World models are often neural network-based models that attempt to approximate an entire video game. Existing world models are not practical for game developers due to their large scale, lack of accessibility, their prompt-based interfaces, and their nature as black box models where developers cannot access the code. In this paper, we propose an approach, Finite Automata Extraction (FAE), that learns a neuro-symbolic world model represented as programs in a novel domain-specific language (DSL): Retro Coder. The neuro-symbolic world model structure allows for low data learning, meaning we can learn these models from a single gameplay video. This model’s structure means that developers can directly access code to change the behaviour of the model, and it’s low data cost makes it more accessible. In a comparison to prior neural world model approaches, FAE learns a more precise model of the environment and it learns more general code than prior DSL-based approaches.

We presentlatent combinational game design—an approach for generating playable games that blend a given set of games in a desired combination using deep generative latent variable models. We use Gaussian mixture variational autoencoders (GMVAEs), which model the VAE latent space via a mixture of Gaussian components. Through supervised training, each component encodes levels from one game and lets us define blended games as linear combinations of these components. This enables generating new games that blend the input games as well as controlling the relative proportions of each game in the blend. We also extend prior blending work using conditional VAEs and compare against the GMVAE and additionally introduce a hybrid conditional GMVAE architecture, which lets us generate whole blended levels and layouts. Results show that these approaches can generate playable games that blend the input games in specified combinations. We use both platformers and dungeon-based games to demonstrate our results.

In this article, we introduce the concept of procedural content generation via knowledge transformation (PCG-KT), a new lens and framework for characterizing PCG methods and approaches in which content generation is enabled by the process of knowledge transformation: transforming knowledge derived from one domain in order to apply it in another. Our work is motivated by a substantial number of recent PCG works that focus on generating novel content via repurposing derived knowledge. Such works have involved, for example, performing transfer learning on models trained on one game's content to adapt to another game's content, as well as recombining different generative distributions to blend the content of two or more games. Such approaches arose in part due to limitations in PCG via machine learning, such as producing generative models for games lacking training data and generating content for entirely new games. In this article, we categorize such approaches under this new lens of PCG-KT by offering a definition and framework for describing such methods and surveying existing works using this framework. Finally, we conclude by highlighting open problems and directions for future research in this area.

Prior work using skill chains for matchmaking-based dynamic difficulty adjustment in human computation games required skill chains to be manually defined for a game, and each level to be manually annotated with the individual skills needed to complete that level. In this work, we present two approaches for defining level orderings for DDA in the platformer HCG Iowa James without using such manually-defined skill chains and annotations. The first involves sequences of action-context pairs found in gameplay traces. The second consists of applying K-means clustering on segments of levels. Our results show that both new approaches outperform baseline random level ordering and perform similarly to the skill chain approach.

Variational autoencoders (VAEs) have been used in prior works for generating and blending levels from different games. To add controllability to these models, conditional VAEs (CVAEs) were recently shown capable of generating output that can be modified using labels specifying desired content, albeit working with segments of levels and platformers exclusively. We expand these works by using CVAEs for generating whole platformer and dungeon levels, and blending levels across these genres. We show that CVAEs can reliably control door placement in dungeons and progression direction in platformer levels. Thus, by using appropriate labels, our approach can generate whole dungeons and platformer levels of interconnected rooms and segments respectively as well as levels that blend dungeons and platformers. We demonstrate our approach using The Legend of Zelda, Metroid, Mega Man and Lode Runner.

We present a fully online system for skill and ratings-based dynamic difficulty adjustment (DDA) in human computation games (RCGs). Prior work used an initial offline phase for collecting level ratings to avoid cold-start when using the system online. Further, such systems set a fixed target score win/lose threshold for each level. In this work, we address these issues by 1) using an ∊-greedy variant of the ratings and skill-based DDA algorithm and 2) applying rating arrays, proposed in past work but not yet used in an online setting. We demonstrate our system in two online matchmaking experiments using two HCGs. Results suggest that the ∊-greedy modification helps address the cold-start and that using rating arrays leads to players completing more levels.

Player engagement and task effectiveness are crucial factors in human computation games. However, collecting data and making design changes towards these goals can be time-consuming. In this work, we incorporate rapid crowdsourced playtesting via the ARAPID (As Rapid As Possible Iterative Design) system to iterate on the design of a human computation platformer game. For each level in the game, the player’s goal is to collect items relevant to a given scenario while avoiding irrelevant items. We extended the visualization modules in the existing ARAPID system to include a multi-level data visualization and item collection task effectiveness plot. A designer from the project team used the system to iterate on the game’s level design, with the goal of increasing relevant and decreasing irrelevant items collected by players. A large-scale test with the game versions created during the iterative analysis found that the designer was able to use ARAPID to improve the specified goal parameters.

Several works have demonstrated the use of variational autoencoders (VAEs) for generating levels in the style of existing games and blending levels across different games. Further, quality-diversity (QD) algorithms have also become popular for generating varied game content by using evolution to explore a search space while focusing on both variety and quality. To reap the benefits of both these approaches, we present a level generation and game blending approach that combines the use of VAEs and QD algorithms. Specifically, we train VAEs on game levels and run the MAP-Elites QD algorithm using the learned latent space of the VAE as the search space. The latent space captures the properties of the games whose levels we want to generate and blend, while MAP-Elites searches this latent space to find a diverse set of levels optimizing a given objective such as playability. We test our method using models for 5 different platformer games as well as a blended domain spanning 3 of these games. We refer to using MAP-Elites for blending as Blend-Elites. Our results show that MAP-Elites in conjunction with VAEs enables the generation of a diverse set of playable levels not just for each individual game but also for the blended domain while illuminating game-specific regions of the blended latent space.

This paper presents a comparative analysis of two popular control approaches, namely, Classical Control and Model Predictive Control (MPC) applied to a bidirectional quasi Z-Source converter (qZSC). The paper describes the topology of the bidirectional quasi Z-source converter, the basic philosophy of classical control, and the basic concept of model predictive control. The small signal models of the qZSC required for design of classical controllers, and discrete predictive models of the qZSC required for the MPC are also presented in this paper. Using these models and control algorithms, the systems were simulated in Matlab/Simulink and the results were compared. The comparisons were performed on the basis of transient and steady state response, robustness to parameter variations, and harmonic content of the resultant output waveforms. The comparative analysis shows that both the approaches have certain strengths and weaknesses and one may be chosen over the other based on varieties of factors.

In recent years, machine learning (ML) systems have been increasingly applied for performing creative tasks. Such creative ML approaches have seen wide use in the domains of visual art and music for applications such as image and music generation and style transfer. However, similar creative ML techniques have not been as widely adopted in the domain of game design despite the emergence of ML-based methods for generating game content. In this paper, we argue for leveraging and repurposing such creative techniques for designing content for games, referring to these as approaches for Game Design via Creative ML (GDCML). We highlight existing systems that enable GDCML and illustrate how creative ML can inform new systems via example applications and a proposed system.

Existing methods of level generation using latent variable models such as VAEs and GANs do so in segments and produce the final level by stitching these separately generated segments together. In this paper, we build on these methods by training VAEs to learn a sequential model of segment generation such that generated segments logically follow from prior segments. By further combining the VAE with a classifier that determines whether to place the generated segment to the top, bottom, left or right of the previous segment, we obtain a pipeline that enables the generation of arbitrarily long levels that progress in any of these four directions and are composed of segments that logically follow one another. In addition to generating more coherent levels of non-fixed length, this method also enables implicit blending of levels from separate games that do not have similar orientation. We demonstrate our approach using levels from Super Mario Bros., Kid Icarus and Mega Man, showing that our method produces levels that are more coherent than previous latent variable-based approaches and are capable of blending levels across games.

Procedural content generation via machine learning (PCGML) has demonstrated its usefulness as a content and game creation approach, and has been shown to be able to support human creativity. An important facet of creativity is combinational creativity or the recombination, adaptation, and reuse of ideas and concepts between and across domains. In this paper, we present a PCGML approach for level generation that is able to recombine, adapt, and reuse structural patterns from several domains to approximate unseen domains. We extend prior work involving example-driven Binary Space Partitioning for recombining and reusing patterns in multiple domains, and incorporate Variational Autoencoders (VAEs) for generating unseen structures. We evaluate our approach by blending across 7 domains and subsets of those domains. We show that our approach is able to blend domains together while retaining structural components. Additionally, by using different groups of training domains our approach is able to generate both 1) levels that reproduce and capture features of a target domain, and 2) levels that have vastly different properties from the input domain.

Player engagement within a game is often influenced by its difficulty curve: the pace at which in-game challenges become harder. Thus, finding an optimal difficulty curve is important. In this paper, we present a flexible and formal approach to transforming game difficulty curves by leveraging function composition. This allows us to describe changes to difficulty curves, such as making them "smoother", in a more precise way. In an experiment with 400 players, we used function composition to modify the existing difficulty curve of the puzzle game Paradox to generate new curves. We found that transforming difficulty curves in this way impacted player engagement, including the number of levels completed and the estimated skill needed to complete those levels, as well as perceived competence. Further, we found some transformed curves dominated others with respect to engagement, indicating that different design goals can be traded-off by considering a subset of curves.

Prior work has focused on formalizing difficulty curves by using function composition to give precise definitions to curves and their transformations. However, the proposed framework was demonstrated using a single game, and the curves and transformations were defined with respect to the game's ratings-based dynamic difficulty system. In this work, we infer difficulty curves from gameplay data using a method that is based on the aforementioned difficulty system but that can also be generalized to other games for which information on player-vs-level win/loss outcomes is available. Moreover, since this method uses the same difficulty mechanism as past work, it lets us similarly leverage function composition to compare difficulty curves across games, having either a fixed or dynamic level ordering, using a clearly defined vocabulary. We use four different games to demonstrate our method, which relies on an adjustment to traditional playback of ratings-based match data, which we also present in this work.

Rating systems (like Elo and Glicko-2) have previously been used for predicting the expected score that a player will achieve on a level. We present an approach that predicts not a single score, but an approximate cumulative distribution function over possible scores. This approach assigns each level an array of multiple ratings for different score thresholds. Our long-term goal is twofold: first, to dynamically change level difficulty for each player by using this CDF to tailor the target score required to complete a level; second, in human computation games (HCGs), to identify players capable of setting new high scores that could correspond to improved solutions to underlying tasks. To move towards this goal, we explore the rating array approach using two datasets: one gathered from the HCG Paradox, and one generated from idealized players and levels. We examine the accuracy of the CDF and the expected scores it predicts, as well as its use in serving levels to players who could set new high scores.

Previous work has demonstrated the effectiveness of rating system-based matchmaking for level ordering within the particular constraints of human computation games. However, players were not informed about the rating system, nor allowed to choose the difficulty of upcoming levels. Informing players of the ratings used in the system and offering them choice of upcoming level difficulty may enhance feelings of competence and control respectively, thereby further improving player engagement. Thus, we attempted to improve player experience by both exposing players to the underlying rating system, as well as offering them choice of level difficulty. We found that players cognizant of ratings both attempted and completed more levels than those who were not. Though additionally offering choice did not significantly affect behavior, we found that player choice was influenced by the outcome of the preceding level. Moreover, we did not observe any significant impact on self-reported measures of subjective experience.

Paid platforms like Mechanical Turk are popular for recruiting players for playtesting and experiments. However, it is unclear if paid players have similar behavior or experiences as volunteers (i.e. players recruited for free through banner ads or game portals). In this work, we studied the impact of recruitment within human computation games, using two experiments. First, we compared voluntary recruitment versus paid recruitment with different compensation levels. We found that the highest paid players completed more levels (i.e. achieved a higher volume of completed tasks) and reported greater engagement than both volunteers and players paid less while volunteers completed levels of higher difficulty (i.e. achieved a higher quality of completed tasks) than paid players. Additionally, we also varied both recruitment strategy and the game's design and found no interaction effects, suggesting that while differences exist between volunteer and paid players, experimental changes do not impact those players differently.

Human computation games lack established ways of balancing the difficulty of tasks or levels served to players, potentially contributing to their low engagement rates. Traditional player rating systems have been suggested as a potential solution: using them to rate both players and tasks could estimate player skill and task difficulty and fuel player-task matchmaking. However, neither the effect of difficulty balancing on engagement in human computation games nor the use of player rating systems for this purpose has been empirically tested. We therefore examined the engagement effects of using the Glicko-2 player rating system to order tasks in the human computation game Paradox. An online experiment (n=294) found that both matchmaking-based and pure difficulty-based ordering of tasks led to significantly more attempted and completed levels than random ordering. Additionally, both matchmaking and random ordering led to significantly more difficult tasks being completed than pure difficulty-based ordering. We conclude that poor balancing contributes to poor engagement in human computation games, and that player rating system-based difficulty rating may be a viable and efficient way of improving both.