面向重大公共卫生风险治理的应急物流协同演化仿真

为提高重大公共卫生风险治理过程中的应急物流效率,在分析政府与物流企业行为特征的基础上,设计了面向重大公共卫生风险治理的高效应急物流协同机制。通过构建地方政府与物流企业的演化博弈模型,探究了地方政府监管和物流企业协同的演化规律与路径,然后利用数值仿真来验证所提模型的可行性和有效性。结果表明,与商业物流协同机制相比,面向重大公共卫生风险治理的应急物流协同机制更依赖于地方政府的监管力度,并且该机制使得物流企业的协同水平在0.25与0.9之间反复波动;而建立针对地方政府的动态奖惩机制后,在博弈次数达到30时,物流企业的协同水平为0.46,并一直维持稳定,可见这个动态奖惩机制显著提高了应急物流协同机制的稳定性。     

DPoS共识机制改进的演化博弈及策略研究

基于演化博弈将监察机制与奖惩制度引入授权股份证明（delegated proof of stake,DPoS）共识机制,构建以代理节点、投票节点、监管节点为主体的三方演化博弈模型;分析共识方案改进前后节点的行为策略选择变化,在不同奖惩力度和惩罚因子下节点行为策略的演化趋势,并用Matlab仿真。研究结果表明：（1）改进方案能遏制恶意节点的合谋行为并提高投票节点的积极性;（2）奖惩力度能影响节点行为策略;（3）惩罚因子可以影响节点行为趋向稳定点的速度。     

生产厂商逆向供应链演化稳定策略分析

生产型企业通过实施逆向供应链策略取代传统供应链的单向运作模式,可以减少对环境的负面影响和对资源的过度依赖,对本企业生产的废旧产品回收再利用成为当前发展新趋势。将逆向供应链作为一类复杂适应系统,基于复制动态方程和演化稳定策略,构建了逆向供应链演化博弈模型,分析和讨论了逆向供应链中每一个供应商决策如何影响供应链绩效。在市场机制下,供应商的额外收益超出实施逆向供应链的成本,供应商才会采取实施逆向供应链策略,而在政府管制下,相应规制可以有效促进逆向供应链策略的实施。     

A Matrix Approach to the Analysis and Control of Networked Evolutionary Games with Bankruptcy Mechanism

This paper investigates the evolutionary dynamic and control problem for a kind of networked evolutionary games with bankruptcy mechanism by using semi‐tensor product of matrices, and presents a number of new results. First, this kind of games are expressed as logical dynamic networks and converted into their algebraic forms, based on which, the evolutionary dynamics of the given games can be discussed. Second, the control problem is considered, and a control sequence is designed to guarantee that none of players goes bankrupt as the control target requires. Finally, an illustrative example is given to show the effectiveness of our main results.     

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.     

N人合作博弈的Nash及演化均衡稳定策略分析

在有限理性的基础上,对N人合作博弈的对称Nash均衡进行了分析,并引入演化博弈理论分析了参与人的演化均衡稳定策略,得到了不同策略选择下的均衡点。进而应用生物复制动态理论对离散时间及连续时间下的复制动态稳定集进行了研究。最后通过实例说明了该方法在博弈均衡选择上的有效性。     

Dynamics and stability for a class of evolutionary games with time delays in strategies一类具有时滞策略的演化博弈的动力学和稳定性

This paper investigates the modeling and stability of a class of finite evolutionary games with time delays in strategies. First, the evolutionary dynamics of a sequence of strategy profiles, named as the profile trajectory, is proposed to describe the strategy updating process of the evolutionary games with time delays. Using the semi-tensor product of matrices, the profile trajectory dynamics with two kinds of time delays are converted into their algebraic forms respectively. Then a sufficient condition is obtained to assure the stability of the delayed evolutionary potential games at a pure Nash equilibrium.     

激励机制下合作行为的演化动力学

探索复杂系统中控制自私个体合作演化的激励机制,是国际系统与控制等诸多领域关注的重要科学问题.研究者曾探讨了引入惩罚机制对系统中个体合作的促进作用.但实际中,惩罚者可能会受到奖励的正激励,以及被惩罚个体报复的负激励影响.本文基于演化博弈论分别研究分散式和集中式惩罚机制下的合作演化,重点关注对惩罚行为施加不同的激励作用对系统演化的影响.研究发现,当系统中存在对惩罚行为的负激励时,分散式惩罚机制对合作行为的促进作用被完全抑制;然而集中式惩罚机制却依然可以促进合作行为的涌现.另一方面,对惩罚行为的正激励可以有效地抵制负激励的负面影响,从而使合作涌现.特别地,在采用集中式激励的大规模种群中,合作行为和惩罚行为能够在自然选择意义下占优.激励机制的研究对于复杂系统优化调度与配置、群体机器人协同控制等实际问题具有重要的理论意义和应用价值.     

DPOS共识机制的改进方案

针对委托权益证明（DPOS）共识机制节点投票不积极以及恶意节点勾结现象提出了一种改进方案。首先,引入非结构化网络信任模型,根据每个节点的历史记录和其他节点的推荐值计算综合信任值。根据综合信任值进行投票,使得选择的节点更可信。引入推荐算法,节点的权益得到了分散,降低了中心化程度。其次,加入了奖惩机制,针对积极投票的节点给予信用值的奖励,使其有机会成为共识节点,针对恶意节点给予信任值的惩罚。实验结果表明,基于综合信任值投票计算的DPOS共识机制能够快速剔除错误节点,维护系统稳定性,具有较高的安全性。     

复杂网络上的演化博弈

主要介绍了近年来复杂网络上的演化博弈研究现状和研究方向．复杂网络理论的发展为描述博弈关系提供了系统且方便的框架，网络上的节点表示博弈个体，边代表与其邻居的博弈关系．介绍了经典演化博弈论中的演化稳定策略概念和复制动力学方程，以及二者的相互联系．介绍了混合均匀有限人口中随机演化动力学问题，并给出了与确定复制方程的相互转化关系．介绍了小世界、无标度等复杂网络上演化博弈的研究结论，给出了复杂网络上演化博弈论的未来发展方向．     

Dynamics and stability of potential hyper-networked evolutionary games

This paper considers the modeling and convergence of hyper-networked evolutionary games (HNEGs). In an HNEG the network graph is a hypergraph, which allows the fundamental network game to be a multi-player one. Using semi-tensor product of matrices and the fundamental evolutionary equation, the dynamics of an HNEG is obtained and we extend the results about the networked evolutionary games to show whether an HNEG is potential and how to calculate the potential. Then we propose a new strategy updating rule, called the cascading myopic best response adjustment rule (MBRAR), and prove that under the cascading MBRAR the strategies of an HNEG will converge to a pure Nash equilibrium. An example is presented and discussed in detail to demonstrate the theoretical and numerical results.     

Contribution Games in Networks

We consider network contribution games, where each agent in a network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we use a reward function for each relationship. Every agent is trying to maximize the reward from all relationships that it is involved in. We consider pairwise equilibria of this game, and characterize the existence, computational complexity, and quality of equilibrium based on the types of reward functions involved. When all reward functions are concave, we prove that the price of anarchy is at most?2. For convex functions the same only holds under some special but very natural conditions. Another special case extensively treated are minimum effort games, where the reward of a relationship depends only on the minimum effort of any of the participants. In these games, we can show existence of pairwise equilibrium and a price of anarchy of 2 for concave functions and special classes of games with convex functions. Finally, we show tight bounds for approximate equilibria and convergence of dynamics in these games.     

The Peer’s Dilemma: A general framework to examine cooperation in pure peer-to-peer systems

The exploration of social dilemmas is being considered a major foundation for encountering the enforced necessities of cooperation in self-organizing environments. Such environments are characterized by self-interested parties and the absence of trusted third parties. Recent approaches apply evolutionary socio-inspired games to formally prove the existence and further prolongation of cooperation patterns within communities. For instance, the Prisoner’s Dilemma game has thus provided a rich opportunity to examine self-interested behaviors in pure peer-to-peer networks. However, assuming a total absence of coalitions, incentives and punishment mechanisms, several works argue against a durable maintenance of cooperation neither at single-shot nor repeated-scenarios. In this article, we formally and experimentally demonstrate a counterexample for the latter by applying evolutionary game theory and a particular instance of the Rock–Scissors–Paper game. Our framework proves that the cyclic dominance of certain type of nodes within a P2P system has an impact and introduces a strategic aspect to the evolution of the overall community.     

Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method

Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of evolutionary networked games with “myopic best response adjustment” rule, and presents a number of new results. First, the dynamics of the evolutionary networked game is converted to an algebraic form via the semi-tensor product, and an algorithm is established to construct the algebraic formulation for the game. Second, based on the algebraic form, the dynamical behavior of evolutionary networked games is discussed, and some interesting results are presented. Finally, the strategy optimization problem is considered by adding a pseudo-player to the game, and a free-type control sequence is designed to maximize the average payoff of the pseudo-player. The study of an illustrative example shows that the new results obtained in this paper work very well.     

Modelling and strategy optimisation for a kind of networked evolutionary games with memories under the bankruptcy mechanism

This paper investigates the evolutionary dynamic and strategy optimisation for a kind of networked evolutionary games whose strategy updating rules incorporate ‘bankruptcy’ mechanism, and the situation that each player's bankruptcy is due to the previous continuous low profits gaining from the game is considered. First, by using semi-tensor product of matrices method, the evolutionary dynamic of this kind of games is expressed as a higher order logical dynamic system and then converted into its algebraic form, based on which, the evolutionary dynamic of the given games can be discussed. Second, the strategy optimisation problem is investigated, and some free-type control sequences are designed to maximise the total payoff of the whole game. Finally, an illustrative example is given to show that our new results are very effective.     

局部信息约束下网络演化博弈的动力学与优化

网络演化博弈的优化问题是混合值逻辑网络的一个自然推广.本文研究了一类网络演化博弈的优化控制问题,其中每个控制个体在极大化自己的收益时只能获取到邻域信息.首先,利用矩阵的半张量积,将局部信息约束下控制网络演化博弈的动力学转化为相应的代数形式.然后得到了局部信息约束下确定型网络演化博弈的最优控制序列.最后,基于动态规划的解,研究了局部信息约束下概率型网络演化博弈的优化控制问题,得到了最优控制序列的简单计算公式.两个数值例子验证了本文的理论结果.     

Perceptions of virtual reward systems in crowdsourcing games

The gaming approach to crowdsourcing is a major way to foster engagement and sustained participation. Also known as crowdsourcing games, players contribute their effort to tackle problems and receive enjoyment in return. As in any game, a fundamental mechanism in crowdsourcing games is its virtual reward system. This paper investigates how virtual reward systems evoke intrinsic motivation, perceived enjoyment and output quality in the context of crowdsourcing games. Three mobile applications for crowdsourcing location-based content were developed for an experimental study. The Track version offered a points-based reward system for actions such as contribution of content. The Badge version offered different badges for collection while the Share version served as a control which did not have any virtual reward system. For each application, participants performed a series of tasks after which a questionnaire survey was administered. Results showed that Badge and Track enhanced enjoyment emotionally, cognitively and behaviorally. They also increased perceptions of the quality of outputs when compared to Share. As well, they better satisfied the motivational needs for autonomy and competence than Share. Interestingly, there were also significant differences in how Badge and Track were perceived.     

Evolutionary forwarding games in delay tolerant networks: Equilibria,mechanism design and stochastic approximation

In this paper, we apply evolutionary games to non-cooperative forwarding control in Delay Tolerant Networks (DTNs). The main focus is on mechanisms to rule the participation of the relays to the delivery of messages in DTNs. Thus, we express the success probability as a function of the competition that takes place within a large population of mobiles, and we characterize the effect of reward-based mechanisms on the performance of such systems. Devices acting as active relays, in fact, sacrifice part of their batteries in order to support message replication and thus increase the probability to reach the destination. In our scheme, a relay can choose the strategy by which they participate to the message relaying. A mobile that participates receives a unit of reward based on the reward mechanism selected by the network. A utility function is introduced as the difference between the expected reward and the energy cost, i.e., the cost spent by the relay to sustain forwarding operations. We show how the evolution dynamics and the equilibrium behavior (called Evolutionary Stable Strategy – ESS) are influenced by the characteristics of inter contact time, energy expenditure and pricing characteristics.We extend our analysis to mechanisms that the system can introduce in order to have the message delivered to the destination with high probability within a given deadline and under energy constraints which bound the number of released copies per message. Finally, we apply our findings in order to devise decentralized forwarding algorithms that are rooted in the theory of stochastic approximations. Thus, we demonstrate that the ESS can be attained without complete knowledge of the system state and letting the source monitor number of released copies per message only. We provide extensive numerical results to validate the proposed scheme.     

Equilibrium Trajectories in Dynamical Bimatrix Games with Average Integral Payoff Functionals

This paper considers models of evolutionary non-zero-sum games on the infinite time interval. Methods of differential game theory are used for the analysis of game interactions between two groups of participants. We assume that participants in these groups are controlled by signals for the behavior change. The payoffs of coalitions are defined as average integral functionals on the infinite horizon. We pose the design problem of a dynamical Nash equilibrium for the evolutionary game under consideration. The ideas and approaches of non-zero-sum differential games are employed for the determination of the Nash equilibrium solutions. The results derived in this paper involve the dynamic constructions and methods of evolutionary games. Much attention is focused on the formation of the dynamical Nash equilibrium with players strategies that maximize the corresponding payoff functions and have the guaranteed properties according to the minimax approach. An application of the minimax approach for constructing optimal control strategies generates dynamical Nash equilibrium trajectories yielding better results in comparison to static solutions and evolutionary models with the replicator dynamics. Finally, we make a comparison of the dynamical Nash equilibrium trajectories for evolutionary games with the average integral payoff functionals and the trajectories for evolutionary games with the global terminal payoff functionals on the infinite horizon.     

Average-price-per-reward games on hybrid automata with strong resets

We study price-per-reward games on hybrid automata with strong resets. They generalise average-price games previously studied and have applications in scheduling. We obtain decidability results by a translation to a novel class of finite graphs with price and reward information, and games assigned to edges. The cost and reward of following an edge are determined by the outcome of the edge game that is assigned to it.