Static Game Research Articles

Big ideas in sports analytics and statistical tools for their investigation

AbstractSports analytics—broadly defined as the pursuit of improvement in athletic performance through the analysis of data—has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this article, we connect four big ideas that are common across multiple sports: the expected value of a game state, win probability, measures of team strength, and the use of sports betting market data. For each, we explore both the shared similarities and individual idiosyncracies of analytical approaches in each sport. While our focus is on the concepts underlying each type of analysis, any implementation necessarily involves statistical methodologies, computational tools, and data sources. Where appropriate, we outline how data, models, tools, and knowledge of the sport combine to generate actionable insights. We also describe opportunities to share analytical work, but omit an in‐depth discussion of individual player evaluation as beyond our scope. This article should serve as a useful overview for anyone becoming interested in the study of sports analytics.This article is categorized under: Applications of Computational Statistics > Education in Computational Statistics

Player Identification for Collectible Card Games with Dynamic Game States

Collectible card games are a fruitful test space for studying resource allocation and battle strategy, given that their structures promote reactionary combat styles and allow players to obtain variable amounts of combat power by expending fixed resources. However, their large action spaces also allow for flexibility in play styles, thus facilitating behavioral analysis at the individual level rather than the aggregate level. When presented with the same options and the same amount of resources, a player's selection of cards and their choice of moves gives insight into their unique play style and decision-making tendencies. As such, we use the virtual collectible card game Legends of Code and Magic to determine whether we can identify a player from their actions and, conversely, predict the future actions of a known player. Our main contributions to this task are the creation of a comprehensive dataset of Legends of Code and Magic game states and actions, as well as the first use of large transformer-based language models to address this problem.

DETERMINING THE OPTIMAL PRICING STRATEGY FOR ONLINE CINEMAS USING AN AGENT-BASED MODEL ON THE EXAMPLE OF IVI AND KINOPOISK

The relevance of the study is justified by the phenomenon of the ever-increasing demand for online cinema services in the presence of free «pirate» resources, the heterogeneity of consumers of online cinemas that form the demand for their services, hence the low predictability of demand. The purpose of the study is to determine the optimal pricing policy in the conditions of competition of online cinemas. The constructed model predicts the demand for the services of the two leaders of the online cinema market with a reliability of more than 99%. Results: in a static game with full information, the price of a Kinopoisk subscription roughly corresponds to the best answer to the Ivi strategy to set the price at the current level; the Ivi subscription price corresponds to one of the Pareto optimal outcomes of the game, characterized by the symmetry of the strategy profile, the Nash equilibrium has not been achieved in reality.

Evolution of cooperation with nonlinear environment feedback in repeated public goods game

The mutual feedback between the environment and the strategy is a significant mechanism in the evolution of cooperation. A feedback-evolving repeated public goods game model with nonlinear effects is explored. The players' behaviors in the current round may influence the environment, leading the environment feedback on the behavior by the modulation of payoffs in the form of positive or negative. Under the former case, the groups realize the synergy effect of payoffs in the next round. Vice versa, the discount effect will be instead. The introduction of nonlinear effects enables heterogeneous feedback of the environment on different groups without introducing too many environmental states. The results show the enhancing role of the nonlinear effects on the evolution of cooperation compared to linear switching of enforcement factors. Compared to static game environments, the dynamic feedback scenario can realize better performance in the evolution of cooperation. The effect is more pronounced as the synergy factor increases or the discount factor decreases. The results are verified when the game environment changes between two or three states and under different environment transition structures. In addition, under the scenarios of probabilistic transition, the results are explored by taking into account the cases of state-independent and state-dependent, where both the homogeneity and heterogeneity transition probability are considered in the state-independent case, respectively. The probabilistic transition results further emphasized the transition probability's significant role in the evolution of cooperation when cooperation behaviors are more likely incentivized to interact in the valuable environment.

Modeling, analysis, and dynamics of Bayesian games via matrix-based method

A matrix-based framework for the modeling, analysis and dynamics of Bayesian games are presented using the semi-tensor product of matrices. Static Bayesian games are considered first. A new conversion of Bayesian games is proposed, which is called an action-type conversion. Matrix expressions are obtained for Harsanyi, Selten, and action-type conversions, respectively. Certain properties are obtained, including two kinds of Bayesian Nash equilibria. Then the verification of Bayesian potential games is considered, which is proved to test the solvability of corresponding linear equations equivalently. Finally, the dynamics of evolutionary Bayesian games are considered. Two learning rules for Bayesian potential games are proposed, which are type-based myopic best response adjustment and logit response rule, respectively. Markovian dynamic equations are obtained for the proposed strategy updating rules and convergence is proved.

Evidence for Spinozan "Unbelieving" in the Right Inferior Prefrontal Cortex.

Humans can think about possible states of the world without believing in them, an important capacity for high-level cognition. Here, we use fMRI and a novel "shell game" task to test 2 competing theories about the nature of belief and its neural basis. According to the Cartesian theory, information is 1st understood, then assessed for veracity, and ultimately encoded as either believed or not believed. According to the Spinozan theory, comprehension entails belief by default, such that understanding without believing requires an additional process of "unbelieving." Participants (N = 70) were experimentally induced to have beliefs, desires, or mere thoughts about hidden states of the shell game (e.g., believing that the dog is hidden in the upper right corner). That is, participants were induced to have specific "propositional attitudes" toward specific "propositions" in a controlled way. Consistent with the Spinozan theory, we found that thinking about a proposition without believing it is associated with increased activation of the right inferior frontal gyrus. This was true whether the hidden state was desired by the participant (because of reward) or merely thought about. These findings are consistent with a version of the Spinozan theory whereby unbelieving is an inhibitory control process. We consider potential implications of these results for the phenomena of delusional belief and wishful thinking.

Finding Wordle Strategies That Can be Mastered by Humans

Wordle is a popular web game. Players use strategies and hints to figure out the correct answer of a daily puzzle. In general, there are several strategies to solve it efficiently, but which is the best depends on the game’s current states. This paper designed 4 individual strategies which is learnable for both computers and human players, and trained an AI based on Q-learning to solve the game automatically with a win rate of over 80%. The decision this AI made is only based on the word list, not including other information (e.g., frequency of appearance on the Internet). Based on the analysis, it can give players advices in various kinds of situations and offer useful combos. By using this AI players, it is feasible to figure out what is the best choice and improve their skills. However, it still cannot solve some rare situations efficiently, which may require more training or a new way of setting the game states.

AN EFFICIENT APPROACH FOR THE IMPLEMENTATION OF THE GOBANG GAME USING ARTIFICIAL INTELLIGENCE METHODS

Gobang is one of the most ancient abstract strategy games for two players. The game is traditionally played on a board with black and white stones, where players take turns placing a colored stone on an empty intersection. The winner is the first player to form an unbroken chain of five stones, either horizontally, vertically, or diagonally. Although the rules of Gobang seem pretty straightforward, the game tree complexity is enormous since the board state is more intuitive than in other games. In this paper, we will implement an algorithm that will solve the Gobang game using artificial intelligence (AI) methods. The program will begin learning from scratch, then use self-play to produce training data, and eventually steadily build up its strength. 
 The present work first focuses on the implementation of the supervised learning algorithm in the identification procedure in order to identify the position of the current fallen piece. This will be achieved by utilizing image processing and a convolutional neural network. Then a Gobang game procedure will be implemented using a game search algorithm, in which the state of the game is judged by means of a human-set function. After that, the function of judging the game state in the above game search algorithm will be changed to an artificial neural network (ANN) model, since it is convenient to train a model with a small dataset. Finally, the reinforcement learning algorithm will be applied to learn the artificial neural network model so that the playing level of the Gobang game program can be continuously improved.

Still Rings Movements Recognition in Gymnastics Sport Based on Deep Learning

The methods of detecting objects and tracking their movements are among the methods that are relied upon in many fields, whether medical or industrial, and others. One of these areas that will rely on deep learning meth-ods in discovering and distinguishing the player's movements is the sports field and is very useful in games in which the player's degree depends on the accura-cy of the performance of the movement, such as the gymnastics game, where it was applied to the static ring gymnastics game, where the distinction of move-ments was discovered the stability in this game is based on a convolutional neu-ral network. Models. The neural network was trained on five of the most im-portant stability movements in this game after creating the data set based on a set of videos of tournaments held in the period from 2016-2022, where an aver-age of 1500 images were obtained for each stability movement, which was di-vided into 80% for training and 20 % for testing, after training the convolution-al neural network model, it was applied to a group of video clips for different tournaments. Many criteria were adopted to measure the efficiency of the model after training and practical application, which showed the efficiency of the pro-posed system.

Dynamics of n-person Cournot games with asymmetric information and heterogeneous expectations

This paper proposes an n-person Cournot game with asymmetric information and studies the stability of its Bayesian Nash equilibria. In such a game, a probability θ of high costs and a ratio γ of firms with incomplete information are introduced to express the asymmetric information. Furthermore, to relax rationality, we assume all firms with the same marginal costs always imitate each other in most periods except for sporadically using adaptive expectation. Theoretical analysis shows three important results. Firstly, in static n-person Cournot games, γ plays a negative role in the excess equilibrium output on asymmetric information as θ>0.5. However, γ has a positive influence if θ<0.5. Secondly, based on adaptive expectation, Bayesian Nash equilibria of dynamic n-person Cournot games are globally asymptotically stable. Thirdly, based on heterogeneous expectations, Bayesian Nash equilibria of dynamic n-person Cournot games are locally asymptotically stable under certain conditions of parameters. Besides, a larger θ or a smaller γ is more likely to cause bifurcations and chaos in oligopoly markets with asymmetric information by simulations.

SHARP TEST FOR EQUILIBRIUM UNIQUENESS IN DISCRETE GAMES WITH PRIVATE INFORMATION AND COMMON KNOWLEDGE UNOBSERVED HETEROGENEITY

This paper proposes a test of the single equilibrium in the data assumption commonly maintained when estimating static discrete games of incomplete information. By allowing for discrete common knowledge payoff-relevant unobserved heterogeneity, the test generalizes existing methods attributing all correlation between players’ decisions to multiple equilibria. It does not require the estimation of payoffs and is therefore useful in empirical applications leveraging multiple equilibria to identify the model’s primitives. The procedure boils down to testing the emptiness of the set of data generating processes that can rationalize the sample through a single equilibrium and a finite mixture over unobserved heterogeneity. Under verifiable conditions, this testable implication is generically sufficient for degenerate equilibrium selection. The main identifying assumption is the existence of an observable variable that plays the role of a proxy for the unobservable heterogeneity. Examples of such proxies are provided based on empirical applications from the existing literature.

Application of game theory in risk management of urban natural gas pipelines

This paper presents a game theory methodology for risk management of urban natural gas pipelines, which is a collaborative participation mechanism of the stakeholders, including government, pipeline companies, and the public. Firstly, the involvement proportion of stakeholders in risk management under rational conditions is estimated by the static game theory. Subsequently, the system dynamics (SD) simulation is used to establish an evolution game model of stakeholders in risk management under the irrational conditions, in which the stability of the evolution game process is analyzed. The stakeholders’ involvement proportions from the static game model are utilized as the inputs for the evolution game model to simulate the dynamic evolution behavior of risk management strategies with different involvement proportions of stakeholders. Eventually, the dynamic evaluation game can extract an optimal strategy for risk management of urban natural gas pipelines. A case study is used to illustrate the methodology. In essence, this methodology can be extended for implementing risk management of urban infrastructure.

PRD-MADDPG: An efficient learning-based algorithm for orbital pursuit-evasion game with impulsive maneuvers

This paper comprehensively investigates the problem of impulsive orbital pursuit-evasion games (OPEGs) by using an artificial intelligence-based approach. First, the mathematical model for the impulsive OPEGs in which the pursuer and evader both perform their orbital maneuvers by imposing the impulsive velocity increments is constructed. Second, the problem of impulsive OPEGs is transformed into a bilateral optimization problem with a minimum–maximum optimization index in terms of terminal time and multiple constraints such as maneuverability, total fuel consumption, and mission time, etc. To determine the optimal impulsive maneuvers for both sides, a PRD-MADDPG (Predict-Reward-Detect Multi-Agent Deep Deterministic Policy Gradient) algorithm in the frame of multi-agent reinforcement learning is designed. This novel algorithm uses the basic MADDPG to achieve the strategies training and learning, and applies the supplemental PRD to predict the change of game state during the interval between two adjacent impulsive maneuvers and incorporate these information into the algorithm training in the form of predicted reward. Finally, some pursuit-evasion missions near the Geosynchronous Earth Orbit are numerically analyzed to verify the validness and effectiveness of the algorithm. The results prove that the PRD-MADDPG algorithm is very efficient to find applicable strategies even considering rather complex constraints. It is also shown that the learning-based strategies can be effectively applied in the extended scenarios which are not seen in the training process.

Using Temporal Convolutional Networks to estimate ball possession in soccer games

The use of tracking data in the field of sport analytics has increased in the last years as a starting point for in-depth tactical analyses. This work investigates the use of Temporal Convolutional Networks (TCNs), a powerful architecture for sequential data analysis, to extract ball possession information from tracking data. This task is a crucial step for many tactical analyses and is nowadays carried out manually by a human operator in the stadium, which is costly, difficult to implement, and prone to errors. In this work, several classification approaches are explored to classify the game state as dead, ball owned by the home team, or by the away team: as a single-branch, ternary prediction, or as two binary predictions, first detecting whether the game is dead or alive and then which team owns the ball. TCNs are exploited to create independent trajectory embeddings from tracking data of each object; since there is no semantic ordering among the tracked objects, we investigate different permutation-invariant layers to combine the embeddings, namely, an element-wise sum over the embeddings, a self-attention module, and the use of 2D convolutions. Performance evaluation on tracking data from professional soccer games shows that the proposed method outperforms state-of-the-art rule-based methods, achieving 86.2% accuracy in possession estimation (＋7.3% compared to the state of the art) and 89.2% accuracy in dead-alive classification (＋33.2% compared to the state of the art). Extensive ablation studies were conducted to investigate how different input data concur to the final prediction.

A Modified Hooke–Jeeves Algorithm in Two-Player Nonlinear Static Game: With an Application in Forest Management

Strategy considerations for optimal outcomes play the key roles in every decision-making problems. Game theory in itself preserves the sustainability to draw some decision-making conclusions. Different forms of game exist in literature. This article is concerned with two-player nonlinear static game. We consider here the solution of the game problems through the algorithmic structures, with some modification, of Hooke–Jeeves (HJ) algorithm which is a tool to encounter unconstrained optimization. Basically, we lay emphasis on the modification of the considered function which is to be optimized. Hence, the name of the proposed algorithm is modified HJ algorithm. Numerous articles present different solutions of various real-life problems using HJ algorithm. Forest management problem is considered here under modified HJ algorithm to get solution. This article concludes with some comparative analysis with respect to some different methods, for example, analytical method and graphical method. Our proposed methodology gives better results than the results obtained in analytical method and graphical method with respect to optimal strategy sets and optimal payoff values.

Research on the Pricing Strategy of New Energy Medium-sized Vehicles Based on Game Theory: Taking Tesla and BYD as Examples

In recent years, the demand for new energy vehicles has been increasing. As foreign cars enter the Chinese market, the competition for new energy vehicles in China has become increasingly fierce; inevitably resulting in price wars, but blind price wars will only damage the interests of all parties. This paper uses a static game and a repeated game to analyze how firms can adopt pricing strategies to maximize their benefits. The results show that no matter what the situation is, if a company uses price cuts to capture the market, it may increase its own revenue in the short term, but in the long term, it will cause losses to itself and other companies. Finally, reasonable suggestions are made for new energy vehicle companies facing pricing problems. The research conducted in this paper on pricing can, to a certain extent, enable enterprises to carry out the correct pricing strategy, improve the interests of the enterprises as well as the whole enterprise, and thus promote the development of the new energy vehicle industry.

Research on Security Defense of Coupled Transportation and Cyber-Physical Power System Based on the Static Bayesian Game

The driving and charging behavior of an increasing number of electric vehicles (EVs) have strengthened the connection between transportation network (TN) and cyber-physical power system (CPPS). Cyber-attacks imposed on the coupled system will cause a big disturbance to the power network (PN), which will further affect the travel behavior of EVs in the TN. To improve the ability of the coupled system to resist attacks, this paper presents the framework of coupled transportation and cyber-physical power system with a defense mechanism. From a defense perspective, considering comprehensive load shedding loss of load buses, an active defense model driven by static Bayesian game theory is built at the information network (IN) level of CPPS, which provides a defense strategy selection method against attacks at a certain moment. Moreover, a charging guidance model for EVs based on dynamic vehicles travel simulation is developed to describe the impact of charging station (CS) outage induced by the unsuccessful defense, and to mitigate disturbance on the TN. Simulation experiments with a modified Sioux Falls traffic network and IEEE 30-bus power grid coupled system verify the effectiveness of the proposed method and model.

Rinascimento: Playing Splendor-Like Games With Event-Value Functions

In the realm of games research, artificial general intelligence algorithms often use score as the main reward signal for learning or playing actions. However, this has shown its limitations in scenarios where the rewards are very rare or absent until the end of the game. The problem is even more severe when the computational budget available is limited. This article proposes a new approach based on event logging: the game state triggers an event every time one of its features changes. These events are processed by an event-value function (EF) that assigns a value to a single action or a sequence. Experiments show that this approach can mitigate the problem of scarce rewards and improve the artificial intelligence performance compared with both the point-based heuristics and state-value functions. Furthermore, this represents a step forward in a finer control of the strategy adopted by the artificial agent, by describing a much richer and controllable behavioral space through EFs. Tuned EFs are able to neatly synthesize the relevance of the events in the game. Agents using an EF are also more robust when playing games with several opponents.

Can counter-advertising exposing alcohol sponsorship and harms influence sport spectators’ support for alcohol policies? An experimental study

BackgroundExposure to alcohol advertising and sponsorship through elite sport is associated with harmful use of alcohol. Owing to strong financial and cultural ties between alcohol and sport in Australia, policy action to restrict alcohol sport sponsorship is unlikely to occur without strong public support for change. This study tested whether exposure to counter-advertising exposing industry marketing of harmful products—a technique shown to be effective in tobacco control—promotes higher support for policy change and less favourable beliefs about the alcohol industry among sport spectators.MethodsA sample of 1,075 Australian adults aged 18–49 years who planned to watch an National Rugby League (NRL) State of Origin series game, featuring prominent alcohol sponsorship, was recruited through an online panel and randomly assigned to one of three conditions: control (neutral advertisement); counter-advertisement exposing alcohol harms; counter-advertisement exposing alcohol sponsorship and harms. Participants completed a pre-test questionnaire and viewed their assigned counter-advertisement multiple times in the 5–7 days before the NRL game. Within four days of watching the game, participants completed post-test measures.ResultsCompared to both the control advertisement and the counter-advertisement exposing alcohol harms, participants who viewed the counter-advertisement exposing alcohol sponsorship and harms were significantly more likely to indicate support for each of four policies aimed at restricting sports-related alcohol marketing, including the complete removal of alcohol sponsorship from sport (51% vs. 32% and 37%). They were also significantly less likely to agree with statements such as “alcohol companies should be allowed to sponsor sport since their products are legal” (39% vs. 63% and 60%) and significantly less likely to report liking alcohol companies in general (38% vs. 59% and 54%). There were no significant differences in policy support or industry beliefs between participants who saw the counter-advertisement exposing alcohol harms and those who saw the control advertisement.ConclusionCounter-advertising employing messages that expose and critique the intent and impact of pervasive alcohol sponsorship in sport has potential to bolster public support for policies targeting alcohol sport sponsorship, diminish beliefs supportive of alcohol industry marketing strategies and enhance negative views of alcohol companies and their marketing practices.

Game study on safety supervision of imported aquatic products in China

With the expanding scale of aquatic product imports, safety issues have arisen. Among them, the lack of supervision by government agencies, illegal importation by unscrupulous enterprises and the lack of regulatory bodies such as consumers are major reasons for the occurrence of unsafe imported aquatic products. Therefore, this paper adopts a two-by-two static game model between government agencies and importers, importers and consumers, and a three-way sequential dynamic game model between government agencies, importers and consumers to analyze the causes of quality and safety problems of imported aquatic products in China. The results show that when the safety problems of imported fishery products occur, consumers choose to report importers when the compensation they receive due to reporting increases or when the cost of reporting is reduced by not reporting; government agencies choose to strictly regulate importers when the cost of regulation is reduced by loose regulation and reputation loss increases, or when the revenue from fines obtained by strict regulation increases. It is further verified through empirical evidence that both government agency regulation and consumer monitoring have positive effects on importers’ self-regulation. Finally, countermeasures to ensure the quality and safety of imported aquatic products in China are proposed.