Learning Through Redesigning a Game in the STEM Classroom

Background Play is an important part of the childhood. The learning potential of playing and creating non-digital games, like tabletop games, however, has not been fully explored. Aim The study discussed in this paper identified a range of activities through which learners redesigned a mathematics-oriented tabletop game to develop their ideas and competencies in an integrated STEM (science, technology, engineering, and mathematics) class. Method Third and fourth graders worked as teams to make changes on Triominos over a period of six weeks. Considering what could be changed from the original game, each group provided a different design for Triominos to accommodate the changes introduced. We gathered data through weekly observations of two classes (about 45 learners, ranging from age eight to ten) in a west-Canada school. In this paper, we present the works of three groups of three teammates. Results We found that any change made by learners not only influenced mechanics, dynamics, and aesthetics of the game but also helped engage learners, encourage unconventional ideas, promote learning, and solve problems. Based on our findings, we suggest redesigning games facilitated learners deepen their understanding of mathematical concepts as part of a designed game system in STEM classes.

Marginality and convexity in partition function form games

In this paper an order on the set of embedded coalitions is studied in detail. This allows us to define new notions of superaddivity and convexity of games in partition function form which are compared to other proposals in the literature. The main results are two characterizations of convexity. The first one uses non-decreasing contributions to coalitions of increasing size and can thus be considered parallel to the classic result for cooperative games without externalities. The second one is based on the standard convexity of associated games without externalities that we define using a partition of the player set. Using the later result, we can conclude that some of the generalizations of the Shapley value to games in partition function form lie within the cores of specific classic games when the original game is convex.

Returning to Azeroth: Nostalgia, Sense of Place, and Social Presence in World of Warcraft Classic

World of Warcraft (WoW) Classic (released August 2019) allows players to return to the original game experience. This study considers how WoW players experience game content through media nostalgia and sense of place and investigates how social presence impacts these components of experience. Survey questions addressed 306 participants’ experiences in WoW, feelings of nostalgia and sense of place in Azeroth, and experiences with social presence in WoW; open-ended questions were asked about their motivations to play WoW. Prior overall WoW experience and higher sense of social presence increase personal nostalgia scores (replicating previous research). Sense of place scores increased with higher sense of social presence but were overall lower for current WoW Classic players. Social presence proved an important component of both personal nostalgia and sense of place. These findings expand and extend researchers’ understanding of the relationships between nostalgia, sense of place, and social presence within this unique site of study.

IMPLICATION THE CROSS-PLATFORM LOVE2D ENGINE FOR RENDERING AND ARTIFICIAL INTELLEGENCE DEVELOPMENT

Recently, the market for consoles and mobile games is growing, and therefore to find a game engine that meets the demanding requirements of users is not an easy task. Technology platforms have become clear favorites of many developers. However, the market is volatile, and therefore the question of choosing a game engine will not lose its relevance in the near future and is the first, main, relevant and important subject of choice in this work. The relevance of this article is to write an original algorithm for 2D computer game, taking into account the latest intelligent technologies, which will be different from previous versions by its uniqueness: a new procedural generation, improved artificial intelligence of characters, original game mechanics, which necessitated the creation of a key to unlock levels. To work on this task, the open cross-platform LOVE2D engine and the Lua programming language a powerful, efficient and easy to learn language were substantiated. The reason for choosing the LOVE2D game engine is that its technology is unique in itself. Simple text was used in the development of the game algorithm. A significant number of issues were resolved in unique way from scratch while developing. Original positions of game mechanics are created such as unlocking the end of the level, the infinity of the game and focusing on the maximum "Score", increasing the size of each subsequent level, compared to the previous one, improved artificial intelligence of characters are the main differences from existing approaches used to create previous Super Mario Bros projects. The reason that makes this project more advanced and a little more random than the original game: it's a procedural level generation. Since the game is infinite it's really important to keep levels random and different. The obtained results made it possible to say that the work done is a new step forward in comparison with previous developments of algorithms for this 2D game. The original algorithm and code for 2D computer game, using the capabilities of modern information technologies, can be useful not only for creating mobile games, but also for solving virtual reality, augmented reality, TV presentation, visualization effects of the hologram. The project presented in the paper is made exclusively for the purpose of implementation in the educational process.

The Connection between the PQ Penny Flip Game and the Dihedral Groups

This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study the original game and its possible extensions. In this paper, it is shown that the PQ penny flip game can be associated, in a precise way, with the dihedral group D8 and that within D8 there exist precisely two classes of equivalent winning strategies for Q. This is achieved by proving that there are exactly two different sequences of states that can guarantee Q’s win with probability 1.0. It is demonstrated that the game can be played in every dihedral group D8n, where n≥1, without any significant change. A formal examination of what happens when Q can draw their moves from the entire U(2), leads to the conclusion that, again, there are exactly two classes of winning strategies for Q, each class containing an infinite number of equivalent strategies, but all of them sending the coin through the same sequence of states as before. Finally, when general extensions of the game, with the quantum player having U(2) at their disposal, are considered, a necessary and sufficient condition for Q to surely win against Picard is established: Q must make both the first and the last move in the game.

Two-Level Cooperative Game on Hypergraph

In the paper, the cooperative game with a hypergraph communication structure is considered. For this class of games, a new allocation rule was proposed by splitting the original game into a game between hyperlinks and games within them. The communication possibilities are described by the hypergraph in which the nodes are players and hyperlinks are the communicating subgroups of players. The game between hyperlinks and between players in each hyperlink is described. The payoff of each player is influenced by the actions of other players dependent on the distance between them on hypergraph. Constructed characteristic functions based on cooperative behaviour satisfy the convexity property. The results are shown by the example.

Subgame‐perfect equilibrium in games with almost perfect information: Dispensing with public randomization

Harris, Reny, and Robson (1995) added a public randomization device to dynamic games with almost perfect information to ensure existence of subgame perfect equilibria (SPE). We show that when Nature's moves are atomless in the original game, public randomization does not enlarge the set of SPE payoffs: any SPE obtained using public randomization can be “decorrelated” to produce a payoff‐equivalent SPE of the original game. As a corollary, we provide an alternative route to a result of He and Sun (2020) on existence of SPE without public randomization, which in turn yields equilibrium existence for stochastic games with weakly continuous state transitions.

NOSTALGIA FOR THE NEW: VIDEO GAME "REMAKES" AND THE LIMITS OF REFLECTION

In this paper I consider comments posted on the official trailers of Final Fantasy VII Remake and Yakuza Kiwami (from the verified Playstation YouTube channel) as iterations of nostalgia within the context of fifth- and sixth-generation digital game “remakes,” where the narrative and characters (Mäyrä’s (2008) “shell”) of the original game have been retained, but the game’s engine and mechanics (Mäyrä’s “core”) have been wholly replaced with modern technology. Using these comments, I attempt to place responses to these games into Garda’s (2013) nostalgia continuum as a way of testing the possibilities and limitations of “nostalgia” as a framework for understanding AAA remakes.

Automated Construction of Bounded-Loss Imperfect-Recall Abstractions in Extensive-Form Games (Extended Abstract)

Information abstraction is one of the methods for tackling large extensive-form games (EFGs). Removing some information available to players reduces the memory required for computing and storing strategies. We present novel domain-independent abstraction methods for creating very coarse abstractions of EFGs that still compute strategies that are (near) optimal in the original game. First, the methods start with an arbitrary abstraction of the original game (domain-specific or the coarsest possible). Next, they iteratively detect which information is required in the abstract game so that a (near) optimal strategy in the original game can be found and include this information into the abstract game. Moreover, the methods are able to exploit imperfect-recall abstractions where players can even forget the history of their own actions. We present two algorithms that follow these steps -- FPIRA, based on fictitious play, and CFR+IRA, based on counterfactual regret minimization. The experimental evaluation confirms that our methods can closely approximate Nash equilibrium of large games using abstraction with only 0.9% of information sets of the original game.

Canon Anxiety?

Canons—of music, video games, or people—can provide a shared pool of resources for scholars, practitioners, and fans; but the formation of canons can also lead to an obscuring or devaluing of materials and people outside of a canon. The four authors in this colloquy interrogate issues of canons relating to video game music and sound from a variety of perspectives. Each author considers an aspect of canonization and argues for a wider purview. In “Rewritable Memory: Concerts, Canons, and Game Music History,” William Gibbons examines the ways in which concerts of video game music may create canons and reinforce particular historical narratives. In “On Canons as Music and Muse,” Julianne Grasso views the music originally presented in a video game as itself a type of canon and argues that official and fan arrangements of original game music may provide windows into lived experiences of play. In “The Difficult, Uncomfortable, and Imperative Conversations Needed in Game Music and Sound Studies,” Hyeonjin Park highlights issues of diversity and representation in the field of video game music and sound studies, with respect to the people and music that make up the subjects of the field, the people who produce scholarship in the field, and the people who engage with game music and sound. In “Canon Anxiety?” Karen Cook pulls together various issues of academic canons to question the scope, focus, and diversity of the growing field in which the Journal of Sound and Music in Games exists.