Static Game Research Articles

Empirical Framework for Two-Player Repeated Games with Random States

Abstract We provide methods for the empirical analysis of a class of two-player repeated games with i.i.d. shocks, allowing for non-Markovian strategies. The number of possible equilibria in these games is large and, usually, theory is silent about which equilibrium will be chosen in practice. Thus, our method remains agnostic about selection among these multiple equilibria, which leads to partial identification of the parameters of the game. We propose a profiled likelihood criterion for building confidence sets for the structural parameters of the game and derive an easily computable upper bound on the critical value. We demonstrate good finite-sample performance of our procedure using a simulation study. We illustrate the usefulness of our method by studying the effect of repealing the Wright Amendment on entry and exit into Dallas airline markets and find that the static game approach overestimates the negative effect of the law on entry into these markets.

Game analysis on the quality and safety control of pork supply chain - The case study of China

Using the method of static game analysis, the potential risk and responsibility across the entire pork supply chain are discussed from the perspective of all stakeholders involved. Included in the analysis are pig suppliers, slaughterers, pork processors, pork sellers and consumers. The results indicate the following: firstly, the lower the probability of inspections on downstream businesses and the higher the single inspection fee, the greater the probability of harmful substances used by upstream businesses and the higher the costs. Secondly, businesses that actively manufacture and transfer harmful substances in the supply chain cannot add extra costs. Finally, the quality and risk factors in pork production may not follow a strictly linear growth. This study might explain the unique problems that occur in pork supply chain management in large developing countries such as China.

On the complexity of computing Markov perfect equilibrium in general-sum stochastic games.

Similar to the role of Markov decision processes in reinforcement learning, Markov games (also called stochastic games) lay down the foundation for the study of multi-agent reinforcement learning and sequential agent interactions. We introduce approximate Markov perfect equilibrium as a solution to the computational problem of finite-state stochastic games repeated in the infinite horizon and prove its PPAD-completeness. This solution concept preserves the Markov perfect property and opens up the possibility for the success of multi-agent reinforcement learning algorithms on static two-player games to be extended to multi-agent dynamic games, expanding the reign of the PPAD-complete class.

Mobile game Marketing Strategy: A Case study of PUBG mobile

This article focuses on the current mobile gaming market and state of the art. At the same time, some current marketing strategies for mobile games are discussed. Many of these methods are widely used. This post focuses on PUBG Mobile. PUBG mobile is a domestic mobile game with anti-terrorism military competition experience type developed by Tencent Photon Studio Group. Moreover, through the four P's method, namely product, price, promotion, and place, the marketing strategy of the PUBG mobile is analyzed. This paper analyzes the advantages and disadvantages of the PUBG mobile and the forms of income. For example, PUBG mobile followed by IP linkage, to give the audience players to different IP linkage effect. It not only propagandizes the IP, but also let the players experience more gameplay, which can be said to kill two birds with one stone. In addition, the PUBG mobile faces problems. It's overpriced, it's one-dimensional. A lot of players who are less willing to pay don't get relatively beautiful skins. Finally, some suggestions for the future marketing strategies of this game are put forward.

Bridging Level-K to Nash Equilibrium

Abstract We introduce NLK, a model that connects the Nash equilibrium (NE) and level-k. It allows a player in a game to believe that her opponent may be either less or as sophisticated as she is, a view supported in psychology. We apply NLK to data from five published papers on static, dynamic, and auction games. NLK provides different predictions from those of the NE and level-k; moreover, a simple version of NLK explains the experimental data better in many cases, with the same or fewer parameters. We discuss extensions to games with more than two players and heterogeneous beliefs.

Mixed Strategy Analysis in Attack-Defense Game Model Based on 5G Heterogeneous Network of CPS Using ncPSO

The development of the 5th Generation Mobile Communication Technology not only brings convenience to people but also brings many network security problems. Based on the static game theory of complete information, a game model of attack and defense with limited resources in heterogeneous networks of Cyber Physical Systems is established. This model analyzes the basic rules of the offensive and defensive strategies of both parties when the offensive and defensive resources are limited in the 5th Generation Mobile Communication Technology network environment. The model can also describe the interaction between attackers and defenders. A novel compact particle swarm optimization algorithm is proposed to solve the difficult problem of solving the Nash equilibrium of this game model. The simulation experiment proves that novel compact particle swarm optimization algorithm has good optimization ability and shows that the algorithm can effectively solve the Nash equilibrium of the model. The simulation experiment provides a strategic reference for the attack-defense game with limited resources.

Game Theory Analysis of Commercial Banks and Micro-Enterprises Credit in Post - epidemic Era

Micro-Enterprises are an important component of the economy and have made significant contributions to economic development. Especially in the post-epidemic period, the need for national economic growth and the importance of micro-enterprise development is gradually prominent. Micro-Enterprises still face the problem of “financing difficulty”, unable to get enough bank loans. In this paper, from the perspective of game theory, the incomplete information static game between micro-enterprises and commercial banks will be constructed. This paper mainly discusses the pre-loan investigation of commercial banks for micro-enterprises and provides some suggestions for the financing difficulty of micro-enterprises.

Stakeholders′ ecological-economic compensation of river basin: A multi-stage dynamic game analysis

The growth of natural resources is an important consequence of green recovery and sustainable development measures. Protecting the ecological resources of the basin and implementing the ecological compensation system are important means to promote the sustainable development of the basin. This paper adopts the methods of static evolutionary game and dynamic evolutionary game to analyze the relevant decision-making behaviors among stakeholders of ecological compensation and the stability of dynamic evolutionary game between upstream and downstream governments and the entire game system. The results show that in the ecological compensation of the watershed, the optimal strategy of social expectations cannot be achieved only by the independent choice between the upstream and downstream governments (that is, the upstream government uses the "protection" strategy, and the downstream government uses the "compensation" strategy). Instead, through the intervention of the central government, a corresponding incentive and restraint mechanism should be established to regulate the behavior of upstream and downstream governments, so that the upstream government can choose the "protection" strategy, and the downstream government can choose the "compensation" strategy. Therefore, the ecological compensation of the river basin can maximize its benefits only if the upstream and downstream governments participate together. To adopt a socially optimal river basin ecological compensation strategy, the central government must intervene, adopt reward and punishment measures, and regulate the behavior of upstream and downstream governments. It is suggested that green strategies are urgently required to offset misuse of natural resources and urge stakeholders to play prominent role in addressing the problem.

Judgment on the evolution state of asymmetric games

In this article, we probe into two-role two-player two-strategy asymmetric evolutionary games by utilizing replicator dynamic equations and present all equilibrium points and their stability conditions. Further, the resulting evolution state of the system can be depicted directly according to the specific payoff matrix and initial values. This study facilitates and perfects the research of asymmetric evolutionary games.

A Study of Primary Students’ Technology Acceptance and Flow State When Using a Technology-Enhanced Board Game in Mathematics Education

Mathematics is a major subject for primary students. However, in mathematics education, many abstract concepts may lead students to lose learning motivation and further affect their learning performance. Therefore, several papers have proposed various board games to support traditional mathematics education. However, teachers have applied traditional board games to support mathematics education in a way that makes it difficult to monitor or capture each student’s learning status and problems during game processes. As mentioned above, this study proposed an educational mathematics board game with mobile and sensor technologies to assist students in learning the concept of prime factorization. The proposed board game can guide students to conduct the game and support teachers to capture the students’ learning status during the game process. To evaluate students’ acceptance and flow state regarding the proposed board game, thirty-nine primary students were invited to participate in an experiment. The experimental results indicated that the students had a high technology acceptance with regard to the proposed board game and high flow state when playing the proposed board game. For high-achieving students, the proposed board game was more entertaining, while low-achieving students might feel a little challenged. In addition, boys were more engaged than girls when playing this board game.

GgViz: Accelerating Large-Scale Esports Game Analysis

While esports organizations are increasingly adopting practices of conventional sports teams, such as dedicated analysts and data-driven decision-making, video-based game review is still the primary mode of game analysis. In conventional sports, advances in data collection have introduced systems that allow for sketch-based querying of game situations. However, due to data limitations, as well as differences in the sport itself, esports has seen a dearth of such systems. In this paper, we leverage player tracking data for Counter-Strike: Global Offensive (CSGO) to develop ggViz, a visual analytics system that allows users to query a large esports data set through game state sketches to find similar game states. Users are guided to game states of interest using win probability charts and round icons, and can summarize collections of states through heatmaps. We motivate our design through interviews with esports experts to especially address the issue of game review. We demonstrate ggViz's utility through detailed case studies and expert interviews with coaches, managers, and analysts from professional esports teams.

The emergence of critical incidents in Rugby Union matches using Markov chain analysis

ABSTRACT During a rugby match, teams are continually trying to cause instabilities of different magnitudes on each other. Once a perturbation occurs, a phase transition emerges. Markov chain analysis has the potential to investigate emerging patterns in rugby union. This study examined the probability of a critical incident (CI; penalties and tries) occurring during Rugby Union matches, and whether differences would exist between winning and losing. The Markov chain analysis was used to identify the probability of a transition from a game state to a further state, due to the analysis of the preceding state. A game phase was defined as a technical and tactical match action which occurred between two consecutive advantage lines. Contingency tables were assembled from 280 phases registered during 11 matches of Brazilian Rugby Union XV A Series Championship. The results showed that previous technical and tactical actions made from rucks had the highest probability of generating a transition phase leading to a CI. The results suggest that the winning teams adopt a more flexible approach to the environmental changes that occur throughout a game and demonstrated more flexibility during transitional state occurrences, with higher variability in technical and tactical actions related to a previous game phase.

Non-cooperative game algorithms for computation offloading in mobile edge computing environments

Mobile Edge Computing (MEC) has become a promising technology for 5G networks. Computation offloading is an essential issue of MEC, which enables mobile User Equipment (UE) to enjoy rich wireless resources and huge computing power anywhere. This paper considers the Quality-of-Experience (QoE) of UEs in 5G MEC systems and presents a dynamic non-cooperative game (QCOG-DG) algorithm and a static non-cooperative game (QCOG-SG) algorithm for computation offloading of MEC applications. We establish an MEC computation offloading model by considering the QoE requirements of UEs, and discuss the communication overheads, computation cost, and energy consumption models to minimize the energy consumption and time delay of each UE. Considering that there are multiple UEs who want to offload their computation tasks to a resource-constrained MEC server, and each UE is selfish and competitive, we formulate the problem of computation offloading decision as a non-cooperative game model. We prove the existence of a Nash Equilibrium (NE) solution for the proposed game model. In addition, we propose an algorithm that jointly optimizes energy consumption and time delay under QoE preferences to achieve optimal offloading benefits for each UE. Moreover, we respectively propose a dynamic non-cooperative game (QCOG-DG) algorithm and a static non-cooperative game (QCOG-SG) algorithm to efficiently find the NE solution. Extensive simulation experiments are conducted to verify the effectiveness of the proposed MEC computation offloading model and the QCOG-DG and QCOG-SG algorithms. Simulation results show that the proposed QCOG-DG algorithm can efficiently find the NE solutions in the MEC scenarios with UEs of different sizes.

A geometric approach to reach‐avoid games with time limits

The differential games have been widely used to analyze the conflicts between intelligent agents. Motivated by the fact that the agents always have finite energy or time requirements, a novel reach-avoid game with time limits is investigated in this work. The attacker aims to reach the target region without being captured or reaching its time limit, while the defender strives to intercept the attacker or delay it. This game is beyond the scope of the classical Hamilton-Jacobi-Isaacs (HJI) approach. To make the problem possible to solve, we introduce the concept of reaching region and provide the optimal strategies of the players based on it. Using these strategies, we construct a hypersurface, called the barrier, in the game state space which partitions it into two parts that lead to different outcomes of the game. In this work, the complete analytical expressions of the barrier in all possible situations are provided. The game results can be obtained by substituting the initial states into the related expression and there is barely any computational burden. Compare to the existing works, the game with time limits is more practical. Also, this work provides the foundation for analyzing general multiple-attacker-multiple-defender games.

Evolutionary Game Analysis for Grassland Degradation Management, Considering the Livelihood Differentiation of Herders

Grassland degradation has become one of the most important ecological and environmental problems in the world, affecting the ecological balance of grassland and the welfare of residents. To reveal the impact mechanism of herders’ livelihood constraints on grassland degradation, and to explore the comprehensive management methods to ensure herders’ livelihoods and grassland ecological restoration, this paper constructed an evolutionary game model considering local governments and herders. It is found that the ideal stable equilibrium game can be achieved when certain conditions are met, that is, when the local governments actively regulate and herders moderate grazing, the grassland degradation caused by overgrazing can be reduced. The livelihood differentiation of herders significantly affects the stable equilibrium state of the evolutionary game. The local government’s regulation is the key to promoting moderate grazing of herders. The effect of incentive measures on the moderate grazing of herders is limited, while punishment measures can significantly restrict the excessive grazing behavior of herders. Policy support for household livelihood differentiation can effectively motivate herders to moderate grazing and achieve their survival and development needs to a greater extent through a non-grazing livelihood. The research results help decision-makers to formulate policies to combat grassland degradation, and promote the improvement of herders’ lives.

The effect of three violent videogame engagement states on aggressive behavior: A partial least squares structural equation modeling approach.

Debate on violent games and their effect on aggressive behavior remains inconclusive. This study aims to study the predicting role of cognitive, affective, and behavioral engagement states in violent videogames on aggressive behavior, which remains nebulous to date. We visited gaming zones and administered the study survey to collect data from violent videogame users. We collected 208 valid responses that were further analyzed. The present study used SmartPLS (3.3.3) software to perform partial least squares structural equation modeling (PLS-SEM) analysis in two stages. In the first stage, the measurement model assessment reported that cognitive, affective, behavioral, and aggressive behavior proved to be reliable reflective-formative composite constructs. Whereas, the second phase illustrated that cognitive engagement in violent videogames fails to impact aggressive behavior. The other two engagement states (affective and behavioral) in violent games showed a positive impact on aggressive behavior. Our study contributes to aggressive behavior literature by understanding how violent videogame engagement states impact aggressive behavior, which is crucial to recognize aggression so that steps can be taken toward addressing it. This study also contributes methodologically by utilizing the hierarchical component model (HCM) approach to estimate, specify, and validate the hierarchical structure of higher-order constructs (i.e., consumer violent videogame engagement dimensions (cognitive, affective, and behavioral) and aggressive behavior) as reflective-formative composite models.

AlphaDDA: strategies for adjusting the playing strength of a fully trained AlphaZero system to a suitable human training partner

Artificial intelligence (AI) has achieved superhuman performance in board games such as Go, chess, and Othello (Reversi). In other words, the AI system surpasses the level of a strong human expert player in such games. In this context, it is difficult for a human player to enjoy playing the games with the AI. To keep human players entertained and immersed in a game, the AI is required to dynamically balance its skill with that of the human player. To address this issue, we propose AlphaDDA, an AlphaZero-based AI with dynamic difficulty adjustment (DDA). AlphaDDA consists of a deep neural network (DNN) and a Monte Carlo tree search, as in AlphaZero. AlphaDDA learns and plays a game the same way as AlphaZero, but can change its skills. AlphaDDA estimates the value of the game state from only the board state using the DNN. AlphaDDA changes a parameter dominantly controlling its skills according to the estimated value. Consequently, AlphaDDA adjusts its skills according to a game state. AlphaDDA can adjust its skill using only the state of a game without any prior knowledge regarding an opponent. In this study, AlphaDDA plays Connect4, Othello, and 6x6 Othello with other AI agents. Other AI agents are AlphaZero, Monte Carlo tree search, the minimax algorithm, and a random player. This study shows that AlphaDDA can balance its skill with that of the other AI agents, except for a random player. AlphaDDA can weaken itself according to the estimated value. However, AlphaDDA beats the random player because AlphaDDA is stronger than a random player even if AlphaDDA weakens itself to the limit. The DDA ability of AlphaDDA is based on an accurate estimation of the value from the state of a game. We believe that the AlphaDDA approach for DDA can be used for any game AI system if the DNN can accurately estimate the value of the game state and we know a parameter controlling the skills of the AI system.

Poisoning Attack Against Estimating From Pairwise Comparisons.

As pairwise ranking becomes broadly employed for elections, sports competitions, recommendation, information retrieval and so on, attackers have strong motivation and incentives to manipulate or disrupt the ranking list. They could inject malicious comparisons into the training data to fool the target ranking algorithm. Such a technique is called "poisoning attack" in regression and classification tasks. In this paper, to the best of our knowledge, we initiate the first systematic investigation of data poisoning attack on the pairwise ranking algorithms, which can be generally formalized as the dynamic and static games between the ranker and the attacker, and can be modeled as certain kinds of integer programming problems mathematically. To break the computational hurdle of the underlying integer programming problems, we reformulate them into the distributionally robust optimization (DRO) problems, which are computational tractable. Based on such DRO formulations, we propose two efficient poisoning attack algorithms and establish the associated theoretical guarantees including the existence of Nash equilibrium and the generalization ability bounds. The effectiveness of the suggested poisoning attack strategies is demonstrated by a series of toy simulations and several real data experiments. These experimental results show that the proposed methods can significantly reduce the performance of the ranker in the sense that the correlation between the true ranking list and the aggregated results with toxic data can be decreased dramatically.

Dynamic market share through advertising and loyalty reward programs: A case study of Ofo versus Mobike

The emerging business models have impelled firms’ competition in a brand-new and fast-growing market. This study examines such a competition for market share through advertising and loyalty reward programs. Two stages can be distinguished based on the transformation of the competition strategies. These stages can be formulated as a dynamic differential game model and a static Hotelling game model. The operation strategies and performances of two firms are determined and compared via analytical studies and case analyses toward a bicycle-sharing program, i.e., Ofo versus Mobike. Historical data are used to fit the curve of the market size and to estimate the parameter values of these models. The results show that during the first stage, the difference in market share between these firms gradually decreases (increases) when the advertising response constant is low (high). Meanwhile, in the second stage, these firms offer converse reward strategies.

Strategic confrontation within monetary and financial authorities, and foreign exchange market participants in Iran: non-cooperative static games approach

Strategic confrontation within monetary and financial authorities, and foreign exchange market participants in Iran: non-cooperative static games approach