Static Game Research Articles

Gradient-Based Algorithms With Intermediate Observations in Static and Differential Games

Gradient-Based Algorithms With Intermediate Observations in Static and Differential Games

Expected game value (xGV): a novel approach for strategic decision-making in rugby union

ABSTRACT This study introduces expected Game Value (xGV), a new analytical model for rugby union that quantifies the value of each game state. Unlike traditional methods relying on overall match data, xGV provides an intra-game perspective by weighting the impact of each action based upon its context. While comparable measures used in other sports often rely on machine learning methods, xGV employs generalised additive mixed models (GAMM), which account for the impact of teams as random effects while maintaining parameter flexibility through the use of penalised splines. The exclusion of these random effects from the final estimations enables the model to provide outputs that can be consistently compared across teams, regardless of their baseline strength while accounting for the repeated structure of the dataset. Built using spatio-temporal data derived from major competitions at elite standards, the model highlights teams with strong performances during this period, identifying them as top performers across various aspects of the game. As such, xGV provides valuable information to coaches and analysts and can help refine tactical decision-making and arguably represents a significant advance in rugby analysis by quantifying the value of the game at any given moment, enabling objective comparisons across teams and strategies.

Dilemma and sustainable development strategy of sharing teaching resources for big data majors in universities based on game theory

In the process of sharing teaching resources for big data majors in universities, the competition and cooperation between universities are complex, and there are problems such as unfair resource allocation and information asymmetry. Resource sharing faces many difficulties. In response to these issues, this article constructed a dynamic information evolution game model based on game theory, which integrated three sub models: static game, incomplete information game, and evolutionary game. The static game model was used to analyze the strategic choices of universities in a certain environment; the incomplete information game model revealed the game behavior under information asymmetry; the evolutionary game model simulated the dynamic evolution process of university strategies. This article combined a simulation case of the teaching resource sharing project for big data majors in university alliances, and used this model to identify and analyze the practical difficulties of resource sharing in universities, revealing the deep-seated reasons why resource sharing is difficult to achieve in competitive and cooperative relationships. On this basis, this article proposed a series of sustainable development strategies, including optimizing resource allocation mechanisms, improving information transparency, etc., providing theoretical support and practical reference for the effective sharing of teaching resources in big data majors in universities. Experimental data showed that in the resource sharing simulation process of five universities (A, B, C, D, E), the strategy adjustment values of each university decreased from around 0.8 to below 0.2.

A Propositional Cirquent Calculus for Computability Logic

Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability logic—the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main technical result of the article is a proof of the soundness and completeness of CL18 with respect to the semantics of computability logic.

VIGOR: Reviving Cloud Gaming Sessions

Cloud gaming is a multi-billion dollar industry. A client in cloud gaming sends its movement to the game server on the Internet, which renders and transmits the resulting video back. In order to provide a good gaming experience, a latency below 80 ms is required. This means that video rendering, encoding, transmission, decoding, and displaying have to finish within that time frame, which is especially challenging to achieve due to server overload, network congestion, and losses. In this paper, we propose VIGOR, a new method to revive cloud gaming sessions by recovering lost or corrupted video frames. Unlike traditional video frame recovery, VIGOR uses game states to enhance recovery accuracy significantly and utilizes partially decoded frames to recover lost portions. We develop a holistic system that consists of (i) efficiently extracting game states, (ii) modifying H.264 video decoder to generate a mask to indicate which portions of video frames need recovery, and (iii) designing a novel neural network to recover either complete or partial video frames. VIGOR is extensively evaluated using iPhone 12 and laptop implementations, and we demonstrate the utility of game states in the game video recovery and the effectiveness of our overall design.

NarrativeGenie: Generating Narrative Beats and Dynamic Storytelling with Large Language Models

Interactive narrative in games utilize a combination of dynamic adaptability and predefined story elements to support player agency and enhance player engagement. However, crafting such narratives requires significant manual authoring and coding effort to translate scripts to playable game levels. Advances in pretrained large language models (LLMs) have introduced the opportunity to procedurally generate narratives. This paper presents NarrativeGenie, a framework to generate narrative beats as a cohesive, partially ordered sequence of events that shapes narrative progressions from brief natural language instructions. By leveraging LLMs for reasoning and generation, NarrativeGenie, translates a designer’s story overview into a partially ordered event graph to enable player-driven narrative beat sequencing. Our findings indicate that NarrativeGenie can provide an easy and effective way for designers to generate an interactive game episode with narrative events that align with the intended story arc while at the same time granting players agency in their game experience. We extend our framework to dynamically direct the narrative flow by adapting real-time narrative interactions based on the current game state and player actions. Results demonstrate that NarrativeGenie generates narratives that are coherent and aligned with the designer’s vision.

SC-Phi2: A Fine-Tuned Small Language Model for StarCraft II Build Order Prediction

Background: This article introduces SC-Phi2, a fine-tuned StarCraft II small language model. Small language models, like Phi2, Gemma, and DistilBERT, are streamlined versions of large language models (LLMs) with fewer parameters that require less computational power and memory to run. Method: To teach Microsoft’s Phi2 model about StarCraft, we create a new SC2 text dataset with information about StarCraft races, roles, and actions and use it to fine-tune Phi-2 with self-supervised learning. We pair this language model with a Vision Transformer (ViT) from the pre-trained BLIP-2 (Bootstrapping Language Image Pre-training) model, fine-tuning it on the StarCraft replay dataset, MSC. This enables us to construct dynamic prompts that include visual game state information. Results: Unlike the large models used in StarCraft LLMs such as GPT-3.5, Phi2 is trained primarily on textbook data and contains little inherent knowledge of StarCraft II beyond what is provided by our training process. By using LoRA (Low-rank Adaptation) and quantization, our model can be trained on a single GPU. We demonstrate that our model performs well at build order prediction, an important StarCraft macromanagement task. Conclusions: Our research on the usage of small models is a step towards reducing the carbon footprint of AI agents.

Initial state diversification for efficient AlphaZero-style training

AlphaZero has achieved superhuman performance in Go, chess, and shogi with a general reinforcement learning (RL) algorithm. This achievement is remarkable because AlphaZero does not rely on any training dataset of strong players. However, AlphaZero-style training requires substantial computational resources. Gumbel AlphaZero, a recently introduced more efficient version of AlphaZero, reduces the computational cost of AlphaZero training. The goal of this study is to further improve the playing strength of Gumbel AlphaZero under a limited amount of computational resources. We focus on the diversity in training games, inspired by procedural generation and domain randomization in RL studies, and propose a novel method, initial state diversification. This method diversifies the initial states of a self-play game to encourage the RL agent to understand the game in a more general manner through diverse experiences. For example, in shogi, the initial state of each self-play game is diversified by rearranging the pieces under realistic domain constraints. Experiments demonstrated that training with initial state diversification improves the playing strength of Gumbel AlphaZero in shogi, within the same computational budget for training.

Identifying influential nodes in social networks from the perspective of attack-defense game.

Influence spread analysis, a critical component of social network studies, focuses on the patterns and effects of information dissemination among interconnected entities. The core of influence spread analysis is to identify influential nodes that involve two distinct aspects: influence maximization (IM) and influence blocking maximization (IBM). However, when IM and IBM occur simultaneously, identifying influential nodes becomes an intricate decision-making challenge. This study addresses identifying influential nodes in social networks through an attack-defense game perspective, where an attacker maximizes influence and a defender minimizes it. We first develop a two-player static zero-sum game model considering resource constraints. Based on the equilibrium strategy of this game, we redefine the concept of influential nodes from various viewpoints. Extensive experiments on synthetic and real-world networks show that, in most cases, the defender preferentially defends critical nodes, while the attacker adopts the decentralized strategy. Only when resources are unevenly matched do both players tend to adopt centralized strategies. This study expands the connotation of influential nodes and provides a novel paradigm for the social network analysis with significant potential applications.

EXPLORING THE LIMITS OF MCTS IN PAC-MAN: MAZE SIZE, SIMULATIONS, AND PERFORMANCE

This paper explores the performance and limitations of Monte Carlo Tree Search (MCTS) when applied to the Pac-Man game, with a particular focus on how maze complexity and the number of simulations affect the agent’s decision-making process. The game serves as a dynamic environment where the MCTS agent must navigate mazes filled with rewards (capsules and food) and avoid adversarial agents (ghosts), creating a challenging testbed for decision-making algorithms. The primary objective of this work is to assess the efficiency of MCTS across mazes of varying sizes and configurations, from small, optimized layouts to large, non-optimized ones. We aim to understand the trade-offs between computational resources (e.g., number of simulations) and the agent's overall performance, particularly in terms of score, win rate, and decision-making time. The experiments were conducted using different numbers of simulations per move, allowing the MCTS agent to build decision trees that guide its actions. This enabled us to observe how performance metrics evolve as the complexity of the environment increases. The findings indicate that MCTS performs effectively in smaller, optimized mazes where paths are clearer, and the decision space is more manageable. However, as maze complexity grows—particularly in non-optimized environments filled with obstacles and unpredictable paths—the agent's performance deteriorates. A key insight is that increasing the number of simulations does improve decision quality to an extent, but only up to a point; beyond that, additional simulations incur a computational overhead that does not yield proportional gains in performance. Moreover, the experiments reveal that optimized maze designs allow the MCTS agent to make more informed and efficient decisions, while non-optimized mazes exacerbate the agent’s struggle with unpredictability and more complex decision spaces. These findings underscore the limitations of MCTS in handling dynamic and irregular environments. Key conclusions include the necessity of enhancing MCTS for complex scenarios by incorporating more advanced heuristic functions to evaluate game states more accurately, along with adaptive simulation strategies to better manage computational resources. Additionally, combining MCTS with reinforcement learning or neural networks could offer more robust solutions for tackling the growing complexity of both in-game and real-world environments. This research highlights several promising avenues for future exploration, particularly in applying MCTS to more intricate AI challenges such as autonomous navigation and real-time decision-making in robotics.

Industrial Accident Prevention Training with Time Travel Prevention Games: Adaptive Personalized Story Experiences by Artificial Intelligence

Industrial accident prevention is a problem of societal relevance. It is worth the investment of contemporary education theory and up-to-date information and communication technologies including Artificial Intelligence (AI). Apparent deficiencies of AI that is based on Large Language Models (LLMs) und Generative Pre-trained Transformers (GPTs) bear abundant evidence for the need of going beyond the limits of sub-symbolic AI. Game based training is attractive to practitioners and advantageous over conventional educational methods. There is developed, implemented, and applied the original concept of time travel prevention games. The approach is generic and applies to other domains such as crime prevention and health care as well. The key idea is interactive story engagement that allows, if necessary, for virtual time travel to impact the fate. Trainees experience stories of success. Digital storyboarding is an AI design methodology derived from approaches to dynamic plan generation. Technically, a storyboard is a hierarchically structured family of graphs. Semantically, it determines a potentially infinite space of different stories. Single stories unfold at execution time, i.e. during game play, dynamically in response to human activities and environmental conditions. The game AI analyzes the history of game play represented as a string of actions and events. Operationally, string processing, counting letters in strings, finding properties of strings, and the like is key. The prepared alternatives of unfolding game play represent the interdisciplinary designer team's intelligence based on domain knowledge, education theory, learning psychology, game design principles, VR technology, and the like. The storyboard is the place where AI resides. Keywords: industrial accident prevention, prevention training, time travel prevention games, education theory, Artificial Intelligence, sub-symbolic AI, symbolic AI, adaptivity, play state, game state, storyboarding, storyboard interpretation technology

Current State of Serious Games in Human Trafficking: Evaluation, Gaps, and Future Research Directions

Addressing human trafficking is crucial due to its severe impact on human rights, dignity, and well-being. Serious games refer to digital games that are designed to entertain while also accomplishing at least one additional objective, such as learning or health promotion. Serious games play a significant role in raising awareness, training professionals, fostering empathy, and advocating for policy improvements related to human trafficking. In this study, we systematically examine and assess the current landscape of serious games addressing human trafficking to unveil the existing state, pinpoint gaps, and propose future research avenues. Our investigation encompassed academic publications, gray literature, and commercial games related to human trafficking. Furthermore, we conducted a thorough review of evaluation criteria and heuristics for the comprehensive assessment of serious games. Subsequently, incorporating these evaluation metrics and heuristics, the games were subjected to evaluation by both players and experts. Following a combined qualitative and quantitative analysis, the results were deliberated upon, and their implications were expounded. Five serious games related to human trafficking were identified and evaluated using the SGES and EGameFlow scales, along with both game-specific and serious game heuristics. Player and expert evaluations ranked “(Un)TRAFFICKED” and “Missing” as the best-performing games, while “SAFE Travel” received the lowest ratings. Players generally rated the games higher than experts, particularly in usability, feedback, and goal clarity, although the games scored poorly in audiovisual quality and relevance. Experts highlighted deficiencies in motivation, challenge, and learning outcomes. The lack of personalization and the absence of social gaming elements point to the need for more targeted human trafficking games adapted to different demographics, cultures, and player types.

A game-based decision-making method for multi-ship collaborative collision avoidance reflecting risk attitudes in open waters

A game-based decision-making method for multi-ship collaborative collision avoidance reflecting risk attitudes in open waters

How Could They Win? An Exploration of Win Condition for Esports Narratives in Dota 2

Data analytics is commonly used to enable storytelling and enhance esport coverage. One prominent use of it is win prediction, where machine learning models predict the winner of the game before its conclusion. However, predictions are most commonly results of black-box systems, forcing commentators to produce ad-hoc interpretations. Additionally, broadcasters generally rely other metrics to build narratives, limiting the impact of win prediction models for storytelling. This paper explores an alternative method to win prediction, identifying the needs of broadcasters to guide development of a novel win condition model. By focusing on existing storytelling points, the proposed win condition model can offer greater storytelling opportunities to broadcasters, focusing on the user needs identified from within the esport domain. Rather than utilising game state data to predict the winner, as it is usually done in win prediction, the proposed win condition model uses an exploration of the possible winners to predict the game state needed for each team to win. Lastly, the features identified for win condition are evaluated through a series of machine learning models, which provide a data-driven metric to test and predict win condition in the context of Dota 2, a popular esport title.

Optimal strategies for virtual power plants to participate in medium- and long-term power trading in the context of contracts for difference (CFDs)

Abstract In the context of virtual power plants gradually joining the medium-and long-term power market transactions, the decision-making problem of this new subject in the transaction process has attracted wide attention. Since virtual power plants possess distributed power sources on the supply side, as well as variable loads, energy storage, and other resources on the customer side, they are able to participate in both the sale and purchase of electricity in the medium-and long-term electricity market at the same time, which leads to the need for the relevant analysis to be divided into the two cases of sale and purchase of electricity. At the same time, due to the wide application of the CFD mechanism, power transactions should also take into account the compensation adjustment brought by this mechanism in addition to the market price. To sum up, this paper constructs a static game model for the virtual power plant’s power sales and purchasing strategies in the medium-and long-term power market under the premise of the CFD mechanism. The analysis shows that the optimal trading volume is related to the CFD volume, the total volume of power supplied by the bidding, the market price, etc. The relevant conclusions will help market managers to grasp the market price. The conclusions of the analysis help market managers grasp the key transaction information and assist virtual power plants to participate in medium-and long-term power transactions in an orderly manner.

Rationalizable self-confirming equilibrium in static games with unawareness

Rationalizable self-confirming equilibrium in static games with unawareness

Cloud security in the age of adaptive adversaries: A game theoretic approach to hypervisor-based intrusion detection

Cloud security in the age of adaptive adversaries: A game theoretic approach to hypervisor-based intrusion detection

Towards a foundation large events model for soccer

AbstractThis paper introduces the Large Events Model (LEM) for soccer, a novel deep learning framework for generating and analyzing soccer matches. The framework can simulate games from a given game state, with its primary output being the ensuing probabilities and events from multiple simulations. These can provide insights into match dynamics and underlying mechanisms. We discuss the framework’s design, features, and methodologies, including model optimization, data processing, and evaluation techniques. The models within this framework are developed to predict specific aspects of soccer events, such as event type, success likelihood, and further details. In an applied context, we showcase the estimation of xP+, a metric estimating a player’s contribution to the team’s points earned. This work ultimately enhances the field of sports event prediction and practical applications and emphasizes the potential for this kind of method.

Models for dual-channel remanufacturing supply chain with reference price effect under static and dynamic games

With the diversity of shopping styles, reference prices have become a consideration in consumers’ purchasing decisions. It is critical to understand how manufacturers and retailers make optimal decisions based on consumer behavior. To this end, we develop a manufacturer-led Stackelberg (M-Stackelberg) game model to investigate the impact of consumer proportion, reference price effect (RPE), and the channel preference coefficient on the decision of the remanufacturing supply chain (RSC) in dual-channel structures. Through comparing different game scenario models, we find that when the reference price coefficient is relatively small, the optimal decisions for the manufacturer and the retailer are the same regardless of whether the RPE is considered. The manufacturer and E-tailer always benefit from RPE, while the traditional retailer (T-retailer) is uncertain. The numerical analysis revealed that the profits of supply chain members are inversely proportional to the proportion of consumers. The smaller the proportion of primary consumers, the more favorable the supply chain. In particular, the higher the channel preference coefficient, the higher the profits of the manufacturer and E-tailer, while the lower the benefit of the T-retailer. Further, in the dynamic game, the total supply chain profit is highest when the T-retailer prices earlier than the E-tailer.

Baseboll för anarkister

The aim of this article is to examine the emergence and establishment of the ball game ‘brännboll’ (lit. burnball) in Sweden. In doing so, it contributes to the knowledge of how sports have spread historically and how they have changed when established in new places. First of all, the existence of the concept of brännboll throughout history is examined. Although it can be traced back to the 17th century, the game we now commonly call brännboll is a modified form of the English game of rounders that was introduced to Sweden at the end of the 19th century. Unlike the closely related game of baseball, brännboll never developed into a modern sport with standardised rules, organisations and bureaucracy. This is seen in the study as a consequence of the fact that brännboll gained a foothold in the ‘play movement’ rather than in the modern sports movement, and that physical education was considered more important in brännboll than performance and results. As a result of this process of pedagogisation, the game developed into a simplified, stripped-down and more static game compared to its English predecessor.