic game character By JoleenBlom, Amsterdam: Amsterdam University Press. 2023. pp. 208. €104.00 (hardcover)

Video game characters and transmedia storytelling: The dynamic game character By JoleenBlom, Amsterdam: Amsterdam University Press. 2023. pp. 208. €104.00 (hardcover)

Unbending strategies shepherd cooperation and suppress extortion in spatial populations

Evolutionary game dynamics on networks typically consider the competition among simple strategies such as cooperation and defection in the Prisoner’s Dilemma and summarize the effect of population structure as network reciprocity. However, it remains largely unknown regarding the evolutionary dynamics involving multiple powerful strategies typically considered in repeated games, such as the zero-determinant (ZD) strategies that are able to enforce a linear payoff relationship between them and their co-players. Here, we consider the evolutionary dynamics of always cooperate (AllC), extortionate ZD (extortioners), and unbending players in lattice populations based on the commonly used death-birth updating. Out of the class of unbending strategies that can foster reciprocal cooperation and fairness among extortionate players, we consider a particular candidate, pre-optimized through the machine-learning method of particle swarm optimization (PSO), called PSO Gambler. We derive analytical results under weak selection and rare mutations, including pairwise fixation probabilities and long-term frequencies of strategies. In the absence of the third unbending type, extortioners can achieve a half-half split in equilibrium with unconditional cooperators for sufficiently large extortion factors. However, the presence of unbending players fundamentally changes the dynamics and tilts the system to favor unbending cooperation. Most surprisingly, extortioners cannot dominate at all regardless of how large their extortion factor is, and the long-term frequency of unbending players is maintained almost as a constant. Our analytical method is applicable to studying the evolutionary dynamics of multiple strategies in structured populations. Our work provides insights into the interplay between network reciprocity and direct reciprocity, revealing the role of unbending strategies in enforcing fairness and suppressing extortion.

Economic optimization scheduling of virtual power plants considering an incentive based tiered carbon price

Against the backdrop of China's carbon peak and carbon neutrality goals, the use of virtual power plants for electricity economic dispatch has gradually become a research hotspot. The virtual power plant includes both supply and demand sides. If the inherent conflicts of interest between both parties cannot be effectively addressed, there are significant hidden dangers in the sustainable operation of the virtual power plant. On the basis of existing research, this article constructs a regional virtual power plant. With the goal of maximizing supply and demand utility, a two-stage Stackelberg dynamic game model was established between virtual power plant operators and users in the electricity market and carbon trading market mechanisms, and an incentive based hierarchical carbon price constraint was designed in the optimization model. In the model constructed in this article, the operator of a virtual power plant will consider environmental benefits based on expected returns, adjust the output of controllable units to change the electricity supply strategy, and formulate a pricing strategy. At the same time, users will adjust their electricity consumption strategy based on their own electricity consumption characteristics, and both will achieve a game equilibrium. Based on the optimization results, this article conducted a sensitivity analysis on the incentive coefficient of graded carbon prices and obtained the optimal incentive coefficient under the case conditions. The research results indicate that the model can coordinate and meet the interests and needs of both the power generation and consumption sides, and the implementation of incentive based hierarchical carbon pricing strategies has certain advantages compared to traditional carbon pricing strategies in different user types scenarios. The research conclusion of this article has good reference value for the sustainable green operation of virtual power plants.