Dynamic Game Research Articles

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.

Location and Price Competition on a Uniform Path with Different Pricing Policies

AbstractThis paper models duopolistic competition between an online retailer and a physical store retailer with the online retailer modelled as a firm with uniform delivered pricing policy and the physical store as a firm with a mill pricing policy. Both firms seek to maximize their respective profits through an appropriate choice of location and price. The market is assumed to be given by a “uniform path” - a tree whose node weights and arc lengths are equal. Modelling reality, we consider two alternate types of transportation costs faced by the online retailer: either dependent on the relative location of the firm and a customer or independent of it. Beginning with the framework of a Stackelberg, i.e., sequential game, optimal location and price strategies are analytically derived for both sequences of market entry by the two competitors. Cases in which the leader faces the first entry paradox or can become a monopolist by strategically deterring entry by the follower are delineated. Thereafter, Nash Equilibrium solutions to the simultaneous game are identified. Salient insights from the results include: (a) the competitive pressure faced by the physical store in the presence of online competition (b) the inability of an online retailer to compete in “large” markets under the first type of transportation cost and (c) the advantage to the physical retailer of being a market leader.

Open access publishing and quantum game theory under modified EWL scheme

Game theory deals with the strategies of rational players to obtain the best possible outcomes for a player in a game. Quantum game theory is an extension of classical game theory, where players can adopt quantum strategies to maximize their payoff advantage. In quantum game theory, we have two prominent quantization schemes, namely the Eisert Wilkens-Lewenstein (EWL) scheme and the Marinatto Weber (MW) scheme. Recently, modified EWL scheme is being used to study the game dynamics. In the era of digital information revolution, scientists have unrestricted access to most of the scientific information. Different scientific disciplines prefer different paths of publication either open access or traditional. Taking this as a framework, we model an open-access game played by scientists with open access and traditional publishing as their strategies. In this work, we study these publication patterns using the quantum game theory approach under the modified EWL quantization scheme. Specifically, we investigate the role of entangling operators and players’ strategies in maximizing the payoff (reputation) for the scientists playing in the open-access game.

Evolutionary Dynamics of Passive Housing Initiatives in New Rural Construction

In the context of China’s ambitious dual carbon goals, this study introduces an innovative reward–penalty incentive mechanism, grounded in evolutionary game theory, to develop a tripartite evolutionary game model concerning the construction of passive rural housing. This research meticulously analyzes the equilibrium and stability strategies of all involved parties and employs data simulation to examine the influence of varying parameters on the game dynamics. Our findings reveal that the government’s cost–benefit calculations significantly influence its decisions regarding passive housing initiatives. The study identifies optimal cost and benefit strategies for various developmental phases. Furthermore, the level of governmental rewards and penalties plays a crucial role in determining whether enterprises and farmers opt for passive housing solutions. The study establishes the efficacy of different incentive schemes at various stages. Importantly, the economic interests of enterprises and farmers are pivotal in their decision-making process regarding passive housing. The study advocates for a comprehensive set of measures to safeguard these interests, with a special emphasis on protecting farmers. In conclusion, this research offers substantial guidance for policy decisions aimed at transforming existing rural housing into passive housing, thereby aligning with China’s environmental and sustainability objectives.

Evolutionary dynamics of any multiplayer game on regular graphs

Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n-strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs.

Game Theory and Adversarial Machine Learning: Analyzing Strategic Interactions in Cybersecurity

When it comes to cybersecurity, the way that attackers and defenders work together strategically is becoming more and more like how games work in general. Adversarial machine learning (AML) has become an important area of hacking. In AML, attackers use complex methods to avoid being caught and take advantage of flaws in machine learning models. The goal of this study is to give a full picture of how strategies combine in cybersecurity by looking at where game theory and AML meet. You can think of the strategic exchanges in cybersecurity as a game between attackers and defenders. Defenders want to keep systems and data safe, and enemies want to break into them for bad reasons. In this game, players have to make a lot of decisions. Defenders have to think ahead and prepare for possible attacks, while attackers change their plans all the time to avoid being caught and take advantage of defenses' weaknesses. Game theory gives us a way to formally model these interactions, which lets us look at the best tactics and results that are in balance. During AML, defenders use machine learning models to find and stop security risks, while attackers change these models using methods like escape attacks, poisoning attacks, and model inversion attacks. In these hostile tactics, there is a strategic element added to cybersecurity, where defenders must think about the goals and skills of attackers when creating and using defenses. This paper looks at the research that has already been done on using game theory to study hacking and how these models can be used to study how strategies combine in AML. It talks about different types of games, like rigid and dynamic games, and what they mean for protecting against threats from other players. Besides that, it looks into how uneven knowledge, doubt, and strategy learning affect the results of computer games. This paper helps us understand the strategy problems that both attackers and defenders face in cybersecurity better by combining game theory with AML. It shows how important it is to think strategically and build weapons that can change to deal with risks that change, and it sets the stage for future study in this field, which is changing very quickly.

Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players

In this research article, we explore the complex dynamics of a quantum Stackelberg game and its chaos control involving players with heterogeneous expectations. We utilize the Iqbal & Toor scheme to quantize the classical Stackelberg game and observe that the first mover advantage is diminished in the quantum version of the game. By examining the game from an evolutionary perspective, where the leader firm employs bounded rational expectations and the follower firm adopts adaptive expectations, we discover that the quantum Stackelberg game exhibits complex behaviors, such as cyclic and chaotic states. The local stability of the quantum game depends on the initial state of the game. Additionally, the occurrence of chaos is delayed in the quantum game. To further investigate, we implement the time-delayed feedback method to control the chaos in the quantum game and demonstrate that the techniques used for controlling the classical game are still effective in the quantum game.