Search results for: stochastic game

Authors: Andre M. Carvalho, Pedro Sebastiao

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This article is based on a dissertation that intends to analyze and make a model, intelligently, algorithms based on stochastic processes of a gamification application applied to marketing. Gamification is used in our daily lives to engage us to perform certain actions in order to achieve goals and gain rewards. This strategy is an increasingly adopted way to encourage and retain customers through game elements. The application of gamification aims to encourage children between 6 and 10 years of age to have healthy habits and the purpose of serving as a model for use in marketing. This application was developed in unity; we implemented intelligent algorithms based on stochastic processes, web services to respond to all requests of the application, a back-office website to manage the application and the database. The behavioral analysis of the use of game elements and stochastic processes in children’s motivation was done. The application of algorithms based on stochastic processes in-game elements is very important to promote cooperation and to ensure fair and friendly competition between users which consequently stimulates the user’s interest and their involvement in the application and organization.

Keywords: engage, games, gamification, randomness, stochastic processes

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Authors: Alexander Aurell

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One of the latest trends in the modeling of human crowds is the mean-field game approach. In the mean-field game approach, the motion of a human crowd is described by a nonstandard stochastic optimal control problem. It is nonstandard since congestion is considered, introduced through a dependence in the performance functional on the distribution of the crowd. This study extends the class of mean-field pedestrian crowd models to allow for non-local congestion and arbitrary, but finitely, many interacting crowds. The new congestion feature grants pedestrians a 'personal space' where crowding is undesirable. The model is treated as a mean-field type game which is derived from a particle picture. This, in contrast to a mean-field game, better describes a situation where the crowd can be controlled by a central planner. The latter is suitable for decentralized situations. Solutions to the mean-field type game are characterized via a Pontryagin-type Maximum Principle.

Keywords: congestion, crowd dynamics, interacting populations, mean-field approximation, optimal control

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Authors: Abderrahim Elmoataz

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More and more contemporary applications involve data in the form of functions defined on irregular and topologically complicated domains (images, meshs, points clouds, networks, etc). Such data are not organized as familiar digital signals and images sampled on regular lattices. However, they can be conveniently represented as graphs where each vertex represents measured data and each edge represents a relationship (connectivity or certain affinities or interaction) between two vertices. Processing and analyzing these types of data is a major challenge for both image and machine learning communities. Hence, it is very important to transfer to graphs and networks many of the mathematical tools which were initially developed on usual Euclidean spaces and proven to be efficient for many inverse problems and applications dealing with usual image and signal domains. Historically, the main tools for the study of graphs or networks come from combinatorial and graph theory. In recent years there has been an increasing interest in the investigation of one of the major mathematical tools for signal and image analysis, which are Partial Differential Equations (PDEs) variational methods on graphs. The normalized p-laplacian operator has been recently introduced to model a stochastic game called tug-of-war-game with noise. Part interest of this class of operators arises from the fact that it includes, as particular case, the infinity Laplacian, the mean curvature operator and the traditionnal Laplacian operators which was extensiveley used to models and to solve problems in image processing. The purpose of this paper is to introduce and to study a new class of normalized p-Laplacian on graphs. The introduction is based on the extension of p-harmonious function introduced in as discrete approximation for both infinity Laplacian and p-Laplacian equations. Finally, we propose to use these operators as a framework for solving many inverse problems in image processing.

Keywords: normalized p-laplacian, image processing, stochastic game, inverse problems

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Authors: Kenny Raharjo, Ramon Lawrence

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Game designers have the challenging task of building games that engage players to spend their time and money on the game. There are an infinite number of game variations and design choices, and it is hard to systematically determine game design choices that will have positive experiences for players. In this work, we demonstrate how multi-arm bandits can be used to automatically explore game design variations to achieve improved player metrics. The advantage of multi-arm bandits is that they allow for continuous experimentation and variation, intrinsically converge to the best solution, and require no special infrastructure to use beyond allowing minor game variations to be deployed to users for evaluation. A user study confirms that applying multi-arm bandits was successful in determining the preferred game variation with highest play time metrics and can be a useful technique in a game designer's toolkit.

Keywords: game design, multi-arm bandit, design exploration and data mining, player metric optimization and analytics

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Authors: Eui Jun Jeong, Hye Rim Lee, Ji Hye Yoo

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Recent studies have verified the significant relationship of user personality with Internet use. However, in game studies, little research has emphasized on the effects of personality traits on game addiction. This study examined whether big five personality traits affect game addiction with control of psychological, social, and demographic factors. Specifically, using data from a survey of 789 game users in Korea, we conducted a regression analysis to see the associations of psychological (loneliness/depression), social (activities with family/friends), self-efficacy (game/general), gaming (daily gaming time/perception), demographic (age/gender), and personality traits (extraversion, neuroticism conscientiousness, agreeableness, & openness) with the degree of game addiction. Results showed that neuroticism increase game addiction with no effect of extraversion on the addiction. General self-efficacy negatively affected game addiction, whereas game self-efficacy increased the degree of game addiction. Loneliness enhanced game addiction while depression showed a negative effect on the addiction. Results and implications are discussed.

Keywords: game addiction, big five personality, social activities, self-efficacy, loneliness, depression

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Authors: Ratima Damkham, Natasha Dejdumrong, Priyakorn Pusawiro

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This paper explored the solution in game design to help game designers in the educational game designing using digital educational game model canvas (DEGMC) and digital educational game form (DEGF) based on Outcome-based Education program. DEGMC and DEGF can help designers develop an overview of the game while designing and planning their own game. The way to clearly assess players’ ability from learning outcomes and support their game learning design is by using the tools. Designers can balance educational content and entertainment in designing a game by using the strategies of the Business Model Canvas and design the gameplay and players’ ability assessment from learning outcomes they need by referring to the Constructive Alignment. Furthermore, they can use their design plan in this research to write their Game Design Document (GDD). The success of the research was evaluated by four experts’ perspectives in the education and computer field. From the experiments, the canvas and form helped the game designers model their game according to the learning outcomes and analysis of their own game elements. This method can be a path to research an educational game design in the future.

Keywords: constructive alignment, constructivist theory, educational game, outcome-based education

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Authors: Diogo Santos, Nelson Zagalo, Carla Morais

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No Man’s Sky (NMS) is a sci-fi video game about survival and exploration where players fly spaceships, search for elements, and use them to survive. NMS isn’t a serious game, and not all the science in the game is presented with scientific evidence. To find how players felt about the scientific content in the game and how they perceive the chemistry in it, a survey was sent to NMS’s players, from which were collected answers from 124 respondents from 23 countries. Chemophobia is still a phenomenon when chemistry or chemicals are a subject of discussion, but 68,9% of our respondents showed a positive attitude towards the presence of chemistry in NMS, with 57% stating that playing the video game motivated them to know more about science. 8% of the players stated that NMS often prompted conversations about the science in the video game between them and teachers, parents, or friends. These results give us ideas on how an entertainment game can potentially help scientists, educators, and science communicators reach a growing, evolving, vibrant, diverse, and demanding audience.

Keywords: digital games, science communication, chemistry, informal learning, No Man’s Sky

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Ramy Hammady, Sylvester Arnab

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Significant attention has been directed to adopt game interventions practically to change certain behaviours in many disciplines such as health, education, psychology through many years. That’s due to the intrinsic motivation that games can cause and the substantial impact the games can leave on the player. Many review papers were induced to highlight and measure the effectiveness of the game’s interventions on changing behaviours; however, most of these studies neglected the game design process itself and the game features and elements that can stimuli changing behaviours. Therefore, this paper aims to identify the most game design mechanics and features that are the most influencing on changing behaviour during or after games interventions. This paper also sheds light on the theories of changing behaviours that clearly can led the game design process. This study gives directions to game designers to spot the most influential game features and mechanics for changing behaviour games in order to exploit it on the same manner.

Keywords: behaviour change, game design, serious gaming, gamification, review

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Authors: Kazumoto Tanaka, Takayuki Fujino

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Sports games conducted as a group are a form of therapeutic exercise for aged people with decreased strength and for people suffering from permanent damage of stroke and other conditions. However, it is difficult for patients with different athletic abilities to play a game on an equal footing. This study specifically examines a computer video game designed for therapeutic exercise, and a game system with support given depending on athletic ability. Thereby, anyone playing the game can participate equally. This video-game, to be specific, is a popular variant of balloon volleyball, in which players hit a balloon by hand before it falls to the floor. In this game system, each player plays the game watching a monitor on which the system displays tailor-made video-game images adjusted to the person’s athletic ability, providing players with player-adaptive assist support. We have developed a multiplayer game system with an image generation technique for the tailor-made video-game and conducted tests to evaluate it.

Keywords: therapeutic exercise, computer video game, disability-adaptive assist, tailor-made video-game image

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Authors: Betul Zehra Karagul

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A game consists of strategies that each actor has in his/her own choice strategies, and a game regulates the certain rules in the strategies that the actors choose, express how they evaluate their knowledge and the utility of output results. Game theory examines the human behaviors (preferences) of strategic situations in which each actor of a game regards the action that others will make in spite of his own moves. There is a balance between each player playing a game with the final number of players and the player with a certain probability of choosing the players, and this is called Nash equilibrium. The insurance is a two-person game where the insurer and insured are the actors. Both sides have the right to act in favor of utility functions. The insured has to pay a premium to buy the insurance cover. The insured will want to pay a low premium while the insurer is willing to get a high premium. In this study, the state of equilibrium for insurance pricing was examined in terms of the insurer and insured with game theory.

Keywords: game theory, insurance pricing, Nash equilibrium, utility function

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Authors: Tsugunosuke Sakai, Haruya Tamaki, Ryuichi Yoshida, Ryohei Egusa, Etsuji Yamaguchi, Shigenori Inagaki, Fusako Kusunoki, Miki Namatame, Masanori Sugimoto, Hiroshi Mizoguchi

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We aim to develop a full-body interaction game that could let children cooperate and interact with other children in small groups. As the first step for our aim, the objective of the full-body interaction game developed in this study is to make interaction between children. The game requires two children to jump together with the same timing. We let children experience the game and answer the questionnaires. The children using several strategies to coordinate the timing of their jumps were observed. These included shouting time, watching each other, and jumping in a constant rhythm as if they were skipping rope. In this manner, we observed the children playing the game while cooperating with each other. The results of a questionnaire to evaluate the proposed interactive game indicate that the jumping game was a very enjoyable experience in which the participants could immerse themselves. Therefore, the game enabled children to experience cooperation with others by using body movements.

Keywords: children, cooperation, full-body interaction game, kinect sensor

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Authors: M. Shoukath Ali, Rajendra Prasad Singh

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Game Theory approaches and their application in improving the performance of Wireless Sensor Networks (WSNs) are discussed in this paper. The mathematical modeling and analysis of WSNs may have low success rate due to the complexity of topology, modeling, link quality, etc. However, Game Theory is a field, which can efficiently use to analyze the WSNs. Game Theory is related to applied mathematics that describes and analyzes interactive decision situations. Game theory has the ability to model independent, individual decision makers whose actions affect the surrounding decision makers. The outcome of complex interactions among rational entities can be predicted by a set of analytical tools. However, the rationality demands a stringent observance to a strategy based on measured of perceived results. Researchers are adopting game theory approaches to model and analyze leading wireless communication networking issues, which includes QoS, power control, resource sharing, etc.

Keywords: wireless sensor network, game theory, cooperative game theory, non-cooperative game theory

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Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Mingzhu Lyu, Runlei Ren, Xinyu Dai, Jiaxuan Pi, Kanghua Li

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The study of video game policy in China has been divided into two branches: "pedagogy" and "game industry". The binary perspective of policy reveals the "contradictory" side of policy performance. Based on this suspicion, this paper constructs a three-dimensional sequence of time, content and institutions of game policy, and establishes the "contradictory" aspects of policy performance between 1949 and 2019. A central-level database of game policies, clarifying that our game policies follow a shift from reactive response to proactive guidance, stigmatization and de-stigmatization, the evolutionary logic. The study found that the central government has always maintained a strict requirement and prudent guidance for game policy, and the deep contradictions in game policy stem from the essential conflict between the natural amusement of games and the seriousness of the educational system, and the Chinese government's use of the understanding of the public and private domains and the Managing of the conflict.

Keywords: game industry, gaming policy, public domain, private domain

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: Roopali Kulkarni, Yuliya Khrypko

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A major problem in educational digital game design is that game developers are often focused on maintaining the fun and playability of an educational game, whereas educators are more concerned with the learning aspect of the game rather than its entertaining characteristics. There is a clear need to understand what key aspects of digital learning games make them an effective learning medium in tertiary education. Through a systematic literature review and content analysis, this paper identifies, evaluates, and summarizes twenty-three key attributes of digital games used in tertiary education and presents a summary digital game-based learning (DGBL) model for designing and evaluating an educational digital game of any genre that promotes effective learning in tertiary education. The proposed solution overcomes limitations of previously designed models for digital game evaluation, such as a small number of game attributes considered or applicability to a specific genre of digital games. The proposed DGBL model can be used to assist game designers and educators with creating effective and engaging educational digital games for the tertiary education curriculum.

Keywords: DGBL model, digital games, educational games, game-based learning, tertiary education

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Authors: Ismail Celik, Ismail Sahin, Fetah Eren

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The computer, among the most important inventions of the twentieth century, has become an increasingly important component in our everyday lives. Computer games also have become increasingly popular among people day-by-day, owing to their features based on realistic virtual environments, audio and visual features, and the roles they offer players. In the present study, the metaphors students have for computer games are investigated, as well as an effort to fill the gap in the literature. Students were asked to complete the sentence—‘Computer game is like/similar to….because….’— to determine the middle school students’ metaphorical images of the concept for ‘computer game’. The metaphors created by the students were grouped in six categories, based on the source of the metaphor. These categories were ordered as ‘computer game as a means of entertainment’, ‘computer game as a beneficial means’, ‘computer game as a basic need’, ‘computer game as a source of evil’, ‘computer game as a means of withdrawal’, and ‘computer game as a source of addiction’, according to the number of metaphors they included.

Keywords: computer game, metaphor, middle school students, virtual environments

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Authors: Mifrah Ahmad

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Game designing processes vary with the intentions of the game. Digital games have versatile starting and finishing processes and these have been reported throughout the literature over decades. However, the need to understand how game designers’ practice in designing games is approached in the industry and how do they approach designing games is yet to be informed and whether they consider existing models or frameworks in their practice to assist their designing process of games. Therefore, this paper discusses 17 game designers’ participants' perspectives on how they approach designing games and how their experience of designing various games influences their practice. This research is conducted in an Australian context, through a phenomenology approach, where semi-structured interviews were designed and grounded by theory of experience by John Dewey. The audio data collected was analyzed using NVivo and interpreted using the interpretivism paradigm to contextualize the essence of game designers’ experiences in their practice and unfold their designing, developing, and iterative methodologies. As a result, a generic game-designing model is proposed that illuminates a sequence of steps that enables game designers’ initiatives toward a successful game design process. A ‘Five-Essential-Steps’ model (5ESM) for designing digital games may potentially assist early career game designers, gaming researchers as well as academics pursuing the designing process of games, educational games, or serious games.

Keywords: game designers practice, experiential design, designing models, game design approaches, designing process, software design, top-down model

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Authors: Noel Jeygar Robert, V. K.Vidya

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Cognitive radio is a software-defined radio technology that allows cognitive users to operate on the vacant bands of spectrum allocated to licensed users. Cognitive radio plays a vital role in the efficient utilization of wireless radio spectrum available between cognitive users and licensed users without making any interference to licensed users. The spectrum allocation followed by spectrum sharing is done in a fashion where a cognitive user has to wait until spectrum holes are identified and allocated when the licensed user moves out of his own allocated spectrum. In this paper, we propose a self –coexistence strategy using bargaining and Cournot game model for achieving spectrum allocation in cognitive radio networks. The game-theoretic model analyses the behaviour of cognitive users in both cooperative and non-cooperative scenarios and provides an equilibrium level of spectrum allocation. Game-theoretic models such as bargaining game model and Cournot game model produce a balanced distribution of spectrum resources and energy consumption. Simulation results show that both game theories achieve better performance compared to other popular techniques

Keywords: cognitive radio, game theory, bargaining game, Cournot game

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Authors: YuLung Wu, YuTien Wu, ShuMey Yu

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Game-based learning can enhance the learning motivation of students and provide a means for them to learn through playing games. This study used augmented reality technology to develop an interactive card game as a game-based teaching aid for delivering elementary school science course content with the aim of enhancing student learning processes and outcomes. Through playing the proposed card game, students can familiarize themselves with appearance, features, and foraging behaviors of insects. The system records the actions of students, enabling teachers to determine their students’ learning progress. In this study, 37 students participated in an assessment experiment and provided feedback through questionnaires. Their responses indicated that they were significantly more motivated to learn after playing the game, and their feedback was mostly positive.

Keywords: game-based learning, learning motivation, teaching aid, augmented reality

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Authors: Amirhossein Khazali, Mohsen Kalantar

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Energy storage units can play an important role to provide an economic and secure operation of future energy systems. In this paper, a stochastic energy and reserve market clearing scheme is presented considering storage energy units. The approach is proposed to deal with stochastic and non-dispatchable renewable sources with a high level of penetration in the energy system. A two stage stochastic programming scheme is formulated where in the first stage the energy market is cleared according to the forecasted amount of wind generation and demands and in the second stage the real time market is solved according to the assumed scenarios.

Keywords: energy and reserve market, energy storage device, stochastic programming, wind generation

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Hye Rim Lee, Eui Jun Jeong, Ji Hye Yoo

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This study makes an integrated investigation on how life satisfaction is associated with the Korean game users' psychological variables (self-esteem, game and life self- efficacy), social variables (bonding and bridging social capital), and demographic variables (age, gender). The data used for the empirical analysis came from a representative sample survey conducted in South Korea. Results show that self-esteem and game efficacy were an important antecedent to the degree of users’ life satisfaction. Both bonding social capital and bridging social capital enhance the level of the users’ life satisfaction. The importance of perspectives as well as their implications for the game users and further associated research, are explored.

Keywords: life satisfaction, self-esteem, game efficacy, life-efficacy, social capital

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Authors: Laura V. Gonzalez, Juan B. Duarte, Luis A. Palacio

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Decision making can be conditioned by factors such as the environments, circumstances, behavioral biases, emotions, beliefs and preferences of the participants. The objective of this paper is to analyze the effect ‘amount of information’ and ‘number of options’, on the behavior of competitors under a bilateral negotiation context. For the above, it has been designed an experiment as a classroom game where they negotiate goods, under the condition that none of the players knows exactly the real value of the asset. The game is designed under the concept of zero-sum (non-cooperative game) and focuses on the fact that agents must anticipate the strategies of their opponent to improve their chances of winning in the negotiation. The empirical results show that, contrary to the traditional view of expected utility theory, players prefer to obtain low profits and losses, when faced with a higher expectation of losses, using sub-optimal strategies not in accordance with game theory.

Keywords: bilateral negotiation, classroom game, decision making, game theory

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Authors: Qin Luofeng, Shen Siqi

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For the 58 years since the first video game came into being, the video game industry is getting through an explosive evolution from then on. Video games exert great influence on society and become a reflection of public life to some extent. Video game virtual spaces are where activities are taking place like real spaces. And that’s the reason why some architects pay attention to video games. However, compared to the researches on the appearance of games, we observe a lack of theoretical comprehensive on the construction of video game virtual spaces. The research method of this paper is to collect literature and conduct theoretical research about the virtual space in video games firstly. And then analogizing the opinions on the space phenomena from the theory of literature and films. Finally, this paper proposes a three-layer framework for the construction of video game virtual spaces: “algorithmic space-narrative space players space”, which correspond to the exterior, expressive, affective parts of the game space. Also, we illustrate each sub-space according to numerous instances of published video games. Hoping this writing could promote the interactive development of video games and architecture.

Keywords: video game, virtual space, narrativity, social space, emotional connection

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Authors: Hye Rim Lee, Eui Jun Jeong, Ju Woo Kim

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This study will examine how the therapeutic factors (therapeutic catharsis-seeking and game-efficacy of the game player) and self-construal factors (independent and interdependent self-construal of the game player) as well as social capital factors (bonding and bridging social capital of the game player) affect trait aggression in the game. Results show that both therapeutic catharsis-seeking and game self-efficacy are particularly important to the players since they cause the game players’ aggressive tendencies to be greatly diminished. Independent self-construal reduces the level of the players’ aggression. Interestingly enough, the bonding social capital enhances the level of the players’ aggression, while individuals with bridging social capital did not show any significant effects. The results and implications will be discussed herein.

Keywords: aggression catharsis, game self-efficacy, self-construal, social capital, therapeutic catharsis seeking

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Authors: Mohammad Ebrahim Arbabian

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This paper investigates the impact of 3D printing, also known as additive manufacturing, on a multi-item supply chain comprising a manufacturer and retailer. Operating under a wholesale-price contract and catering to stochastic customer demand, this study delves into the largely unexplored realm of how 3D printing technology reshapes supply chain dynamics. A distinguishing aspect of 3D printing is its versatility in producing various product types, yet its slower production pace compared to traditional methods poses a challenge. We analyze the trade-off between 3D printing's limited capacity and its enhancement of production flexibility. By delineating the economic circumstances favoring 3D printing adoption by the manufacturer, we establish the Stackelberg equilibrium in the retailer-manufacturer game. Additionally, we determine optimal order quantities for the retailer considering 3D printing as an option for the manufacturer, ascertain optimal wholesale prices in the presence of 3D printing, and compute optimal profits for both parties involved in the supply chain.

Keywords: additive manufacturing, supply chain management, contract theory, Stackelberg game, optimization

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Authors: A. Roomy

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The dramatic rise in violence against game officials has affected all levels of sports including recreational, amateur, and professional sports. One way to combat this rise in violence is through the creation of laws specifically aimed at preventing and punishing this kind of violence. This paper will use related legal cases as a starting point to explore possible ways of better protecting the safety of game officials. It will do this by looking at relevant cases, related legal issues, and two specific ways of reducing violence against game officials. In closing, it will be argued that there needs to be a more robust legal approach with emphasis on criminal and civil penalties for assault and battery, and a more comprehensive social approach with emphasis on raising social awareness on the need to protect game officials from violence.

Keywords: game officials, legal issues, safety, violence

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