Continuous Games Research Articles

An evolutionary game theory between finance innovation and financial regulation

ABSTRACT Internet finance is a new type of financial industry that is different from traditional finance. This study constructs an evolutionary game model between financial regulators and Internet financial institutions and discusses the strategy choices of the two participants under different circumstances. When analyzing the stable equilibrium strategy, the results show that when there are stable points in the game, Internet financial institutions tend to ‘excessive innovation’, while regulators’ strategies are affected by costs and benefits. When there is no stable point in the game, financial regulators and Internet financial institutions are in a continuous game of ‘moderate innovation – maintenance regulation – excessive innovation – strengthen regulation – moderate innovation.’ The study also provides policy recommendations to balance Internet financial innovation and regulation.

The [formula omitted]-core in a multi-objective game with set payoffs

For the cooperative equilibria in α-core form, the balancedness and coalitionally C−security of games with usual utilities are extended to the games with discontinuous set payoffs. The existence of α−core for these games is established, which can deduce some typical results for normal form games. For continuous games, a quasi-concave-like set payoff is introduced. Based on the introduced set payoffs, the existence of α−core is also obtained. Examples are given to verify these results. Comparison with existing results in references shows that the introduced conditions are new to guarantee the existence of α−core for games with set payoffs.

AARF: Autonomous Attack Response Framework for Honeypots to Enhance Interaction Based on Multi-Agent Dynamic Game

Highly interactive honeypots can form reliable connections by responding to attackers to delay and capture intranet attacks. However, current research focuses on modeling the attacker as part of the environment and defining single-step attack actions by simulation to study the interaction of honeypots. It ignores the iterative nature of the attack and defense game, which is inconsistent with the correlative and sequential nature of actions in real attacks. These limitations lead to insufficient interaction of the honeypot response strategies generated by the study, making it difficult to support effective and continuous games with attack behaviors. In this paper, we propose an autonomous attack response framework (named AARF) to enhance interaction based on multi-agent dynamic games. AARF consists of three parts: a virtual honeynet environment, attack agents, and defense agents. Attack agents are modeled to generate multi-step attack chains based on a Hidden Markov Model (HMM) combined with the generic threat framework ATT&CK (Adversarial Tactics, Techniques, and Common Knowledge). The defense agents iteratively interact with the attack behavior chain based on reinforcement learning (RL) to learn to generate honeypot optimal response strategies. Aiming at the sample utilization inefficiency problem of random uniform sampling widely used in RL, we propose the dynamic value label sampling (DVLS) method in the dynamic environment. DVLS can effectively improve the sample utilization during the experience replay phase and thus improve the learning efficiency of honeypot agents under the RL framework. We further couple it with a classic DQN to replace the traditional random uniform sampling method. Based on AARF, we instantiate different functional honeypot models for deception in intranet scenarios. In the simulation environment, honeypots collaboratively respond to multi-step intranet attack chains to defend against these attacks, which demonstrates the effectiveness of AARF. The average cumulative reward of the DQN with DVLS is beyond eight percent, and the convergence speed is improved by five percent compared to a classic DQN.

A socio-psychological portrait of a pathological gambler as a prerequisite for preventing gambling addiction (gambling disorder)

Gambling always carries risks for the player's mental health, as it can provoke the development of gaming addiction. A direct connection between the socio-psychological portrait of the player, his gaming behavior, and the risks of game addiction can be traced. The purpose of the work is to form a socio-psychological portrait of a "pathological" gambler. The work was performed based on the State Institution "Institute of Forensic Psychiatry of the Ministry of Health of Ukraine". Methods used: CAWI (Computer Assisted Web Interviewing) questionnaires in online gambling establishments; CAPI (Computer Assisted Per­sonal Interviews - server event tracking method) in land-based casinos (more than 9,000 people were inter­viewed); statis­tical (for selection and analysis of materials). A questionnaire specially developed by the authors with a point evaluation of the results (from 71 to 90 points) allows us to conclude that the interviewee is a pathological gamb­ler. For the first time in Ukraine, the survey was conducted exclusively among gamblers at gambling establishments. The obtained results made it possible to form a statistically reliable р<0.05 socio-psychological portrait of a pathological gambler, mostly men (87.7%) aged 25-35 years (52.4%) with secondary special (43.4%) or higher education (37.7%). In this group, 94% of people declared their inability to resist the desire to play, and 83.0% thought about stealing money to continue. Of pathological gamblers, 85.0% consider gaming as a means of earning money. All interviewed pathological gamers have experienced continuous gaming for more than 5 hours; 79.2% play almost every day. Such players in 95.0% noticed that they lost more money or spent more time than they planned, 96.0% felt culpable for the game, and 95.0% started the day with a game. Based on this portrait, the authors derived quantitative criteria that the organizer of gambling games can use to prevent gambling addiction among players within the framework of the application of the principles of responsible gaming.

Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players’ strategies and realized payoffs using Bayes’ rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games and enable us to characterize conditions under which learning leads to a complete information equilibrium. Funding: Financial support from the Air Force Office of Scientific Research [Project Building Attack Resilience into Complex Networks], the Simons Institute [research fellowship], and a Michael Hammer Fellowship is gratefully acknowledged.

A Necessary and Sufficient Condition Beyond Monotonicity for Convergence of the Gradient Play in Continuous Games

A Necessary and Sufficient Condition Beyond Monotonicity for Convergence of the Gradient Play in Continuous Games

Extended hours of video game play and negative physical symptoms and pain

BackgroundVideo games are a source of positive experiences and joy for many people. However, some interaction styles may lead to negative consequences. We aimed to examine the potential negative physical problems associated with video gaming behaviors. MethodData were from the 2022 International Gaming Study (IGS22), a cross-sectional survey of 955 individuals aged 18–94 (M = 46.10 [16.19]; 45% male) who played video games. We examined the association between prolonged continuous game play and physical problems identified in the past 12 months. ResultsPlaying video games for three or more hours in one session was associated with higher odds of negative physical symptoms (e.g., overall physical problems, OR = 2.80 [95% CI: 1.52–5.16, p < 0.001 and back or neck pain, OR = 2.19 [95% CI: 1.28–3.74], p < 0.01). Those who met the Ten-Item Internet Gaming Disorder Test (IGDT-10) threshold for internet gaming disorder had four times higher odds of physical problems. The positive associations between extended gaming behavior and physical symptoms were not moderated by age, gender, plans to be a professional player, or meeting the diagnostic criteria for internet gaming disorder. ConclusionsPhysical problems and pain occur disproportionately in individuals who engage in extended hours of continuous game play, including risk, women, individuals in older age groups, and those without internet gaming disorder. Video game players across the demographic spectrum should be alerted to these risks,

Solutions to the problem of differential games with electric oscillations by finite difference methods

The article deals with the issues of electromagnetic processes from the point of view of application technology. The problem of voltage normalization in lines in the presence of opposing external forces is studied. The process of realizing the solution of this problem is based on the introduction of a mathematical model of electromagnetic processes occurring in lines as a continuous differential pursuit game described by hyperbolic equations. The finite difference method transforms the continuous pursuit problem into a discrete game. Sufficient conditions are obtained getting into neighbourhood. And with the help of a well-known a priori estimate for the difference between the solutions of a continuous differential and the corresponding discrete game, sufficient conditions are obtained for the possibility of completing the pursuit of a continuous game. A pursuer outputs terminal set, which is voltage normalization.

Computing Bayes–Nash Equilibrium Strategies in Auction Games via Simultaneous Online Dual Averaging

Determining equilibria in auction games is computationally hard in general, and no exact solution theory is known. We introduce an algorithmic framework in which we discretize type and action space and then learn distributional strategies via online optimization algorithms. We show that the equilibrium of the discretized auction game approximates an equilibrium in the continuous game. In a wide variety of auction games, we provide empirical evidence that the approach approximates the analytical (pure) Bayes–Nash equilibrium closely. In standard models in which agents are symmetric, we find equilibrium in seconds. The method allows for interdependent valuations and different types of utility functions, and it can be used to find equilibrium in auction markets and beyond.

Hide-and-Seek Game with Capacitated Locations and Imperfect Detection

We consider a variant of the hide-and-seek game in which a seeker inspects multiple hiding locations to find multiple items hidden by a hider. Each hiding location has a maximum hiding capacity and a probability of detecting its hidden items when an inspection by the seeker takes place. The objective of the seeker (respectively, hider) is to minimize (respectively, maximize) the expected number of undetected items. This model is motivated by strategic inspection problems, where a security agency is tasked with coordinating multiple inspection resources to detect and seize illegal commodities hidden by a criminal organization. To solve this large-scale zero-sum game, we leverage its structure and show that its mixed-strategy Nash equilibria can be characterized using their unidimensional marginal distributions, which are pure equilibria of a lower dimensional continuous zero-sum game. This leads to a two-step approach for efficiently solving our hide-and-seek game: First, we analytically solve the continuous game and derive closed-form expressions of the equilibrium marginal distributions. Second, we design a combinatorial algorithm to coordinate the players’ resources and compute equilibrium mixed strategies that satisfy the marginal distributions. We show that this solution approach computes a Nash equilibrium of the hide-and-seek game in quadratic time with linear support. Our analysis reveals novel equilibrium behaviors driven by a complex interplay between the game parameters, captured by our closed-form solutions. Funding: This work was supported by the Georgia Tech Stewart Fellowship and the Georgia Tech New Faculty Start Up Grant. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2023.0012 .

User Review Analysis of Microtransactions in Freemium Massively Multiplayer Online Role-Playing Games Using Structural Topic Modeling

This study investigated player responses to microtransactions in freemium Massively multiplayer online role-playing games (MMORPG), specifically focusing on the game LostArk using English language review data. To this end, structural topic modeling was employed and the following six microtransaction-relevant topics were identified: microtransactions, developer issues, real money trade (RMT), random number generator (RNG) upgrade system, game content, and collectibles &amp; adventure. The first four topics were classified as being "not recommended". However, the proportions of microtransaction-related topics were relatively lower than the other topics. Additionally, this study did not extract keywords related to unfairness and unethical issues in previous microtransaction research. The last two topics, game content, and collectibles &amp; adventure were "recommended" topics, indicating positive functions of microtransactions such as enhancing the game experience by purchasing virtual items. Moreover, it was found that players who do not engage in microtransactions can still be satisfied through continuous game content updates. Additionally, an examination of the interaction effect between time and recommendation status revealed that while the frequency with which the six microtransaction-related topics were mentioned increased over time in the reviews, the ratio of recommendations to non-recommendations varied differently. This study contributes to game-related research by revealing players' authentic opinions on microtransactions in freemium MMORPGs, thereby providing practical implications for game companies.

Consistent Conjectural Variations Equilibria: Characterization &amp; Stability for a Class of Continuous Games

Consistent Conjectural Variations Equilibria: Characterization &amp; Stability for a Class of Continuous Games

A Hybrid Generative Adversarial Network Model for Ultra Short-Term Wind Speed Prediction

To improve the accuracy of ultra-short-term wind speed prediction, a hybrid generative adversarial network model (HGANN) is proposed in this paper. Firstly, to reduce the noise of the wind sequence, the raw wind data are decomposed using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Then the decomposed modalities are entered into the HGANN network for prediction. HGANN is a continuous game between the generator and the discriminator, which in turn allows the generator to learn the distribution of the wind data and make predictions about it. Notably, we developed the optimized broad learning system (OBLS) as a generator for the HGANN network, which can improve the generalization ability and error convergence of HGANN. In addition, improved particle swarm optimization (IPSO) was used to optimize the hyperparameters of OBLS. To validate the performance of the HGANN model, experiments were conducted using wind sequences from different regions and at different times. The experimental results show that our model outperforms other cutting-edge benchmark models in single-step and multi-step forecasts. This demonstrates not only the accuracy and robustness of the proposed model but also the applicability of our model to more general environments for wind speed prediction.

Generation Method for Shaded Relief Based on Conditional Generative Adversarial Nets

Relief shading is the primary method for effectively representing three-dimensional terrain on a two-dimensional plane. Despite its expressiveness, manual relief shading is difficult and time-consuming. In contrast, although analytical relief shading is fast and efficient, the visual effect is quite different from that of manual relief shading due to the low degree of terrain generalisation, inability to adjust local illumination, and difficulty in exaggerating and selective representation. We introduce deep learning technology to propose a generation method for shaded relief based on conditional generative adversarial nets. This method takes the set of manual relief shading-digital elevation model (DEM) slices as a priori knowledge, optimises network parameters through a continuous game of “generation-discrimination”, and produces a shaded relief map of any region based on the DEM. Test results indicate that the proposed method retains the advantages of manual relief shading and can quickly generate shaded relief with quality and artistic style similar to those of manual shading. Compared with other networks, the shaded relief generated by the proposed method not only depicts the terrain clearly but also achieves a good generalisation effect. Moreover, through the use of an adversarial structure, the network demonstrates stronger cross-scale generation ability.

A New Methodology for Solving Piecewise Quadratic Fuzzy Cooperative Continuous Static Games

This paper deals with n -players fuzzy cooperative continuous static games (FCCSGs). The cost function coefficients are characterized by piecewise quadratic fuzzy numbers. One of the best approximate intervals, namely, the inexact interval of the piecewise quadratic fuzzy number is used. Furthermore, we proposed a new methodology based on the weighted Tchebycheff method to solve CCSG with n -players. The advantages of the approach are the ability to enable the decision-maker to have satisfactory solution and applied for different real-world problems with various types of fuzzy numbers. There is also a stability set of the first kind without differentiability for the optimal compromise solution that was found. In the future, the proposed methodology could be used in different types of real-world problems and multiple decision-makers. This proposed work can also be extended to hypersoft set, fuzzy hypersoft sets, intuitionistic hypersoft sets, bipolar hypersoft sets, and pythagorean hypersoft sets. At the end, a numerical example is given to demonstrate the computational efficiency of the proposed method.

Dynamic Impact of the Perceived Value of Public on Panic Buying Behavior during COVID-19

In this paper, an evolutionary game model for the development of panic buying events in COVID-19 is constructed by studying the dynamic process of the public and the government adjusting their strategic choices and playing a continuous game. This paper uses regret theory to depict the public’s perceived value of the items in the panic buying situation, describes the characteristics of each stage of the rumors spreading process and the evolution process of panic buying events, and introduces the variable of public critical ability to measure the public’s panic buying willingness. The results show that the government’s intervention measures according to the characteristics of different stages can effectively control the continuous fermentation time and influence the scope of panic buying events. The implementation of the government’s rumor-refutation strategy will also significantly affect the volume of public panic buying, which will help the government timely understand the public’s epidemic prevention needs in COVID-19, relieve public panic, and provide a basis for the effective management and scheduling of emergency supplies.

On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

This study attempts to introduce continuous static games with fuzzy parameters. Piecewise quadratic fuzzy numbers (PQFNs) are used to represent the fuzzy parameters. The close interval approximation of the PQFNs, which is one of the most accurate approximations, is applied. To overcome the problem, Stackelberg leaders with min-max follower’s solutions are examined. The given solution is accompanied by a parametric analysis. An algorithm for identifying the first-kind stability set is presented. Finally, to demonstrate and clarify the method’s steps, a numerical example is given

Lobbist Organizations as Conflict Resolution Institute

The study specified in this article is devoted to an important problem in the modern state management practice of Russia - the study of conflict resolution of such a politically significant institute as lobbist organizations. The authors consider the phenomenon from a socio-economic, organizational, political perspective, which is categorized through the conceptual series “government relations - public administration - political institute” and is scientifically justified. The analysis methodology is based on the symbiosis of the neoinstitutional approach and game theory (continuous games) with the rent-oriented behavior of players. The urgency of the problems of lobbist organizations is due to the prolonged political and managerial crisis, both in Europe, the USA and in the countries of Asia. The scientific novelty of this paper is determined by the use of the neoinstitutional approach and the theory of games with the rent-oriented behavior of players as the fundamental methodological direction of the symbiosis when considering lobbist organizations as conflict resolution institutes with all the functions and rules of behavior in a political game inherent in them. The study will be based on the use of such empirical methods as analysis of documents and cases, which justifies the use of a qualitative methodology. The article is one of the first in Russian empirical practice related to the problem of lobbist organizations and, undoubtedly, will make a significant contribution to the study of the conflict logical specific nature of this socio-political institute. The article is part of the grant of the Russian Foundation for Basic Research No. 19-011-31376opn “Conflict logical audit as a system of technologies for influencing ideological youth extremism in modern Russia”.

Toward the Nash Equilibrium Solutions for Large-Scale Pentagonal Fuzzy Continuous Static Games

This study aims to characterize and clarify a pentagonal fuzzy continuous static game (PF-CSG) that constraints and cost functions are fuzzy numbers. Pentagonal fuzzy numbers characterize their fuzzy parameters. The α − Pareto optimal solution concept has specified. The decomposition approach has applied to decompose the problem into subproblems each of them having smaller and independent subproblems. In addition, the Nash equilibrium solution concept was used to obtain the solutions of these subproblems. The advantages of this study are the players independently without collaboration with any of the others and that each player seeks to minimize the cost function. Also, the information available to each player consists of the cost function and constraints. An illustrated numerical example has discussed for proper understanding and interpretation of the proposed concept.

Monitoring Internal and External Load During Volleyball Competition.

The aim of this study was to identify the relationships between continuously measured internal and external load variables during volleyball competition. A total of 8 male elite volleyball athletes (Belgian Liga A and Liga B) were monitored during official competition matches. In total, 63 individual measurements are included in this study. The authors used heart-rate (HR) data as internal load and accelerometer-based activity as external load. Data were recorded at a sampling frequency of 1Hz using wearable technology during official competition. Workload during continuous game play and individual jumps performed while serving and spiking (selected by means of video analysis) were studied using correlation analysis and dynamic time-series modeling. Significant linear correlations were observed between peak acceleration and maximal HR of individual serves (ρ = .62; P = 1.6e-5) and spikes (ρ = .49; P = 1.2e-3) that were performed during the warm-up. These same actions performed during the match did not show significant correlations. The correlation between the mean HR and mean activity throughout the entire match was also found to be significant (ρ = .67; P = 2.0e-9). With respect to the time-series models, the mean value for the goodness of fit (RT2) between HR and activity was equal to .83 and .67 for the individual actions and the entire matches, respectively. The results show that there are strong relationships between internal and external load during volleyball competition. Second-order transfer function models are capable of explaining the main dynamics of HR (internal load) in response to accelerometer-based activity (external load). Time-series analysis of continuously measured workload is proposed for use in practice.