Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

Differential game strategy in three-player evasion and pursuit scenarios

A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strategy. The current approach chooses the miss distance as the outcome of the conflict. Different optimal guidance laws are investigated, and feasible conditions are analyzed for the attacker to accomplish an attacking task. For some given conditions, the attacker cannot intercept the target by only using a one-to-one optimal pursuit guidance law; thus, a guidance law for the attacker to reach a critical safe value is investigated.Specifically, the guidance law is divided into two parts. Before the engagement time between the defender and the attacker, the attacker uses this derived guidance law to guarantee that the evasion distance from the defender is safe, and that the zero-effort-miss(ZEM) distance between the attacker and the target is the smallest.After that engagement time, the attacker uses the optimal one-toone guidance law to accomplish the pursuit task. The advantages and limited conditions of these derived guidance laws are also investigated by using nonlinear simulations.

Effects of the planarity and heterogeneity of networks on evolutionary two-player games

We study the effects of the planarity and heterogeneity of networks on evolutionary two-player symmetric games by considering four different kinds of networks, including two types of heterogeneous networks: the weighted planar stochastic lattice(a planar scale-free network) and the random uncorrelated scale-free network with the same degree distribution as the weighted planar stochastic lattice; and two types of homogeneous networks: the hexagonal lattice and the random regular network with the same degree k_0= 6 as the hexagonal lattice. Using extensive computer simulations, we found that both the planarity and heterogeneity of the network have a significant influence on the evolution of cooperation, either promotion or inhibition, depending not only on the specific kind of game(the Harmony, Snowdrift, Stag Hunt or Prisoner's Dilemma games), but also on the update rule(the Fermi, replicator or unconditional imitation rules).

Multi-Modal Data Analysis Based Game Player Experience Modeling Using LSTM-DNN

Game player modeling is a paradigm of computational models to exploit players’behavior and experience using game and player analytics.Player modeling refers to descriptions of players based on frameworks of data derived from the interaction of a player’s behavior within the game as well as the player’s experience with the game.Player behavior focuses on dynamic and static information gathered at the time of gameplay.Player experience concerns the association of the human player during gameplay,which is based on cognitive and affective physiological measurements collected from sensors mounted on the player’s body or in the player’s surroundings.In this paper,player experience modeling is studied based on the board puzzle game“Candy Crush Saga”using cognitive data of players accessed by physiological and peripheral devices.Long Short-Term Memory-based Deep Neural Network(LSTM-DNN)is used to predict players’effective states in terms of valence,arousal,dominance,and liking by employing the concept of transfer learning.Transfer learning focuses on gaining knowledge while solving one problem and using the same knowledge to solve different but related problems.The homogeneous transfer learning approach has not been implemented in the game domain before,and this novel study opens a new research area for the game industry where the main challenge is predicting the significance of innovative games for entertainment and players’engagement.Relevant not only from a player’s point of view,it is also a benchmark study for game developers who have been facing problems of“cold start”for innovative games that strengthen the game industrial economy.

Players＇ Perception on Game-Centered Approach in Coaching Female Soccer

Game-centered approach has become increasingly recognized in coaching with its potential for improving players＇ motivation and game performance. Since players are the centered component of this approach, players＇ perception can provide useful information for coaches in order to enhance cognitive learning of game play and improve game performance. Thus, the purpose of this study was to determine the players＇ perception for implementing the game-centered approach in coaching. Approximately 30 min of interviews with open-ended questions were conducted with five female collegiate soccer players. The game-centered approach helped participants to recognize their weaknesses and their strengths, to think more tactically and to adapt their performance from practices to competitions. Players were encouraged to tactically analyze their performance, emphasize cognitive learning of game play, and construct game knowledge. The cognitive learning helped players to easily transfer their game performance into competitions. Additionally, there was a positive impact on the players＇ motivation while they experienced enjoyment, challenges, and teamwork. Cognitive learning of game play, the performance adaptability for competitions, as well as the improving players＇ motivation was supported during the game-centered approach. Results provided helpful information for coaches to improve the effectiveness of practices which are truly useful to competitions.

基于Game理论的μ-演算公理化

随着软硬件系统复杂性的不断提高,各种验证技术被越来越广泛的使用.模型检验技术是一种保证软硬件设计、实现正确性的有效技术.在针对软硬件的模型验证技术中,一般采用时序逻辑作为规约语言.模态μ-演算是模态和时序逻辑中应用较为广泛的一种,它具有语法成分简洁、表达能力强等特点.扩展了Lange和Stirling基于Focus Game的LTL和CTL的公理化方法.提出了一种基于Game理论的μ-演算公式的可满足性的测试方法,该种方法能够将模态μ-演算公式的可满足性问题转化为FocusGame的求解问题.进一步,基于这套Game规则,给出了一个新的关于μ-演算可靠完备的推理系统.同已有的μ-演算公理系统相比,该推理系统相对直观、简洁.

An Automated Player Detection and Tracking in Basketball Game

Vision-based player recognition is critical in sports applications.Accuracy,efficiency,and Low memory utilization is alluring for ongoing errands,for example,astute communicates and occasion classification.We developed an algorithm that tracks the movements of different players from a video of a basketball game.With their position tracked,we then proceed to map the position of these players onto an image of a basketball court.The purpose of tracking player is to provide the maximum amount of information to basketball coaches and organizations,so that they can better design mechanisms of defence and attack.Overall,our model has a high degree of identification and tracking of the players in the court.We directed investigations on soccer,basketball,ice hockey and pedestrian datasets.The trial comes about an exhibit that our technique can precisely recognize players under testing conditions.Contrasted and CNNs that are adjusted from general question identification systems,for example,Faster-RCNN,our approach accomplishes cutting edge exactness on three sorts of recreations(basketball,soccer and ice hockey)with 1000×fewer parameters.The all-inclusive statement of our technique is additionally shown on a standard passer-by recognition dataset in which our strategy accomplishes aggressive execution contrasted and cutting-edge methods.

On Topics in Quantum Games

This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game GC has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game GQ with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γc such that for γγc there is a pure strategy Nash equilibrium and for γ≥γc there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.

具身体验的数字再造——中国茶文化在国产游戏中的呈现与接受

数字游戏具有较强的传播功能和文化属性,对于中国茶文化的传承与发展意义重大。本文将近年来国产游戏对传统茶文化这一具身体验的数字再造方式归纳为五类,即将茶作为角色、道具、地图场景、叙事剧情和联动主题。对玩家反馈的文本分析和内容分析显示,玩家对呈现茶文化的游戏具有好感与期待,并希望能在游戏内外深入了解茶文化。在此基础上,本文梳理了国产游戏与传统茶文化结合过程中所面临的挑战,并提出对应策略,希望对游戏行业的创作实践带来启发。

两方零和马尔科夫博弈策略梯度算法及收敛性分析

为了解决基于策略的强化学习方法在两方零和马尔科夫博弈中学习效率低下的问题,提出同时更新双方玩家策略的近似纳什均衡策略优化算法.将两方零和马尔科夫博弈问题描述为最大最小优化问题,针对参数化策略,给出马尔科夫博弈的策略梯度定理,并通过近似随机策略梯度的推导,为算法实施提供可行性基础.通过比较分析不同的最大最小问题梯度更新方法,发现额外梯度相较于其他方法具有更好的收敛性能.基于这一发现,提出基于额外梯度的近似纳什均衡策略优化算法,并给出算法的收敛性证明.在Oshi-Zumo游戏上,使用表格式softmax参数化策略以及神经网络作为参数化策略,验证不同游戏规模场景下算法的有效性.通过对比实验,验证算法相对于其他方法的收敛性和优越性.

2022年女篮世界杯前八名球队实力分析——中国女篮2024年巴黎奥运会的前景展望

为进一步提高中国女子篮球的竞争力,备战巴黎奥运会,运用文献研究法、比较与分析法、数理统计法、录像分析法等方法对2022年女篮世界杯的客观数据进行梳理与比较,并全面分析中国女篮的优势与不足。研究认为:1)中国女篮球员年龄与身高已经达到世界顶级球队水平,内线组合成为优势之一;2)中国女篮在内线得分与后场篮板球方面具备一定优势,但在二次进攻、快攻反击得分和前场篮板球控制方面相对较弱;3)中国女篮多位球员在场均效率值、总得分、场均得分、篮板球、助攻等技术指标上均进入本届世界杯前十行列,达到世界一流水平,在本届世界杯夺得亚军是自身实力的体现;4)在对中国女篮球队各个位置的实力比较中,5号位需要提高前场篮板球控制和罚球命中率,4号位需要提高前场篮板球争夺和场均得分能力,3号位需要提高篮板球争夺和助攻能力,2号位和1号位需要提高出手次数与场均得分能力;5)中国女篮替补球员与先遣队员的技术水平相差较大,尤其是2号位、3号位和4号位,需要针对性培养,缩小差距。通过展望中国女篮2024年巴黎奥运会前景后认为:中国队具备争夺奖牌的实力,美国队仍然具备金牌捍卫者的实力;比利时队、加拿大队将会是中国队争夺奖牌的主要对手;澳大利亚队、塞尔维亚队、法国队、西班牙队、日本队、韩国队仍是潜在对手。

青少年足球运动员心理韧性与比赛表现的相关性研究

为了解青少年足球运动员心理韧性和比赛表现之间的相关性,本文采用文献资料法、问卷调查法、数理统计法,对湖南省280名中学阶段的青少年足球运动员的心理韧性与比赛表现的相关性进行研究。结果发现:青少年足球运动员心理韧性与比赛表现之间存在正相关关系,心理韧性的提升对其提高比赛表现有积极影响;积极认知、人际协助、家庭支持3个维度与比赛表现有显著的相关性,对青少年足球运动员的比赛表现影响较大;在大部分心理韧性维度中,女性青少年足球运动员的分数比男性青少年足球运动员的高,比赛表现更加稳定。

Essential Players in Cooperative Games with Graph Communication Structure

A class of cooperative games with graph communication structure is studied in this paper by considering some important players,namely essential players.Under the assumption that only connected coalitions containing essential players are able to cooperate and obtain their worths,the class of graph games with essential players is proposed as well as an allocation rule.The proposed value follows the spirit of the Myerson value defined by applying the Shapley value on a modified game.Three properties,feasible component efficiency,the inessential component property,and fairness,are provided to fully characterize this value,where feasible component efficiency and fairness follows the same ideas of component efficiency and fairness for classical graph games,and the inessential component property says that the total payoffs of the players in a non-feasible component is zero.Moreover,some computational aspects of the proposed value and comparisons with disjunctive permission value for games with permission structure are also studied,respectively.

反向驯化、符号劳动与媒介依存症:数字游戏世界中的玩家主体性悖论

数字游戏作为一种文化形式,是玩家自我展演的“生命舞台”。数字游戏通过暴力“正当化”的“超真实”符号环境、程序与算法的修辞规训,将玩家悬置于“玩乐回路”中,构成媒介反驯的系统逻辑。玩家以符号劳动为典型的自我驱动,在隐形的“数字工厂”中主动从事符号和文本的生产,形成“媒介依存”的社会症候。面对数字游戏中的主体性悖论,需要寻求处于游戏反讽时代的演进出路,使主体在游戏世界中获得真正意义上的“自由”和“解放”。

电子竞技产业中的“玩星”及其商品化路径

职业电竞产业化发展不仅带来了玩家的正面形象,也催生了“玩星”经济。“玩星”经济指的是围绕明星效应的职业电竞玩家打造的商业模式。基于对X俱乐部“玩星”经济组织过程的参与观察和对从业者的访谈,可揭示“玩星”的商品化逻辑及影响因素。职业电竞玩家在赛场、社交、直播平台的媒介形象是商品化的主要形式。“玩星”形象的商业模式包括赞助商代言及虚拟游戏商品、礼物交易两种。数字技术将粉丝对特定的职业电竞玩家的网络行为转化成为可量化的数据,吸引广告商、赞助商的投资。流量是“玩星”形象的数据基础,网络口碑和正面评价则是流量变现的前提。不论是流量抑或是正面评价,都是由职业电竞玩家竞技实力和成绩驱动的。“竞技—粉丝—商品化(代言、虚拟商品)”是“玩星”经济的主要路径。

《黑神话:悟空》与中国数字游戏的工业化转型:历程、现状与问题

1980—2020年前后,中国数字游戏的主要品类从实体发行的单机游戏发展至数字发行的网络游戏与移动端游戏。在商业、技术等多种因素的影响下,形成了以数值比较与服务型游戏为主导的市场格局和以免费结合内购为核心的商业模式。《黑神话:悟空》的出现是一次对中国数字游戏工业结构的阶段性检验,是对当下游戏从业者编创设计能力、技术积累、供应链结构与商业化程度、多行业协同能力,以及消费群体数量与付费能力的集中检验,暴露出当下产业在面对AAA(3A)单机游戏工业化转型的结构性问题。

后亚运时代篮球运动员力量训练有效方法研究

杭州第19届亚运会半决赛,中国男篮在领先20分的情况下惨遭翻盘,1分惜败,令无数篮球爱好者扼腕痛惜。笔者为蒙古国在读博士,对比了蒙古国和中国的亚运会篮球项目的奖牌获得情况,通过文献分析法、逻辑推演法阐述篮球运动、篮球运动员身体素质以及篮球运动员力量训练的必要性,根据力量训练的不同类别,围绕负荷强度、练习次数与组数、练习持续时间、组间间歇时间等内容,研究篮球运动员力量训练的有效方法,总结各种训练方法的异同点,阐明注意事项,以期为篮球运动员立足科学化训练提供参考。

侵犯游戏类虚拟财产行为定性分析——以关系路径为视角

游戏类虚拟财产包括游戏账号、金币与装备,从权利视角出发,将其定义为物权或债权都存在难以自圆其说之处,以此为基础展开的刑法论证并不严谨。采取利益保护模式,从游戏运营商、玩家和第三人之间迥异的三种法律关系入手可满足游戏类虚拟财产的刑法救济需求。游戏类虚拟财产具有财产属性,作为财产性利益被囊括进财产犯罪对象,其外延应当被限缩。网络游戏运营商具有零成本复制数据的权限,运营商控制下的游戏类虚拟财产因具有可复制性而不是财产犯罪的对象,玩家控制下的虚拟财产因不具有可复制性而可以成为财产犯罪的对象。已经进入玩家市场流通环节的虚拟财产应当以市场价格认定财产价值,尚未进入玩家市场流通环节的虚拟财产应当以被害人投入成本费用和行为人销赃价格折中认定财产价值。

UCT-RAVE算法在多人非完备信息博弈中的应用

针对传统博弈搜索算法无法适用于多人非完备信息博弈,通过分析UCT-RAVE算法的原理和特性,提出了运用UCT-RAVE算法与蒙特卡罗抽样技术相结合的方法。通过蒙特卡罗抽样技术将非完备信息提取为有一定可信度的完备信息,运用UCT-RAVE算法基于此完备信息进行搜索,结合多次蒙特卡罗抽样下的最佳收益,选择最适行动。实例结果表明了该方法的可行性和有效性。