Version Of Game Research Articles

Double Oracle Algorithm for Computing Equilibria in Continuous Games

Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite programming. In general, however, continuous games are not directly amenable to computational procedures. In this contribution, we develop an iterative strategy generation technique for finding a Nash equilibrium in a whole class of continuous two-person zero-sum games with compact strategy sets. The procedure, which is called the double oracle algorithm, has been successfully applied to large finite games in the past. We prove the convergence of the double oracle algorithm to a Nash equilibrium. Moreover, the algorithm is guaranteed to recover an approximate equilibrium in finitely-many steps. Our numerical experiments show that it outperforms fictitious play on several examples of games appearing in the literature. In particular, we provide a detailed analysis of experiments with a version of the continuous Colonel Blotto game.

The Contour to Classification Game

The Contour to Classification game is a browser-based game that teaches middle school students basic concepts in supervised learning. The game is an online variant of the Neural Network game that was presented at AAAI Fall Symposium Teaching AI in K-12 track in 2019. We share preliminary findings from implementing the online version of the original Neural Network game in a pilot research study and describe the game’s evolution to the Contour to Classification game. The new game uses a simulation of a neural network to engage students, through digital drawing and selection interactions, in the classification of images. The players act as nodes in a multi-step process of compositing salient smaller features to form larger features and ultimately a partial contour of an object that is used to make a prediction. After evaluating the prediction, information is sent back through the network in processes mimicking back propagation and gradient descent. Additional rounds of the game can be played to witness how the network evolves and gets “better” at classifying images from contours. Through this game, we aimed for students to learn the structure, components, and functioning of a neural network, and the processes involved in supervised learning. The Contour to Classification game supports online student learning by providing the image classification experience using purely visual inputs to each layer. We will conclude with a discussion of if and how the evolving design addresses classroom needs and scaling considerations.

Identification in simple binary outcome panel data models

SummaryThis paper first reviews some of the approaches that have been taken to estimate the common parameters of binary outcome models with fixed effects. We limit attention to situations in which the researcher has access to a data set with a large number of units (individuals or companies, for example) observed over a number of time periods. We then apply some of the existing approaches to study fixed-effects panel data versions of entry games, like the ones studied in Bresnahan and Reiss (1991) and Tamer (2003).

Time Compression in Virtual Reality

Abstract Virtual-reality (VR) users and developers have informally reported that time seems to pass more quickly while playing games in VR. We refer to this phenomenon as time compression: a longer real duration is compressed into a shorter perceived experience. To investigate this effect, we created two versions of a labyrinth-like game. The versions are identical in their content and mode of control but differ in their display type: one was designed to be played in VR, and the other on a conventional monitor (CM). Participants were asked to estimate time prospectively using an interval production method. Participants played each version of the game for a perceived five-minute interval, and the actual durations of the intervals they produced were compared between display conditions. We found that in the first block, participants in the VR condition played for an average of 72.6 more seconds than participants in the CM condition before feeling that five minutes had passed. This amounts to perceived five-minute intervals in VR containing 28.5% more actual time than perceived five-minute intervals in CM. However, the effect appeared to be reversed in the second block when participants switched display conditions, suggesting large novelty and anchoring effects, and demonstrating the importance of using between-subjects designs in interval production experiments. Overall, our results suggest that VR displays do produce a significant time compression effect. We discuss a VR-induced reduction in bodily awareness as a potential explanation for how this effect is mediated and outline some implications and suggestions for follow-up experiments.

Sex differences in economic decision-making: Exogenous estradiol has opposing effects on fairness framing in women and men

Burgeoning evidence indicates that women are more sensitive to the context of an offer and show a stronger propensity to adjust their behavior with changing fairness frames. We evaluated whether the sex hormone estradiol and associated stereotypical beliefs contribute to fairness framings by administering topical estradiol (2 mg) to 108 healthy women and 104 heathy men in a randomized, double-blind, placebo-controlled between-subject study design. Participants played the role of the responder in a modified version of the Ultimatum Game (UG), in which identical offers for the division of a given amount of money were framed as either fair or unfair. Furthermore, participants completed an unframed UG and a delayed discounting task to probe possible effects of estradiol on altruistic preferences and delay gratification. Our results show that women were more sensitive to fairness frames than men. Intriguingly, however, estradiol had sex-specific effects on fairness sensitivity by increasing the acceptance rate of proposals with a fair frame in men and reducing it in women. Furthermore, the mere belief of receiving estradiol treatment significantly increased the acceptance of unfair-framed offers in both sexes, but estradiol did not significantly alter the response to unframed offers and impulsive decision-making. Collectively, our findings indicate that estradiol has opposing effects on the sensitivity to the perceived fairness of economic offers in women and men. The profound effects of estradiol treatment and stereotypical beliefs provide support for the notion that sex differences in fairness framing are rooted in both biological and environmental factors.

Reviewing Stranger on the Internet: The Role of Identifiability through “Reputation” in Online Decision Making

The stranger on the Internet effect has been studied in relation to self-disclosure. Nonetheless, quantitative evidence about how people mentally represent and perceive strangers online is still missing. Given the dynamic development of web technologies, quantifying how much strangers can be considered suitable for pro-social acts such as self-disclosure appears fundamental for a whole series of phenomena ranging from privacy protection to fake news spreading. Using a modified and online version of the Ultimatum Game (UG), we quantified the mental representation of the stranger on the Internet effect and tested if people modify their behaviors according to the interactors’ identifiability (i.e., reputation). A total of 444 adolescents took part in a 2 × 2 design experiment where reputation was set active or not for the two traditional UG tasks. We discovered that, when matched with strangers, people donate the same amount of money as if the other has a good reputation. Moreover, reputation significantly affected the donation size, the acceptance rate and the feedback decision making as well.

The Hats Game. the Power of Constructors

We analyze the following general version of the deterministic Hats game. Several sages wearing colored hats occupy the vertices of a graph. Each sage can have a hat of one of k colors. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We present an example of a planar graph for which the sages win for k = 14. We also give an easy proof of the theorem about the Hats game on “windmill” graphs.

Robust Pairwise n-Person Stochastic Duel Game

This paper introduces an extended version of a stochastic game under the antagonistic duel-type setup. The most flexible multiple person duel game is analytically solved. Moreover, the explicit formulas are solved to determine the time-dependent duel game model using the first exceed theory in multiple game stages. Unlike conventional stochastic duel games, multiple battlefields are firstly introduced and each battlefield becomes a shooting ground of pairwise players in a multiperson game. Each player selects different targets in different game stages. An analogue of this new theory was designed to find the best shooting time within multiple battlefields. This model is fully mathematically explained and is the basis with which to apply a stochastic duel-type game in various practical applications.

Reduced sensitivity to situational change in individuals with autism spectrum condition

IntroductionIndividuals with autism spectrum condition (ASC) frequently report difficulties in detecting changes in social situations, which considerably hinder interpersonal communications.ObjectivesTo better understand the features of detecting changes in social situations among individuals with ASC.MethodsIndividuals with ASC (N=24) and typical development (TD) (N=24) were included. To examine participants’ sensitivity to situational contexts, we conducted an economic-game task: a modified computer version of the ultimatum game (mod-UG). In UG, two players were offered a chance to win 10 coins after dividing it amongst themselves. The proposer suggests how to split the sum and the responder can accept or reject the deal. After practice, all participants played the role of responders with an imaginary proposer. Participants had to decide whether to accept or reject proposers’ fair/unfair offers. In our mod-UG, additional condition was included that involved intentionality considerations: Unfair offers were displayed with another identical unfair offer. This emphasized the proposers’ inevitable situation of unfair offers. Subsequently, we conducted a 2×2 repeated-measures ANOVA (unfair offers with/without additional cues)×(ASC/TD).ResultsParticipants indeed accepted unfair offers significantly more frequently when the other player’s unfair proposal was unavoidable in cue-added conditions, when compared to unfair offers in no-cue conditions. This suggested that participants considered their opponent’s perspective more attentively in cue-added conditions. However, this effect was significantly decreased in the ASC-group (p<0.05; group-condition interaction).ConclusionsDecreased sensitivity to situational changes among ASC-individuals may be partly due to diminished or inflexible shifting of perspective. Whether this systematized decision-making associates with attentional-bias and stereotyped-behaviors requires further investigation.DisclosureNo significant relationships.

Replicator dynamics of an N-player snowdrift game with delayed payoffs

We consider a version of the N-player snowdrift game in which the payoffs obtained by the players are delayed. The delay in payoffs is shown to lead to a Hopf bifurcation with an associated critical value of the time delay in the replicator dynamics. For time delays larger than the critical time delay, the replicator dynamics oscillate around the equilibrium instead of asymptotically approaching it. The dependence of this critical time delay on the parameters of the game is determined. After developing the analysis for the 2-player game, the same methodology is applied to the N-player version of the game to show how the results change as a function of N, concluding with an analysis of the limiting case of large numbers of players.

Training effects of artificial rules on youth soccer team tactical behavior

ABSTRACT Background and purpose: Historically, sports training methodology, including soccer coaching, has been influenced by the pedagogic tend dominant in each epoch. Of late, the literature has espoused the idea that human learning is individual, nonlinear, and complex. Nonlinear Pedagogy (NLP) takes into account such nonlinearity and complex phenomena and facilitates each person's learning through a methodology of manipulating constraints. This learner–environment-centered approach conducts players and teams to a tactical behavior emerging through playing modified versions of games using a rich range of different constraints, for example the introduction of artificial rules. Despite the attractions of training based on constraints to research, few studies have empirically assessed the effects of these programs from a tactical perspective. The present study applies the NLP pedagogical principles of representativeness and constraints manipulation to provide youth sport academy coaches with empirical evidence of the training effects of modified games on team tactical behavior. Specifically, this study aimed to assess the short-term training effects of modified games introducing artificial rules on team tactical behavior during the team possession game phase in two youth soccer categories. Methods: Thirty-two Spanish male youth soccer players from the under-14 (U14: n = 16; age: 13.0 ± 0.4 years; playing experience: 6 ± 1 years; height: 1.56 ± 0.07 m; body mass: 46.7 ± 5.9 kg) and the under-16 (U16: n = 16; age: 15.9 ± 0.4 years; playing experience: 8 ± 1 years; height: 1.70 ± 0.07 m; body mass: 57.9 ± 8.3 kg) teams of the same club participated in the study. The natural groups were not modified for the study and the participants had some prior experience with modified games. Each team was divided into two groups who played each other during a short-term intervention distributed across four training sessions: control (CON: free play without restrictions) and experimental (EXP: modified games introducing artificial rules). Team tactical behavior was assessed, including the goalkeeper (Gk) and during the team possession game phase, using a local positioning system (LPS) before and after the intervention in an 8-a-side game with the official offside rule. Findings: Linear team tactical behavior change in centroid position, dyads, and total area values barely changed (d = trivial – small [0.01–0.34]) after a short-term intervention of free play and modified games. Team tactical behavior tended toward greater regularity (sample entropy decrease) after artificial rules were introduced in comparison with free play without restrictions. Youth sport academy coaches who opt for organized and regular behavior during the team possession game phase could employ modified games introducing artificial rules to build up repeatable tactical patterns. Conversely, those who prefer being more chaotic and unpredictable in the game could take advantage of free play without restrictions.

Application of Eye Tracking in Puzzle Games for Adjunct Cognitive Markers: Pilot Observational Study in Older Adults.

BackgroundRecent studies suggest that computerized puzzle games are enjoyable, easy to play, and engage attentional, visuospatial, and executive functions. They may help mediate impairments seen in cognitive decline in addition to being an assessment tool. Eye tracking provides a quantitative and qualitative analysis of gaze, which is highly useful in understanding visual search behavior.ObjectiveThe goal of the research was to test the feasibility of eye tracking during a puzzle game and develop adjunct markers for cognitive performance using eye-tracking metrics.MethodsA desktop version of the Match-3 puzzle game with 15 difficulty levels was developed using Unity 3D (Unity Technologies). The goal of the Match-3 puzzle was to find configurations (target patterns) that could be turned into a row of 3 identical game objects (tiles) by swapping 2 adjacent tiles. Difficulty levels were created by manipulating the puzzle board size (all combinations of width and height from 4 to 8) and the number of unique tiles on the puzzle board (from 4 to 8). Each level consisted of 4 boards (ie, target patterns to match) with one target pattern each. In this study, the desktop version was presented on a laptop computer setup with eye tracking. Healthy older subjects were recruited to play a full set of 15 puzzle levels. A paper-pencil–based assessment battery was administered prior to the Match-3 game. The gaze behavior of all participants was recorded during the game. Correlation analyses were performed on eye-tracking data correcting for age to examine if gaze behavior pertains to target patterns and distractor patterns and changes with puzzle board size (set size). Additionally, correlations between cognitive performance and eye movement metrics were calculated.ResultsA total of 13 healthy older subjects (mean age 70.67 [SD 4.75] years; range 63 to 80 years) participated in this study. In total, 3 training and 12 test levels were played by the participants. Eye tracking recorded 672 fixations in total, 525 fixations on distractor patterns and 99 fixations on target patterns. Significant correlations were found between executive functions (Trail Making Test B) and number of fixations on distractor patterns (P=.01) and average fixations (P=.005).ConclusionsOverall, this study shows that eye tracking in puzzle games can act as a supplemental source of data for cognitive performance. The relationship between a paper-pencil test for executive functions and fixations confirms that both are related to the same cognitive processes. Therefore, eye movement metrics might be used as an adjunct marker for cognitive abilities like executive functions. However, further research is needed to evaluate the potential of the various eye movement metrics in combination with puzzle games as visual search and attentional marker.

Investigating learners' engagement and science learning outcomes in different designs of participatory simulated games

AbstractThe purpose of this study was to investigate the affordances of participatory simulations by comparing students' models of engagement and science learning outcomes in a multi‐team participatory simulated game (MPSG) and a single‐team participatory simulated game (SPSG). Two versions of a mobile‐based game about marine fishery management were created. Participants were 105 seventh‐grade students in Taiwan. Research instruments included a Science Game Engagement questionnaire and a Marine Ecosystem and Sustainability Test. Students' interviews and classroom videos were also collected. Students' models of engagement were analyzed by using Partial Least Squares Structural Equation Modeling, and comparisons of subscales of engagement and learning outcomes were made by Analysis of Covariance statistics. The results showed that the students in the MPSG group had a higher level of behavioral engagement and better learning achievement than the students in the SPSG group did. Also, in exploring the interrelationships among the subscales of students' engagement, we found that, in the SPSG group, students' behavioral engagement was positively predicted by their emotional engagement, while in the MPSG group, it was positively predicted by their social engagement. In both groups, behavioral engagement predicted cognitive engagement. This finding was supported by the video data in that more interactions among the group members were observed in the MPSG group. This indicated that the multi‐agent, dynamic modeling in the MPSG may have shifted the quality of the learners' social interactions. The affordances of participatory simulated games are discussed, and future research directions are provided. Practitioner notesWhat is already known about this topic Participatory simulations allow users to participate in simulations by controlling one of the roles in the system which models real‐life settings. Dynamic modeling is an essential feature of participatory simulations that allows the learners to see the exact impact of their participation on changes in the system. Students who learned with the participatory simulations showed significantly better reasoning in concept building and fewer misconceptions than with conventional simulations. However learners can overly emphasize racing to win in multi‐agent participatory simulations and tasks in participatory simulations can be too challenging for some learners. What this paper adds We compared students' engagement models in two versions of a participatory game–a multi‐team participatory simulated game (MPSG) and a single‐team participatory simulated game (SPSG). We found that in the MPSG social engagement predicted behavioral engagement while in the SPSG students' emotional engagement played an important role. Students who participated in the MPSG had better performance in system thinking than the students in the SPSG. Implications for practice and/or policy Dynamic modeling is not only authentic for simulating certain scientific phenomena but also it offers the affordances of improving the quality of learners' social interactions. This should be taken into account in the future design of educational simulations. A multi‐team design of participatory simulation taking advantage of competition among teams and collaboration within teams can help students to learn complex phenomena.

Employing serious game for assessing knowledge of blood transfusion procedure among nurses: A qualitative evaluation and feedback improvement study

BackgroundEmploying serious game for assessing nurses' blood transfusion knowledge and skill competency has gained interest among nurse educators worldwide. However, its acceptance by nurses has not been fully explored. AimTo explore the registered nurses' experiences using serious game for nursing skills competency and gather feedback to improve the quality of learning using serious game. SettingAcute tertiary hospital in Singapore. ParticipantsRegistered nurses in inpatient settings. MethodsThis qualitative evaluation and feedback improvement study was conducted in an acute tertiary hospital in Singapore between September 2019 and November 2019. Registered nurses who had completed the blood transfusion knowledge and skills competency via the serious game platform were invited to participate in this study. Individual face-to-face interviews using a semi-structured questionnaire were conducted. All interviews were audio-recorded and transcribed verbatim. Data analysis was performed inductively using the Braun and Clarke's six-step of thematic analysis. ResultsA total of 11 registered nurses were interviewed from a variety of clinical areas including medical and surgical wards, and intensive care units. The mean age of the participants was 28 years old. The majority of participants were females (81.8%), with their years of experience ranging from 1 to 13 years. Each interview took between 20 and 30 min. Three themes were identified: (1) novel learning experience; (2) varying levels of appreciation towards the serious game; and (3) navigating the interface and technical issues. ConclusionEmploying serious game for nursing skills competency is considered acceptable by the nurses in this sample population. Compared to the traditional modes of competency assessment, the serious game is innovative and stimulates learning. Nevertheless, more rigorous efforts are needed to improve the interface and technical issues to enhance the user learning experience. Future versions of the serious game will need to be more accessible and intuitive for all levels of nursing staffs.

Minority games played by arbitrageurs on the energy market

Along with the energy transition, the energy markets change their organization towards more decentralized and self-organized structures, striving for locally optimal profits. These tendencies may endanger the physical grid stability. One realistic option is the exhaustion of reserve energy due to an abuse by arbitrageurs. We map the energy market to different versions of a minority game and determine the expected amount of arbitrage as well as its fluctuations as a function of the model parameters. Of particular interest are the impact of heterogeneous contributions of arbitrageurs, the interplay between external stochastic events and nonlinear price functions of reserve power, and the effect of risk aversion due to suspected penalties. The non-monotonic dependence of arbitrage on the control parameters reveals an underlying phase transition that is the counterpart to replica symmetry breaking in spin glasses. As conclusions from our results we propose economic and statutory measures to counteract a detrimental effect of arbitrage.

Simultaneously Improving Computational Thinking and Foreign Language Learning: Interdisciplinary Media With Plugged and Unplugged Approaches

This study proposed plugged and unplugged approaches for young students to simultaneously improve their interdisciplinary learning performance in English and Computational Thinking (CT). The plugged approach involved adopting educational robots to enhance CT and to provide English vocabulary and sentence practice via a board game. The unplugged version of the educational board game involved using a conventional board game without a computer, although it was designed for practicing CT as well as some foreign language vocabulary and conversational sentences. The results show that both approaches were helpful for simultaneously improving the students’ English proficiency of the target vocabulary and sentences, and their CT competence. The students’ foreign language learning anxiety during the English conversation in the plugged game was significantly lower than that of the students playing the unplugged game. On one hand, the cooperation tendency of the CT scale improved significantly for the students playing the unplugged game. On the other hand, the critical thinking of the CT scale improved significantly for those using the plugged approach. This research provides an innovation development and evaluation for plugged and unplugged approaches.

DARK TRIAD AND UTILITARIAN CHOICES: A STUDY FROM TURKEY

Purpose of this study is to examine effects of dark triad (narcissism, Machiavellianism and psychopathy) on the utilitarian choices. Data is collected from university students with an online survey using convenience method for sampling. To measure research variables, a version of dictator game that presents a salary raise case to participants and Short Dark Triad Scale (SD3) is used. Reliability analysis is conducted to SD3 which returned 0.611, 0.651 and 0.684 Cronbach’s alpha values for Dark Triad personality traits. Binary logistic regression analysis is used to test research hypotheses. Findings indicate that psychopathy has a significant and positive effect on the utilitarian choice whereas Machiavellianism and narcissism has not. Implications of the results are discussed and future research areas are suggested.

The effect of winning-losing perception on consumers’ variety-seeking behavior

PurposeThis study aims to investigate the effect of winning-losing perception, including the winning or losing result and the closeness of this result, on consumers’ subsequent variety-seeking behavior.Design/methodology/approachFour experimental designs, one with a modified version of the Tetris game, were used to show how and when winning or losing perceptions will influence individuals’ variety-seeking behavior.FindingsConsumers who have failed in a competition or not achieved a goal tend to seek less variety in their later consumption than do consumers who have succeeded because losing feedback weakens consumers’ perception of their control of personal mastery. This effect only exists when the closeness of winning or losing is narrow (e.g. the success is just missed) and diminishes when the result is clear and obvious.Research limitations/implicationsThe current study has systematically explored the interaction between winning-losing outcomes and the closeness of these outcomes.Practical implicationsThis study offers marketing managers practical guidance on how to use competition results to conduct marketing activities, such as transmitting advertisements for classic flavors to those who have lost in a video game or properly increasing the proportion of new flavors or products in stores or vending machines near sports venues.Originality/valueThis research adds to the literature on competition, which has largely overlooked the possible moderating role of the closeness of the competition result and its influence on individuals’ follow-up irrelevant behaviors and it also adds to the work on variety-seeking behavior, which has not explored the impact of winning-losing perception.

Phase transitions in a conservative game of life.

We investigate the dynamics of a conservative version of Conway's Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway's rules but only by swapping their positions, irrespective of their mutual distance. Our study is based on square-lattice simulations as well as a mean-field calculation. As the density of dead cells is increased, we identify a discontinuous phase transition between an inactive phase, in which the dynamics freezes after a finite time, and an active phase, in which the dynamics persists indefinitely in the thermodynamic limit. Further increasing the density of dead cells leads the system back to an inactive phase via a second transition, which is continuous on the square lattice but discontinuous in the mean-field limit.

Cooperative Stochastic Games with Mean-Variance Preferences

In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games.