博弈控制论简述

博弈控制论是近年来出现的博弈与控制的交叉学科,虽然它融合了博弈和控制双方的工具和方法,但无论从研究对象,研究方法与现有的结论看,它都不完全从属于经典博弈或经典控制的范畴,因此,是一个具有自身特色的新学术生长点.本文的目的是对这个新方向做一个简述介绍,内容包括:i)基于博弈的控制;ii)基于势博弈的优化;iii)博弈中的状态空间方法;iv)国内几个研究博弈控制论的团队.最后,对博弈控制论的未来做一展望.     

Semi-tensor product approach to networked evolutionary games

In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs.
To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.     

A decision support framework for security resource allocation under ambiguity

There has been increasing interest in using Stackelberg game (known as a security game) to allocate limited security resources against different attacker types with a specific probability distribution. However, real problems of this kind often face ambiguous information, such as imprecise, unreliable and absent payoffs, and ambiguous assignments of these payoffs. To this end, based on decision theory and the Dempster–Shafer theory of evidence, this paper proposes a novel framework that can handle these common types of ambiguity. More specifically, this paper deploys the underlying principles of existing rules from decision theory, as a way to characterise different attitudes to ambiguity, during the transformation of ambiguous payoffs into point‐valued payoffs. Hence, our framework holds some good properties: (i) it subsumes traditional security games without ambiguous payoffs, (ii) a uniform margin of error will not affect the results and (iii) the influence of complete ignorance can be minimised. Also, our framework is evaluated by using nine different transformation rules, under various conditions and constraints, against 73,000 randomly generated games (a first comprehensive empirical evaluation to date). The evaluation reveals the benefits of each transformation rule and confirms that different rules can model individuals' different attitudes to ambiguity.     

The impact of coupled games on the learning experience of learners at-risk: An empirical study

Offering pervasive game-based learning scenarios to at-risk learners is considered effective and motivating. This experimental study offers a detailed example of an educational setting that couples a mobile game with a PC browser game. It evaluates how this coupling supports engagement and learning for the target group. Nineteen participants aged between 17 and 21 years played and explored the game. The findings through seven-week gaming indicate that coupled games have potential to increase learners’ interest in a topic and can support learning activities.     

A Markov Game-Adaptive Fuzzy Controller for Robot Manipulators

This paper develops an adaptive fuzzy controller for robot manipulators using a Markov game formulation. The Markov game framework offers a promising platform for robust control of robot manipulators in the presence of bounded external disturbances and unknown parameter variations. We propose fuzzy Markov games as an adaptation of fuzzy Q-learning (FQL) to a continuous-action variation of Markov games, wherein the reinforcement signal is used to tune online the conclusion part of a fuzzy Markov game controller. The proposed Markov game-adaptive fuzzy controller uses a simple fuzzy inference system (FIS), is computationally efficient, generates a swift control, and requires no exact dynamics of the robot system. To illustrate the superiority of Markov game-adaptive fuzzy control, we compare the performance of the controller against a) the Markov game-based robust neural controller, b) the reinforcement learning (RL)-adaptive fuzzy controller, c) the FQL controller, d) the H_infin theory-based robust neural game controller, and e) a standard RL-based robust neural controller, on two highly nonlinear robot arm control problems of i) a standard two-link rigid robot arm and ii) a 2-DOF SCARA robot manipulator. The proposed Markov game-adaptive fuzzy controller outperformed other controllers in terms of tracking errors and control torque requirements, over different desired trajectories. The results also demonstrate the viability of FISs for accelerating learning in Markov games and extending Markov game-based control to continuous state-action space problems.     

有限博弈的矩阵半张量积方法

矩阵半张量积被广泛地应用在有限博弈的研究中,例如:1)演化博弈; 2)势博弈; 3)有限博弈的向量空间分解; 4)基于势博弈的优化与控制; 5)合作博弈等.本文的目的,就是对上述各种应用做一个全面的介绍,包括其原理、主要成果、以及尚待解决的问题.     

Antagonistic games with interval parameters

Antagonistic (matrix) games with payoff matrices given to within an interval are considered. The necessan and sufficient conditions of existence of solutions of such games are established. It is shown that the basic theorem of the Von Neumann theory is not valid for such games. The method of solution of an internal game by reducing it to two boundary exact games is proposed. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 149–160, July–August, 1999.     

Three-player conflicting interest games and nonlocality

We outline the general construction of three-player games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the permutations of players; (ii) the existence of an upper bound for total payoff resulting from Bell inequalities; (iii) the existence of both fair and unfair Nash equilibria saturating this bound. Conditions (i)–(iii) imply that we are dealing with conflicting interest games. An explicit example of such a game is given. A quantum counterpart of this game is considered. It is obtained by keeping the same utilities but replacing classical advisor by a quantum one. It is shown that the quantum game possesses only fair equilibria with strictly higher payoffs than in the classical case. This implies that quantum nonlocality can be used to resolve the conflict between the players.     

基于多跟随者Stackelberg博弈的流速控制算法

由于现实网络中,端系统的角色往往并不平等,存在某些端系统制定整个网络的流速控制策略,其他端系统只能跟随这些策略,不能简单地使用非合作博弈理论研究Internet中非合作端系统的贪婪行为。该文在讨论了一次博弈模型和流速控制博弈均衡的解析解的基础上,对多跟随者Stackelberg博弈模型的流速与拥塞控制行为进行了深入研究。提出了多跟随者Stackelberg博弈流速控制模型,论证了Stackelberg均衡的存在性,并推导出在Stackelberg均衡点上领导者和多跟随者流速率的解析解。最后,文章设计了一种基于多跟随者Stackelberg博弈的流速控制算法(FCSM),并讨论了FCSM算法执行的过程。     

The moderating role of locus of control on the links between experiential motives and intention to play online games

Online games represent a burgeoning market sector with growth potential. The distinctive entertainment-oriented features of such games provide experiential motives for users. However, most previous studies have focused on the single dimensional affective motive of online game use. The multi-dimensional affective motivational aspects of entertainment technologies have been relatively neglected. In addition, previous studies report inconsistent relationships between motives and online game usage. To fill these gaps in the literature, the present study proposes five experiential motives such as concentration, enjoyment, escape, epistemic curiosity, and social affiliation as predictors of intention to play online games. External locus of control is also introduced as a moderator in the links between experiential motives and intention. The model was tested with the data from 576 current online game players who answered online survey. Structural equation model analysis confirmed that three experiential motives with the exception of concentration and epistemic curiosity have a positive effect on intention. χ² difference test confirmed that the coefficients linking experiential motives such as concentration, enjoyment, and escape to intention are higher for people with external locus of control than for people with internal locus of control. Implications are discussed in conclusion.     

Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order

A general method for solving game problems of approach for dynamic Volterra-evolution systems is presented. This method is based on the method of resolving functions [5] and the techniques of the theory of multivalued mappings. Properties of resolving functions are studied in more detail. Cases are separated where resolving functions can be derived in an analytical form. The scheme proposed covers a wide range of functional-differential systems, in particular, integral, integro-differential, and differential-difference systems of equations that describe the dynamics of a conflict controlled process. Game problems for systems with fractional Riemann-Liouville derivatives and regularized Dzhrbashyan-Nersesyan derivatives are studied in more detail. We will call them fractal games. An important role in the presentation of solutions of such systems is played by the generalized Mittag-Leffler matrix functions, which are introduced here. The use of asymptotic representations of these functions within the framework of the scheme of the method allows us to establish sufficient conditions of resolvability of game problems. A formal definition of parallel approach is given and illustrated by game problems for systems with fractional derivatives. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–32, May–June, 2000.     

Assessing fraction knowledge by a digital game

Serious or educational games gain increasing research interest as tools to augment traditional instructional approaches on scholastic learning, especially in mathematics education. In this study, we investigated whether game-based approaches may not only be useful to foster numerical learning but may also be valid as an assessment tool. To measure their conceptual knowledge of fractions eleven-year-old students played a math game on tablet computers using tilt-control to navigate an avatar along a number line for a total of 30 min. Findings indicated that hallmark effects of fraction magnitude processing typically observed in basic research, such as the numerical distance effect, were successfully replicated using the game-based assessment. Moreover, fraction comparison performance as well as fraction estimation accuracy correlated significantly with students' math grades. Therefore, the results of the current study suggest that game-based learning environments for fraction education (even using tilt-control) may also allow for a valid assessment of students’ fraction knowledge.     

Towards the design and implementation of computer-modeled opponents for use in entertainment and educational software: Some initial considerations

While advances in computer technology have led to major improvements in the presentation and appearance of modern computer games, there has been no equivalent improvement in the artificial intelligence (AI) performance of these games. Traditional AI designs have had surprisingly little impact on the development of game-based intelligent systems. New approaches to AI, particularly those using autonomous software agents encapsulated in software robots (softbots), have the potential to make an enormous impact on game-based AI systems.Softbot-based autonomous software agents provide a framework capable of supporting psychologically based models of human behavior in a game environment. Used in this manner, softbots provide a new set of tools to explore the synthesis of human-like reasoning in complex and dynamic environments.This paper explores some initial attempts to develop an exploratory, game-based, experimental environment capable of hosting softbot-based, psychological models of human behavior. Some preliminary work in the design and implementation of a simple, extensible, softbot-based, computer-modeled opponent is also discussed.     

Restrictive mechanism of flow control among non-cooperative Internet users

The flow and congestion control methods based on one-shot game model with non-cooperative game theory can explain the non-cooperative behavior of Internet users.However,the low effciency of equilibrium solutions affects their utility.Here the behavior of flow and congestion control based on infinitely repeated game models is addressed;the repeated and infinitely repeated flow and congestion control game model is presented; the existence and optimization of the Nash equilibrium point are proved;the discount ...     

Assessing the educational values of digital games

Abstract   In recent years, digital games have assumed an important place in the lives of children and adolescents. Effective content design is crucial to the success of digital game-based learning. Therefore, the tool for assessing the effectiveness of game design is accordingly very important for parents and teachers, so that they may encourage or discourage students to play. The purpose of this study is to develop an assessment tool to examine the educational values of digital games. In the first phase of this research, the research team developed the indices for assessing the educational values of digital games. An expert panel consisting of game scholars and professional game designers was established to construct the indices for evaluating digital games in three focus group discussions. Seventy-four game evaluation indices were sorted into seven categories: mentality change, emotional fulfilment, knowledge enhancement, thinking skill development, interpersonal skill development, spatial ability development and bodily coordination. In the second phase of the research, the game designers were asked to assess certain games by using the 74 indices. Meanwhile, the game scholars were also asked to evaluate the same pool of games by the same indices. The assessments by both the scholars and designers were then compared and the similarities were found. This research provided a preliminary framework for future game designers, parents and teachers in assessing educational values of digital games.     

复杂系统的主从质量生存对策

在复杂系统生存对策的基础上,引入生存质量函数,提出主从质量生存对策的概念,给出主从质量生存对策存在的充要条件,并讨论了复杂系统主从质量生存对策与一般主从对策的区别.     

The need to achieve: Players' perceptions and uses of extrinsic meta-game reward systems for video game consoles

Microsoft's Xbox and Sony's PlayStation overlay achievement and trophy systems onto their video games. Though these meta-game reward systems are growing in popularity, little research has examined whether players notice, use, or seek out these systems. In this study, game players participated in focus groups to discuss the advantages and disadvantages of meta-game reward systems. Participants described the value of meta-game reward systems in promoting different ways to play games, giving positive feedback about game play, and boosting self-esteem and online and offline social status. Participants discussed completionists, or gamers that want to earn all of the badges associated with the meta-game. Though self-determination theory and its subtheory cognitive evaluation theory suggest that extrinsic rewards might harm players' intrinsic motivation, our findings suggest players may see these systems as intrinsically motivating in this context. The implications of rewards systems for motivation, video game habits, and internet gaming disorder are discussed.     

Decentralized control: a stable proper fractional approach

Three decentralized control problems are considered in a fractional setup for two-channel multivariable systems. All three problems are instances of decentralized control or local output feedback problems. The problems are: (i) making the system stabilizable and detectable through the first channel via dynamic output feedback around the second channel, (ii) the first problem with the constraint of internal stability, and (iii) the decentralized stabilization problem. All three problems are equivalent as far as the solvability conditions are concerned. A characterization of all solutions in each case is given. The results apply to a class of systems having fractional representations over an arbitrary principal ideal domain     

动态协商对策的诱导平衡*

本文动态对策协商的问题，提出了动态对策问题在协商 解处的诱导平衡的概念，研究了诱导平衡存在的必要条件和充分条件，并分析了线性二次型动态对策问题的诱导平衡。