Search results for: Topological game

Authors: Lori L. Scarlatos, Ryan Courtney

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This paper explores the impact that playing a casual game can have on a player's learning and subsequent behavior. A casual mobile game, Container Chaos, was created to teach undergraduate students about the carbon footprint of various disposable beverage containers. Learning was tested with a short quiz, and behavior was tested by observing which beverage containers players choose when offered a drink and a snack. The game was tested multiple times, under a variety of different circumstances. Findings of these tests indicate that, with extended play over time, players can learn new information and sometimes even change their behavior as a result. This has implications for how other casual games can be used to teach concepts and possibly modify behavior.

Keywords: Behavior, carbon footprint, casual games, environmental impact, material sciences.

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Authors: Roman V. Yampolskiy

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Games can be classified as games of skill, games of chance or otherwise be classified as mixed. This paper deals with the topic of scientifically classifying mixed games as more reliant on elements of chance or elements of skill and ways to scientifically measure the amount of skill involved. This is predominantly useful for classification of games as legal or illegal in deferent jurisdictions based on the local gaming laws. We propose a novel measure of skill to chance ratio called the Game Skill Measure (GSM) and utilize it to calculate the skill component of a popular variant of Poker.

Keywords: Chance, Game, Skill, Luck.

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Authors: Sanghun Lee

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Since the advent of the information era, the Internet has brought various positive effects in everyday life. Nevertheless, recently, problems and side-effects have been noted. Internet witch-trials and spread of pornography are only a few of these problems.In this study, problems and causes of malicious replies on internet boards were analyzed, using the key ideas of game theory. The study provides a mathematical model for the internet reply game to devise three possible plans that could efficiently counteract malicious replies. Furthermore, seven specific measures that comply with one of the three plans were proposed and evaluated according to the importance and utility of each measure using the orthogonal array survey and SPSS conjoint analysis.The conclusion was that the most effective measure would be forbidding unsigned user access to malicious replies. Also notable was that some analytically proposed measures, when implemented, could backfire and encourage malicious replies.

Keywords: Conjoint Analysis, Game Theory, Internet, MaliciousReplies, Prisoner's Dilemma

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Authors: M’hamed Outanoute, Mohamed Baslam, Belaid Bouikhalene

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The customers use the best compromise criterion between price and quality of service (QoS) to select or change their Service Provider (SP). The SPs share the same market and are competing to attract more customers to gain more profit. Due to the divergence of SPs interests, we believe that this situation is a non-cooperative game of price and QoS. The game converges to an equilibrium position known Nash Equilibrium (NE). In this work, we formulate a game theoretic framework for the dynamical behaviors of SPs. We use Genetic Algorithms (GAs) to find the price and QoS strategies that maximize the profit for each SP and illustrate the corresponding strategy in NE. In order to quantify how this NE point is performant, we perform a detailed analysis of the price of anarchy induced by the NE solution. Finally, we provide an extensive numerical study to point out the importance of considering price and QoS as a joint decision parameter.

Keywords: Pricing, QoS, Market share game, Genetic algorithms, Nash equilibrium, Learning, Price of anarchy.

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Authors: E. Arsuaga Uriarte, F. Díaz Martín

Abstract:

The SOM has several beneficial features which make it a useful method for data mining. One of the most important features is the ability to preserve the topology in the projection. There are several measures that can be used to quantify the goodness of the map in order to obtain the optimal projection, including the average quantization error and many topological errors. Many researches have studied how the topology preservation should be measured. One option consists of using the topographic error which considers the ratio of data vectors for which the first and second best BMUs are not adjacent. In this work we present a study of the behaviour of the topographic error in different kinds of maps. We have found that this error devaluates the rectangular maps and we have studied the reasons why this happens. Finally, we suggest a new topological error to improve the deficiency of the topographic error.

Keywords: Map lattice, Self-Organizing Map, topographic error, topology preservation.

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Authors: Ollie Hall, Salma ElSayed

Abstract:

Affective adaptation is a creative way for game designers to add an extra layer of engagement to their productions. When player’s emotions are an explicit factor in mechanics design, endless possibilities for imaginative gameplay emerge. Whilst gaining popularity, existing affective game research mostly runs controlled experiments in restrictive settings and rely on one or more specialist devices for measuring player’s emotional state. These conditions albeit effective, are not necessarily realistic. Moreover, the simplified narrative and intrusive wearables may not be suitable for players. This exploratory study investigates delivering an immersive affective experience in the wild with minimal requirements, in an attempt for the average developer to reach the average player. A puzzle game is created with rich narrative and creative mechanics. It employs both explicit and implicit adaptation and only requires a web camera. Participants played the game on their own machines in various settings. Whilst it was rated feasible, very engaging and enjoyable, it remains questionable whether a fully immersive experience was delivered due to the limited sample size.

Keywords: affective games, dynamic adaptation, emotion recognition, game design

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Authors: Omid Noroozi

Abstract:

Digital dialogue games have opened up opportunities for learning skills by engaging students in complex problem solving that mimic real world situations, without importing unwanted constraints and risks of the real world. Digital dialogue games can be motivating and engaging to students for fun, creative thinking, and learning. This study explored how undergraduate students engage with argumentative discourse activities which have been designed to intensify debate. A pre-test, post-test design was used with students who were assigned to groups of four and asked to debate a controversial topic with the aim of exploring various 'pros and cons' on the 'Genetically Modified Organisms (GMOs)'. Findings reveal that the Digital dialogue game can facilitate argumentation-based learning. The digital Dialogue game was also evaluated positively in terms of students’ satisfaction and learning experiences.

Keywords: Argumentation, dialogue, digital game, learning, motivation.

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Authors: Yilun Shang

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In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.

Keywords: random geometric graph, autoregressive process, degree, connectivity, Markovian, wireless network.

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Authors: Malathi Balakrishnan, Shabeshan Rengasamy, Mohd Salleh Aman

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The study investigated the effects of Teaching Games for Understanding approach on students ‘cognitive learning outcome. The study was a quasi-experimental non-equivalent pretest-posttest control group design whereby 10 year old primary school students (n=72) were randomly assigned to an experimental and a control group. The experimental group students were exposed with TGfU approach and the control group with the Traditional Skill approach of handball game. Game Performance Assessment Instrument (GPAI) was used to measure students' tactical understanding and decision making in 3 versus 3 handball game situations. Analysis of covariance (ANCOVA) was used to analyze the data. The results reveal that there was a significant difference between the TGfU approach group and the traditional skill approach group students on post test score (F (1, 69) = 248.83, p < .05). The findings of this study suggested the importance of TGfU approach to improve primary students’ tactical understanding and decision making in handball game.

Keywords: Constructivism, learning outcome, tactical understanding, and Teaching Game for Understanding (TGfU)

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Authors: Marketa Kotova, Jana Kolarova, Ludek Zalud, Petr Dobsak

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A game for training of breath (TRABR) for continuous monitoring of pulmonary ventilation during the patients’ therapy focuses especially on monitoring of their ventilation processes. It is necessary to detect, monitor and differentiate abdominal and thoracic breathing during the therapy. It is a fun form of rehabilitation where the patient plays and also practicing isolated breathing. Finally the game to practice breath was designed to evaluate whether the patient uses two types of breathing or not.

Keywords: Pulmonary ventilation, thoracic breathing, abdominal breathing, breath monitoring using pressure sensors, game TRABR (TRAining of BReath).

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Authors: Chengli Liu, C. K. M. Lee

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The tradition competitive newsvendor game assumes decision makers are rational. However, there are behavioral biases when people make decisions, such as loss aversion, mental accounting and overconfidence. Overestimation of a subject’s own performance is one type of overconfidence. The objective of this research is to analyze the impact of the overestimated demand in the newsvendor competitive game with two players. This study builds a competitive newsvendor game model where newsvendors have private information of their demands, which is overestimated. At the same time, demands of each newsvendor forecasted by a third party institution are available. This research shows that the overestimation leads to demand steal effect, which reduces the competitor’s order quantity. However, the overall supply of the product increases due to overestimation. This study illustrates the boundary condition for the overestimated newsvendor to have the equilibrium order drop due to the demand steal effect from the other newsvendor. A newsvendor who has higher critical fractile will see its equilibrium order decrease with the drop of estimation level from the other newsvendor.

Keywords: Bias, competitive newsvendor, Nash equilibrium, overestimation.

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Authors: Samee Ullah Khan, C. Ardil

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The problem of mapping tasks onto a computational grid with the aim to minimize the power consumption and the makespan subject to the constraints of deadlines and architectural requirements is considered in this paper. To solve this problem, we propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. The proposed game theoretical technique is compared against several traditional techniques. The experimental results show that when the deadline constraints are tight, the proposed technique achieves superior performance and reports competitive performance relative to the optimal solution.

Keywords: Energy efficient algorithms, resource allocation, resource management, cooperative game theory.

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Authors: Ziquan Hu, Kun She, Shahzad Ali, Kai Yan

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Game theory could be used to analyze the conflicted issues in the field of information hiding. In this paper, 2-phase game can be used to build the embedder-attacker system to analyze the limits of hiding capacity of embedding algorithms: the embedder minimizes the expected damage and the attacker maximizes it. In the system, the embedder first consumes its resource to build embedded units (EU) and insert the secret information into EU. Then the attacker distributes its resource evenly to the attacked EU. The expected equilibrium damage, which is maximum damage in value from the point of view of the attacker and minimum from the embedder against the attacker, is evaluated by the case when the attacker attacks a subset from all the EU. Furthermore, the optimal equilibrium capacity of hiding information is calculated through the optimal number of EU with the embedded secret information. Finally, illustrative examples of the optimal equilibrium capacity are presented.

Keywords: 2-Phase Game, Expected Equilibrium damage, InformationHiding, Optimal Equilibrium Capacity.

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: Algebras over integral domains, Alexandroff topology, valuation domains, integral domains.

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Authors: A. S. Mousa, F. Shoman

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We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Keywords: Coherent strategy, split strategy, pure strategy, mixed strategy, Nash Equilibrium, game theory.

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Authors: Gábor Szűcs, Gábor Neszveda, Xin Fang

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In this paper the General Game problem is described. In this problem the competition or cooperation dilemma occurs as the two basic types of strategies. The strategy possibilities have been analyzed for finding winning strategy in uncertain situations (no information about the number of players and their strategy types). The winning strategy is missing, but a good solution can be found by simulation by varying the ratio of the two types of strategies. This new method has been used in a real contest with human players, where the created strategies by simulation have reached very good ranks. This construction can be applied in other real social games as well.

Keywords: competition, cooperation, finding good strategy, General Game

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Authors: Yasuomi D. Sato, Yasutaka Kuriya

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We here propose improved version of elastic graph matching (EGM) as a face detector, called the multi-scale EGM (MS-EGM). In this improvement, Gabor wavelet-based pyramid reduces computational complexity for the feature representation often used in the conventional EGM, but preserving a critical amount of information about an image. The MS-EGM gives us higher detection performance than Viola-Jones object detection algorithm of the AdaBoost Haar-like feature cascade. We also show rapid detection speeds of the MS-EGM, comparable to the Viola-Jones method. We find fruitful benefits in the MS-EGM, in terms of topological feature representation for a face.

Keywords: Face detection, Gabor wavelet based pyramid, elastic graph matching, topological preservation, redundancy of computational complexity.

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Authors: Oluseye A. Adeleke, Mohd. F. M. Salleh

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The performance of any cooperative communication system depends largely on the selection of a proper partner. Another important factor to consider is an efficient allocation of resource like power by the source node to help it in forwarding information to the destination. In this paper, we look at the concepts of partner selection and resource (power) allocation for a distributed communication network. A type of non-cooperative game referred to as Trade-Off game is employed so as to jointly consider the utilities of the source and relay nodes, where in this case, the source is the node that requires help with forwarding of its information while the partner is the node that is willing to help in forwarding the source node’s information, but at a price. The approach enables the source node to maximize its utility by selecting a partner node based on (i) the proximity of the partner node to the source and destination nodes, and (ii) the price the partner node will charge for the help being rendered. Our proposed scheme helps the source locate and select the relay nodes at ‘better’ locations and purchase power optimally from them. It also aids the contending relay nodes maximize their own utilities as well by asking proper prices. Our game scheme is seen to converge to unique equilibrium.

Keywords: Cooperative communication, game theory, node, power allocation, trade-off, utility.

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Authors: H. Nagendra, Vinod Kumar, S. Mukherjee

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In this study, the potential benefits of playing action video game among congenitally deaf and dumb subjects is reported in terms of EEG ratio indices. The frontal and occipital lobes are associated with development of motor skills, cognition, and visual information processing and color recognition. The sixteen hours of First-Person shooter action video game play resulted in the increase of the ratios β/(α+θ) and β/θ in frontal and occipital lobes. This can be attributed to the enhancement of certain aspect of cognition among deaf and dumb subjects.

Keywords: Cognitive enhancement, video games, EEG band powers, Deaf and Dumb subjects.

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Authors: Jimaima Lako, Subramaniam Sotheeswaran, Ketan Christi

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The 15-a-side Fiji rugby team trains well in preparations for any rugby competition but rarely performs to expectations. In order to help the Fiji local based rugby players to identify some key basic areas in improving their performance, a series of workshops were conducted to assess their nutritional status and dietary habits in relation to energy demand during rugby matches. The nutrition workshop included the administration of questionnaires to 19 local based rugby players, requesting the following information: usual food intakes, training camp food intakes, carbohydrate loading, pre-game meals and post-game meals. The study revealed that poor eating habits of the players resulted in the low carbohydrate intake, which may have contributed to increase levels of fatigue leading to loss of stamina even before the second half of the game. It appears that the diet of most 15-a-side players does not provide enough energy to enable them to last the full eightyminutes of the game.

Keywords: Fiji rugby, Food habits, Physical fitness, Training meals

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Authors: Malathi Balakrishnan, Cheng Lee Ooi, Chander Vengadasalam

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The purpose of this study is to explore a case study of trainee teachers’ learning experience on innovating traditional games during the traditional game carnival. It explores issues arising from multiple case studies of trainee teachers learning experiences in innovating traditional games. A qualitative methodology was adopted through observations, semi-structured interviews and reflective journals’ content analysis of trainee teachers’ learning experiences creating and implementing innovative traditional games. Twelve groups of 36 trainee teachers who registered for Sports and Physical Education Management Course were the participants for this research during the traditional game carnival. Semi structured interviews were administrated after the trainee teachers learning experiences in creating innovative traditional games. Reflective journals were collected after carnival day and the content analyzed. Inductive data analysis was used to evaluate various data sources. All the collected data were then evaluated through the Nvivo data analysis process. Inductive reasoning was interpreted based on the Self Determination Theory (SDT). The findings showed that the trainee teachers had positive game participation experiences, game knowledge about traditional games and positive motivation to innovate the game. The data also revealed the influence of themes like cultural significance and creativity. It can be concluded from the findings that the organized game carnival, as a requirement of course work by the Institute of Teacher Training Malaysia, was able to enhance teacher trainers’ innovative thinking skills. The SDT, as a multidimensional approach to motivation, was utilized. Therefore, teacher trainers may have more learning experiences using the SDT.

Keywords: Learning experiences, innovation, traditional games, trainee teachers.

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Authors: Michael Harre, Terry Bossomaier, Ranqing Chu, Allan Snyder

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We introduce a novel approach to measuring how humans learn based on techniques from information theory and apply it to the oriental game of Go. We show that the total amount of information observable in human strategies, called the strategic information, remains constant for populations of players of differing skill levels for well studied patterns of play. This is despite the very large amount of knowledge required to progress from the recreational players at one end of our spectrum to the very best and most experienced players in the world at the other and is in contrast to the idea that having more knowledge might imply more 'certainty' in what move to play next. We show this is true for very local up to medium sized board patterns, across a variety of different moves using 80,000 game records. Consequences for theoretical and practical AI are outlined.

Keywords: Board Games, Cognitive Capacity, Decision Theory, Information Theory.

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Authors: Clara Hertzog, Sho Sakurai, Koichi Hirota, Takuya Nojima

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It is common to see graphics appearing on television while watching a sports game to provide information, but it is less common to see graphics specifically aiming to boost spectators’ dynamism perception. It is even less common to see such graphics designed especially for virtual reality (VR). However, it appears that even with simple dynamic graphics, it would be possible to improve VR sports spectators’ experience. So, in this research, we explain how graphics can be used in VR to improve the dynamism of a broadcasted sports game and we provide a simple example. This example consists in a white halo displayed around the video and blinking according to the game speed. We hope to increase people’s awareness about VR sports spectating and the possibilities this display offers through dynamic graphics.

Keywords: Broadcasting, graphics, sports spectating, virtual reality.

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Authors: Xizhi Li

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Both software applications and their development environment are becoming more and more distributed. This trend impacts not only the way software computes, but also how it looks. This article proposes a Human Computer Interface (HCI) template from three representative applications we have developed. These applications include a Multi-Agent System based software, a 3D Internet computer game with distributed game world logic, and a programming language environment used in constructing distributed neural network and its visualizations. HCI concepts that are common to these applications are described in abstract terms in the template. These include off-line presentation of global entities, entities inside a hierarchical namespace, communication and languages, reconfiguration of entity references in a graph, impersonation and access right, etc. We believe the metaphor that underlies an HCI concept as well as the relationships between a bunch of HCI concepts are crucial to the design of software systems and vice versa.

Keywords: HCI, MAS, computer game, programming language

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Authors: Suguru Ochiai, Toru Yabuki, Yoshiki Yamaguchi, Yuetsu Kodama

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In this paper, we propose a Connect6 solver which adopts a hybrid approach based on a tree-search algorithm and image processing techniques. The solver must deal with the complicated computation and provide high performance in order to make real-time decisions. The proposed approach enables the solver to be implemented on a single Spartan-6 XC6SLX45 FPGA produced by XILINX without using any external devices. The compact implementation is achieved through image processing techniques to optimize a tree-search algorithm of the Connect6 game. The tree search is widely used in computer games and the optimal search brings the best move in every turn of a computer game. Thus, many tree-search algorithms such as Minimax algorithm and artificial intelligence approaches have been widely proposed in this field. However, there is one fundamental problem in this area; the computation time increases rapidly in response to the growth of the game tree. It means the larger the game tree is, the bigger the circuit size is because of their highly parallel computation characteristics. Here, this paper aims to reduce the size of a Connect6 game tree using image processing techniques and its position symmetric property. The proposed solver is composed of four computational modules: a two-dimensional checkmate strategy checker, a template matching module, a skilful-line predictor, and a next-move selector. These modules work well together in selecting next moves from some candidates and the total amount of their circuits is small. The details of the hardware design for an FPGA implementation are described and the performance of this design is also shown in this paper.

Keywords: Connect6, pattern matching, game-tree reduction, hardware direct computation

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Authors: Bassam Shaikh, R. S. A. Jumain

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Game addiction has become an extremely important topic in psychology researchers, particularly in understanding and explaining why individuals become addicted (to video games). In previous studies, effect of online game addiction on social responsibilities, health problems, government action, and the behaviors of individuals to purchase and the causes of making individuals addicted on the video games has been discussed. Extending these concepts in marketing, it could be argued than the phenomenon could enlighten and extending our understanding on consumer loyalty. This study took the Grounded Theory approach, and found that motivation, satisfaction, fulfillments, exploration and achievements to be part of the important elements that builds consumer loyalty.

Keywords: Consumer Loyalty, Video Games Addiction, Video Games, Grounded Theory.

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.

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Authors: Rajneesh Sharma, M. Gopal

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Markov games are a generalization of Markov decision process to a multi-agent setting. Two-player zero-sum Markov game framework offers an effective platform for designing robust controllers. This paper presents two novel controller design algorithms that use ideas from game-theory literature to produce reliable controllers that are able to maintain performance in presence of noise and parameter variations. A more widely used approach for controller design is the H∞ optimal control, which suffers from high computational demand and at times, may be infeasible. Our approach generates an optimal control policy for the agent (controller) via a simple Linear Program enabling the controller to learn about the unknown environment. The controller is facing an unknown environment, and in our formulation this environment corresponds to the behavior rules of the noise modeled as the opponent. Proposed controller architectures attempt to improve controller reliability by a gradual mixing of algorithmic approaches drawn from the game theory literature and the Minimax-Q Markov game solution approach, in a reinforcement-learning framework. We test the proposed algorithms on a simulated Inverted Pendulum Swing-up task and compare its performance against standard Q learning.

Keywords: Reinforcement learning, Markov Decision Process, Matrix Games, Markov Games, Smooth Fictitious play, Controller, Inverted Pendulum.

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Authors: Malathi Balakrishnan, Gananathan M. Nadarajah, Saraswathy Vellasamy, Evelyn Gnanam William George

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The purpose of the study is to explore how the fun game-learning approach enhances teacher trainers’ higher order thinking skills. Two-day fun filled fun game learning-approach was introduced to teacher trainers as a Continuous Professional Development Program (CPD). 26 teacher trainers participated in this Transformation of Teaching and Learning Fun Way Program, organized by Institute of Teacher Education Malaysia. Qualitative research technique was adopted as the researchers observed the participants’ higher order thinking skills developed during the program. Data were collected from observational checklist; interview transcriptions of four participants and participants’ reflection notes. All the data were later analyzed with NVivo data analysis process. The finding of this study presented five main themes, which are critical thinking, hands on activities, creating, application and use of technology. The studies showed that the teacher trainers’ higher order thinking skills were enhanced after the two-day CPD program. Therefore, Institute of Teacher Education will have more success using the fun way game-learning approach to develop higher order thinking skills among its teacher trainers who can implement these skills to their trainee teachers in future. This study also added knowledge to Constructivism learning theory, which will further highlight the prominence of the fun way learning approach to enhance higher order thinking skills.

Keywords: Constructivism, game-learning approach, higher order thinking skill, teacher trainer.

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Authors: Bahare Fatemi, Seyed Mehran Kazemi, Nazanin Mehrasa

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Sudoku is a logic-based combinatorial puzzle game which people in different ages enjoy playing it. The challenging and addictive nature of this game has made it a ubiquitous game. Most magazines, newspapers, puzzle books, etc. publish lots of Sudoku puzzles every day. These puzzles often come in different levels of difficulty so that all people, from beginner to expert, can play the game and enjoy it. Generating puzzles with different levels of difficulty is a major concern of Sudoku designers. There are several works in the literature which propose ways of generating puzzles having a desirable level of difficulty. In this paper, we propose a method based on constraint satisfaction problems to evaluate the difficulty of the Sudoku puzzles. Then we propose a hill climbing method to generate puzzles with different levels of difficulty. Whereas other methods are usually capable of generating puzzles with only few number of difficulty levels, our method can be used to generate puzzles with arbitrary number of different difficulty levels. We test our method by generating puzzles with different levels of difficulty and having a group of 15 people solve all the puzzles and recording the time they spend for each puzzle.

Keywords: Constraint satisfaction problem, generating Sudoku puzzles, hill climbing.

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