Game formulations for structural optimization under uncertainty

We consider structural optimization (SO) under uncertainty formulated as a mathematical game between two players –– a “designer” and “nature”. The first player wants to design a structure that performs optimally, whereas the second player tries to find the worst possible conditions to impose on the structure. Several solution concepts exist for such games, including Stackelberg and Nash equilibria and Pareto optima. Pareto optimality is shown not to be a useful solution concept. Stackelberg and Nash games are, however, both of potential interest, but these concepts are hardly ever discussed in the literature on SO under uncertainty. Based on concrete examples of topology optimization of trusses and finite element-discretized continua under worst-case load uncertainty, we therefore analyze and compare the two solution concepts. In all examples, Stackelberg equilibria exist and can be found numerically, but for some cases we demonstrate nonexistence of Nash equilibria. This motivates a view of the Stackelberg solution concept as the correct one. However, we also demonstrate that existing Nash equilibria can be found using a simple so-called decomposition algorithm, which could be of interest for other instances of SO under uncertainty, where it is difficult to find a numerically efficient Stackelberg formulation.     

Multidisciplinary topology optimization solved as a Nash game

In the present work, multidisciplinary optimization is formulated in the game theory framework. We choose a coupled heat transfer—thermoelastic system as the case study for which a topology design approach is developed. The multidisciplinary optimization problem is solved as a non‐cooperative game and we determine a Nash equilibrium. The game has two players and the parameterization of the design domain is such that the design variables describe the material density and a parameter which influences the heat flow by convection to the surrounding fluid. The first player controls the structure and the second player controls the temperature distribution in the structure. For the second player, we present mathematical proof of existence of a discrete valued optimal solution and it is concluded that no regularization of the suboptimization problem is needed. We present two numerical examples which illustrate the proposed methodology. One of the examples is also solved by weighting the objectives to a scalar valued objective function and the result is compared with the Nash game solution. Copyright © 2004 John Wiley & Sons, Ltd.     

考虑网络零售商有限IT服务能力的产品定价与广告策略分析

研究了网络零售商有限IT服务能力下产品定价与广告投入问题。首先,建立垄断市场中零售商决策模型,研究发现：零售商广告投入水平、零售价格以及消费者剩余都与零售商IT服务能力正相关。其次,在竞争市场中运用博弈论分别建立了两个零售商Nash静态和Stackelberg动态博弈模型。结果显示,零售商动态博弈中所制定的零售价格高于静态博弈时零售价格,而广告投入水平低于静态博弈时的广告投入水平,并且动态博弈时消费者剩余较小。对于零售商1而言静态博弈时最优服务能力大于动态博弈时的最优服务能力,而零售商2结论相反。最后,分析了消费者时间敏感性和广告敏感性对零售商利润以及最优服务能力的影响。     

Topological rationality of supply chain networks

In this study, we apply a topologically distributed bounded rationality model to quantify the level of rationality in supply chain networks. We use the averaged Jensen-Shannon divergence values between Nash and Quantal Response equilibria for all inter-firm strategic interactions, which are represented as Prisoner’s Dilemma games, to characterise the average level of rationality in a given supply chain network. This is based on the game theoretic assumption that as the rationality of a particular interaction increases, it converges towards Nash equilibrium, in a certain strategic decision making scenario. Using this model, we demonstrate that hub-and-spoke topologies are collectively more rational compared to scale-free and random network topologies. Finally, we compare our theoretical results against the empirical findings reported for networked systems in various domains. In particular, it is shown that network topologies comprising higher average rationality levels emerge under increasingly competitive environments.     

Identifying Game Processes Based on Private Working Sets

Fueled by the booming online games, there is an increasing demand for monitoring online games in various settings. One of the application scenarios is the monitor of computer games in school computer labs, for which an intelligent game recognition method is required. In this paper, a method to identify game processes in accordance with private working sets (i.e., the amount of memory occupied by a process but cannot be shared among other processes) is introduced. Results of the W test showed that the memory sizes occupied by the legitimate processes (e.g., the processes of common native windows applications) and game processes followed normal distribution. Using the T-test, a significant difference was identified between the legitimate processes and C/S-based computer games, in terms of the means and variances of their private working sets. Subsequently, we derived the density functions of the private working sets of the considered game processes and those of the legitimate processes. Given the private working set of a process and the derived probability density functions, the probability that the process is a legitimate process and the probability that the process is a game process can be determined. After comparing the two probabilities, we can easily determine whether the process is a game process or not. As revealed from the test results, the recognition accuracy of this method for C/S-based computer games was approximately 90%.     

Optimal process plan selection in networked based manufacturing using game-theoretic approach

This paper proposes a scheme for generating optimal process plans for multi jobs in a networked based manufacturing system. Networked manufacturing offers several advantages in the current competitive atmosphere such as reducing short manufacturing cycle time and maintaining the production flexibility, thereby achieving several feasible process plans. An N-person non-co-operative game with complete information is proposed and a mathematical model has been developed to generate the payoff functions. To be part of a game, we divided the game into two sub-games such as games to address sub-game (GASG) and games to solve sub-game (GSSG) which try to interact with each other and achieve the Nash equilibrium (NE). Consequently, a hybrid dynamic-DNA (HD-DNA) based evolutionary algorithm approach has been developed for more effective solutions of the game and also for finding the perfect NE points. The objective of this game is to generate the optimal process plans to minimise the makespan. Finally, three cases having different job complexities are presented to demonstrate the feasibility of the approach. The proposed algorithm is validated and results are analysed to benefit the manufacturer.     

Bit Rate Reduction in Cloud Gaming Using Object Detection Technique

The past two decades witnessed a broad-increase in web technology and on-line gaming. Enhancing the broadband confinements is viewed as one of the most significant variables that prompted new gaming technology. The immense utilization of web applications and games additionally prompted growth in the handled devices and moving the limited gaming experience from user devices to online cloud servers. As internet capabilities are enhanced new ways of gaming are being used to improve the gaming experience. In cloud-based video gaming, game engines are hosted in cloud gaming data centers, and compressed gaming scenes are rendered to the players over the internet with updated controls. In such systems, the task of transferring games and video compression imposes huge computational complexity is required on cloud servers. The basic problems in cloud gaming in particular are high encoding time, latency, and low frame rates which require a new methodology for a better solution. To improve the bandwidth issue in cloud games, the compression of video sequences requires an alternative mechanism to improve gaming adaption without input delay. In this paper, the proposed improved methodology is used for automatic unnecessary scene detection, scene removing and bit rate reduction using an adaptive algorithm for object detection in a game scene. As a result, simulations showed without much impact on the players’ quality experience, the selective object encoding method and object adaption technique decrease the network latency issue, reduce the game streaming bitrate at a remarkable scale on different games. The proposed algorithm was evaluated for three video game scenes. In this paper, achieved 14.6% decrease in encoding and 45.6% decrease in bit rate for the first video game scene.     

A reinforcement learning approach to stochastic business games

The Internet revolution has resulted in increased competition among providers of goods and services to lure customers by tearing down the barriers of time and distance. For example, a home buyer shopping for a mortgage loan through the Internet is now a potential customer for a large number of lending institutions throughout the world. The lenders (players, in generic game theory nomenclature) seeking to capture this customer are involved in a nonzero-sum stochastic game. Stochastic games are among the least studied and understood of the management science problems, and no computationally tractable solution technique is available for multi-player nonzero-sum stochastic games. We now develop a computer-simulation-based machine learning algorithm that can be used to solve nonzero-sum stochastic game problems that are modeled as competitive Markov decision processes. The methodology based on this algorithm is implemented on a supply chain inventory planning problem with a limited state space. The equilibrium reward obtained from the stochastic game problem is compared with a logical upper bound obtained from the corresponding Markov decision problem in which a single decision maker (player) is substituted for all the competing players in the game. Several numerical versions of the problem are studied to assess the performance of the methodology. The results obtained from our methodology for the inventory planning problems are within 0.8% of the upper bound.     

A sequential-move game for enhancing safety and security cooperation within chemical clusters

The present paper provides a game theoretic analysis of strategic cooperation on safety and security among chemical companies within a chemical industrial cluster. We suggest a two-stage sequential move game between adjacent chemical plants and the so-called Multi-Plant Council (MPC). The MPC is considered in the game as a leader player who makes the first move, and the individual chemical companies are the followers. The MPC's objective is to achieve full cooperation among players through establishing a subsidy system at minimum expense. The rest of the players rationally react to the subsidies proposed by the MPC and play Nash equilibrium. We show that such a case of conflict between safety and security, and social cooperation, belongs to the 'coordination with assurance' class of games, and we explore the role of cluster governance (fulfilled by the MPC) in achieving a full cooperative outcome in domino effects prevention negotiations. The paper proposes an algorithm that can be used by the MPC to develop the subsidy system. Furthermore, a stepwise plan to improve cross-company safety and security management in a chemical industrial cluster is suggested and an illustrative example is provided.     

制造商-供应商协同产品创新合作机制研究

分析了协作产品创新中制造商和供应商的行为及效果,建立了有关努力水平、贡献水平以及在一定分配模式下,制造商和供应商合作产品创新微分博弈模型,分析该微分博弈的Nash均衡,探讨团队Pareto最优及合作机制的设置.     

基于沉浸理论的自闭症儿童体感游戏交互设计

目的 探究可提升自闭症儿童体感游戏用户体验的交互设计方法,提升自闭症儿童在利用体感游戏进行康复训练时的用户体验.方法 以沉浸理论为基础,通过用户研究总结出自闭症儿童体感游戏的设计策略.并将层次分析法(AHP)和逼近理想解排序法(TOPSIS)应用到体感游戏的设计中,以及时的反馈、愉悦的界面表现、有效的操作交互、清晰的目标任务设计策略建立了体感游戏沉浸感设计的量化评估模型,并对设计出的方案进行了评估,选择了最佳方案,并进行深入的设计.结论 总结出了一套自闭症儿童体感游戏的交互设计策略和评估方法,并将其应用到自闭症儿童的体感游戏的设计中,从而创造出科学有效的沉浸式游戏体验,提高游戏干预自闭症儿童康复训练的效果,并为同类产品的设计提供了参考.     

Two-agent cooperative search using game models with endurance-time constraints

In this article, the problem of two Unmanned Aerial Vehicles (UAVs) cooperatively searching an unknown region is addressed. The search region is discretized into hexagonal cells and each cell is assumed to possess an uncertainty value. The UAVs have to cooperatively search these cells taking limited endurance, sensor and communication range constraints into account. Due to limited endurance, the UAVs need to return to the base station for refuelling and also need to select a base station when multiple base stations are present. This article proposes a route planning algorithm that takes endurance time constraints into account and uses game theoretical strategies to reduce the uncertainty. The route planning algorithm selects only those cells that ensure the agent will return to any one of the available bases. A set of paths are formed using these cells which the game theoretical strategies use to select a path that yields maximum uncertainty reduction. We explore non-cooperative Nash, cooperative and security strategies from game theory to enhance the search effectiveness. Monte-Carlo simulations are carried out which show the superiority of the game theoretical strategies over greedy strategy for different look ahead step length paths. Within the game theoretical strategies, non-cooperative Nash and cooperative strategy perform similarly in an ideal case, but Nash strategy performs better than the cooperative strategy when the perceived information is different. We also propose a heuristic based on partitioning of the search space into sectors to reduce computational overhead without performance degradation.     

Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry, the coordinated scheduling problem of parallel machine production and transportation is investigated. The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance. A non-cooperative game model is established, considering the competition and self-interest behavior of jobs from different customers for machine resources. The job from different customers is mapped to the players in the game model, the corresponding optional processing machine and location are mapped to the strategy set, and the makespan of the job is mapped to the payoff. Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model. A Nash equilibrium solution algorithm based on the genetic algorithm (NE-GA) is designed, and the effective solution of approximate Nash equilibrium for the game model is realized. The fitness function, single-point crossover operator, and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium. Rules are also designed to avoid the generation of invalid offspring chromosomes. The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes. Compared with other algorithms such as heuristic algorithms (FCFS, SPT, and LPT), the simulated annealing algorithm (SA), and the particle swarm optimization algorithm (PSO), experimental results show that the proposed NE-GA algorithm has obvious performance advantages.     

An econometric analysis of product variety impact on competitive market conduct in consumer goods markets

Decisions on product variety are a central part of the (strategic) marketing planning process of many consumer goods manufacturers. However, we have only limited information about the effects of product variety on competitive market conduct and profitability. In this paper, we introduce a simple econometric methodology for studying market conduct in prices and variety between rival brands of consumer goods markets. Our study follows the recent trend in empirical industrial organization, it is fully structural and starts from the specification of demand and supply functions. We introduce a number of different game theoretic regimes and characterize the equilibrium of each of these games. The equilibrium of each game is considered to be unique. On the basis of non-nested model selection, we can identify the form of competitive market conduct that is most suitable for the underlying data. Our empirical study identifies Nash behavior in pricing and collusive behavior in variety among the two leading brands in the market. The estimated parameters offer theoretically founded insight into the competitive rules in the market and the impact of prices and variety on profits.     

Application of combinatorial tests in video game testing

Video games comprise a multi-billion-dollar industry. Companies invest huge amounts of money for the release of their games. A part of this money is invested in testing the games. Current game testing methods include manual execution of pre-written test cases in the game. Each test case may or may not result in a bug. In a game, a bug is said to occur when the game does not behave per its intended design. The process of writing the test cases to test games requires standardization. We believe that this standardization can be achieved by implementing experimental design to video game testing. In this research, we discuss the implementation of combinatorial testing, specifically covering arrays, to test games. Combinatorial testing is a method of experimental design that is used to generate test cases and is primarily used for commercial software testing. In addition to the discussion of the implementation of combinatorial testing techniques in video game testing, we present an algorithm that can be used to sort test cases to aid developers in finding the combination of settings resulting in a bug.     

Pricing decisions in a strategic single retailer/dual suppliers setting under order size constraints

In this paper, we study a duopolistic market of suppliers competing for the business of a retailer. The retailer sets the order cycle and quantities from each supplier to minimize its annual costs. Different from other studies in the literature, our work simultaneously considers the order size restriction and the benefit of order consolidation, and shows non-trivial pricing behaviour of the suppliers under different settings. Under asymmetric information setting, we formulate the pricing problem of the preferred supplier as a non-linear programming problem and use Karush–Kuhn–Tucker conditions to find the optimal solution. In general, unless the preferred supplier has high-order size limit, it prefers sharing the market with its competitor when retailer’s demand, benefit of order consolidation or fixed cost of ordering from the preferred supplier is high. We model the symmetric information setting as a two-agent non-zero sum pricing game and establish the equilibrium conditions. We show that a supplier might set a ‘threshold price’ to capture the entire market if its per unit fixed ordering cost is sufficiently small. Finally, we prove that there exists a joint-order Nash equilibrium only if the suppliers set identical prices low enough to make the retailer place full-size orders from both.     

云庙会:元宇宙视角下严肃游戏体验设计研究

目的 以佛山祖庙为对象,在数字文旅背景下从元宇宙视角对庙会进行严肃游戏、体验创新设计,提出新的体验模式——云庙会,对当前庙会旅游存在的问题进行深入挖掘与痛点分析。方法 基于严肃游戏的设计原理对云庙会进行PACT-P系统模式构建,运用H5木疙瘩交互软件进行游戏内容编辑,从庙会的景区、习俗仪式、庙会活动和集市贸易等方面,进行游戏系统化地改造与升级,实现云庙会严肃游戏的便利性、可玩性和互动性。结论 一方面,尝试解决传统庙会旅游中的发展滞后和传播力度不足、游客参与度不高等问题;另一方面,通过严肃游戏的形式使云庙会旅游兼顾游戏性和教育性,不仅给传统庙会旅游提供多元化发展路径,而且为数字文旅发展思路提供实践参考。     

跳-扩散模型下保险公司的博弈问题

本文研究跳-扩散模型下的具有再保险业务的保险公司非零和博弈问题．假定金融市场可供保险公司投资的金融工具有两种：一种无风险资产（如债券）和一种风险资产（如股票）．保险公司可购买比例再保险,同时再保险公司以期望保费原则收取再保险保费,进而建立描述保险公司盈余过程的跳-扩散模型．以两家保险公司终端财富相对差值绩效最大化为目标,建立了两家保险公司的相对绩效最优的HJB方程．通过博弈理论和随机动态规划的方法,证明两家保险公司竞争纳什均衡解的存在性,并给出了纳什均衡耦合系统的隐式解．在特定的保险公司竞争关系下,对两家保险公司之间的最优投资和再保险策略进行分析,分析了模型参数对最优投资策略的影响,并给出相应的经济解释．     

Weakly strict equilibria in finite normal form games

In this paper we introduce the weakly strict equilibrium for (mixed extensions of) finiten-person games. For those games we prove that our new concept is a strict refinement of the undominated Nash equilibrium concept. We show that their set of weakly strict equilibria is nonempty and coincides with their set of strict equilibria (when the latter is also non-empty) and we study the relation between our refinement and other noncooperative concepts.We thank Xunta de Galicia for financial support through project XUGA20702B93     

Second‐order optimal control algorithm for complex systems

The solution to large‐scale optimal control problems, characterized by complex dynamics and extended time periods, is often computationally demanding. We present a solution algorithm with favourable local convergence properties as a way to reduce simulation times. This method is based on using a trapezoidal direct collocation to convert the differential equations into algebraic constraints. The resulting constrained minimization problem is then solved with an augmented Lagrangian formulation to accommodate both equality and inequality constraints. In contrast to the prevalent optimal control software implementations, we calculate analytical first and second derivatives. We then apply a generalized Newton method to the augmented Lagrangian formulation, solving for all unknowns simultaneously. The computational costs of the Hessian formation and matrix solution remain manageable as the system size increases due to the sparsity of all tensor quantities. Likewise, the total iterations for convergence scale well due to the local quadratic convergence of the generalized Newton method. We demonstrate the method with an inverted pendulum problem and a neuromuscular control problem with complex dynamics and 18 forcing functions. The optimal control solutions are successfully found. In both examples, we obtain quadratic convergence rates in the neighbourhood of the solution. Copyright © 2002 John Wiley & Sons, Ltd.