Evolutionary Stable State Research Articles

Evolutionary Game Approach to Uplink NOMA Random Access Systems

This letter considers non-orthogonal multiple access (NOMA) as an uplink random access (RA) scheme. User equipments (UEs) in this RA system (re)transmit with some probability by selecting one of the target receive power levels. The packets received at the base station (BS) can be ordered with predetermined target power levels such that the BS can decode them using successive interference cancellation (SIC). We characterize this NOMA RA system using evolutionary game (EG) to show that the proportion of UEs of adopting a specific target power level upon retransmission is identified as evolutionary stable state (ESS).

Promoting Strategy of Chinese Green Building Industry: An Evolutionary Analysis Based on the Social Network Theory

Developing green building industry (GBI) is an effective way to promote sustainable economic development, realize energy savings, and reduce emissions. In this paper, an evolutionary game model is developed to examine the interactions between technology, knowledge transfer, and enterprises' behaviors in innovation networks. Through analysis of the evolutionary trend of the game, the cost of cooperative innovation is found to be an important factor that determines the evolutionary stable state or strategy (ESS). The government grant and financial support are deemed critical to promote the development of green building products (GBP). The government supervision, government procurement, and R&D are important for the GBI.

RIMNet: Recommendation Incentive Mechanism based on evolutionary game dynamics in peer-to-peer service networks

In peer-to-peer service networks, autonomous agents gain utilities through getting services from others. However, providing services is so costly that rational agents may prefer to defect rather than to cooperate. In order to provide scalable and robust services in such networks, incentive mechanisms need to be introduced. In this paper, we propose a novel approach RIM (Recommendation Incentive Mechanism) by building a cooperative agents recommendation system. And, in order to investigate the acceptance and performance of the proposed RIM, evolutionary game theory has been used. By studying the evolutionary stable state, we demonstrate the performance of the RIM-based model by both considering two scenarios PRIM/IRIM (Perfect/Imperfect Recommendation Incentive Mechanism). To comprehensively confirm the robustness of our mechanism: (1) OCMP (One Consumer Multi-service Providers) method has been discussed, in which agent could simultaneously request services from k (k>1) different agents; (2) a FS (Four-Strategies) game model has been further introduced; (3) QS (Quantity Sensitivity) scenario has been researched, in which the utility of an agent is sensitive to the amount of received services. By using the Lyapunov stability theory, it is qualitatively proved that non-cooperative agents can be well suppressed in our proposed RIM. Finally, extensive numerical and simulation experiments are conducted to highlight the performance and validate the theoretical properties of our model.

The asymmetric game of production technology in a manufacturing supply chain network: the influence of number of manufacturing partners

We consider the influence of the number of manufacturing partners on the game of production technologies, which takes place between two manufacturers with different production technologies in a two-echelon manufacturing supply chain network. Firstly, this study analyzes the influence of the number of manufacturing partners on the bilateral production cooperative relation between upstream and downstream manufacturers, finding that the number of manufacturing partners significantly influences bilateral cost-sharing proportion caused by “eliminating production technology differences between them.” Furthermore, we explore corresponding conditions for reaching different evolutionary stable strategy of the two parties in the game of production technology, concluding that manufacturers would not have better performance and either they have more and more or fewer and fewer manufacturing partners. Instead, there exists a critical interval in the number of manufacturing partners in which manufacturers regularly choose certain evolutionary stable strategies all the time. Finally, according to the example analysis on evolutionary stable states in the game and the sensitivity analysis on relevant parameters that affect the game relationship, it is shown that whether the “collaborate” strategy would eventually be chosen by the manufacturer was correlated negatively with its cost coefficient for eliminating production technology differences, but positively with the other party’s cost coefficient and extra profit in bilateral cooperation.

Emergence of evolutionarily stable communities through eco-evolutionary tunnelling.

Ecological and evolutionary dynamics of communities are inexorably intertwined. The ecological state determines the fate of newly arising mutants, and mutations that increase in frequency can reshape the ecological dynamics. Evolutionary game theory and its extensions within adaptive dynamics have been the mathematical frameworks for understanding this interplay, leading to notions such as evolutionarily stable states (ESS) in which no mutations are favoured, and evolutionary branching points near which the population diversifies. A central assumption behind these theoretical treatments has been that mutations are rare so that the ecological dynamics has time to equilibrate after every mutation. A fundamental question is whether qualitatively new phenomena can arise when mutations are frequent. Here, we describe an adaptive diversification process that robustly leads to complex ESS, despite the fact that such communities are unreachable through a step-by-step evolutionary process. Rather, the system as a whole tunnels between collective states over a short timescale. The tunnelling rate is a sharply increasing function of the rate at which mutations arise in the population. This makes the emergence of ESS communities virtually impossible in small populations, but generic in large ones. Moreover, communities emerging through this process can spatially spread as single replication units that outcompete other communities. Overall, this work provides a qualitatively new mechanism for adaptive diversification and shows that complex structures can generically evolve even when no step-by-step evolutionary path exists.

Fitness potentials and qualitative properties of the Wright-Fisher dynamics

We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain an expression for the amount of work necessary for a given type to reach fixation. In particular, within this interpretation, we develop a graphical analysis — similar to the one used in classical mechanics — providing the basic tool for a simple heuristic that describes both the short and long term dynamics. As a by-product, we provide a new definition of an evolutionary stable state in finite populations that includes the case of mixed populations. We finish by showing that our theory – rigorous for two types evolution without mutations– is also consistent with the multi-type case, and with the inclusion of rare mutations.

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

The Trilateral Evolutionary Game of Agri-Food Quality in Farmer-Supermarket Direct Purchase: A Simulation Approach

The prevalence of opportunistic behaviors in agri-food production and circulation results in frequent quality accidents in emerging economies. Numerous researches have discussed effective countermeasures to this problem, but few of them focus on the effectiveness and stability of quality assurance systems. Owing to the bounded rationality and information asymmetry, the dynamic quality game among producers, marketers, and consumers has significant characteristics of complexity. This paper aims at discussing the farmer-supermarket direct purchase’s contributions to ensure the agri-food quality and analyzing the effectiveness, stability, and key factors of this new industrial organization. Based on the evolutionary game theory, we establish the trilateral-game payoff matrix, build up the replicator dynamic equations, and discuss possible evolutionary stable states. The simulation results show that the evolutionary system converges to desired stability faster, when the high-quality agri-food’s market premium increases and the penalty for violating quality standards increases. Furthermore, when farmers share more high-quality agri-food’s market premiums and marketers compensate more for violating the quality standards than before, the evolutionary system also converges to desired stability faster. Therefore, the quality information tracing technology, farmers and marketers’ fair distribution of profits and risks, and consumers’ capabilities to safeguard their legal rights are the three key factors to maintain the effectiveness and stability of quality assurance systems.

Nash Equilibrium-Based Asymptotic Stability Analysis of Multi-Group Asymmetric Evolutionary Games in Typical Scenario of Electricity Market

This paper introduces new theoretical insights into Nash equilibrium-based asymptotic stability (NEAS) of two-group and three-group asymmetric evolutionary games in typical scenarios of electricity market (EM). EM competition has become a complex dynamic evolution process accomplished by more complex characteristics of market economy behavior. Replicator dynamics in evolutionary game theory, as well as Lyapunov stability theory, are employed to solve incomplete-information and bounded-rationality game issues in EM, so as to overcome theoretical demerits of classical game theory in solving multi-group games in EM. First, the NEAS of a unilateral two-group asymmetric evolutionary game (AEG) is investigated. Then, this is expanded to a complicated $2\times 2\times 2$ trilateral multi-group AEG, and the NEAS of it under different game situations in EM is thoroughly discussed. Finally, a practical case study is conducted for verification. The case illustrates how the factors affect the payoff matrix which will change ultimate evolutionary stable state of the multi-group AEG in EM. One main finding demonstrates the complete dynamics behavior and multi-group evolutionary stable strategy (MESS) of the AEG system in 3-D mixed strategy space. The other one reveals that EM policies formulated by government and other factors can gradually influence the MESS via changing the payoff distribution matrix.

A fuzzy logic and game theory based adaptive approach for securing opportunistic networks against black hole attacks

SummaryOpportunistic networks (OppNets) are networks that can be used in situations of sparse network connectivity. Strategies for implementing secure transmission of messages in OppNets offer complex and distinctive problems that are wholly different from traditional networks using TCP/IP protocols for data transmission. In this paper, a security protocol named FuzzyPT is proposed which combats black hole attacks in OppNets. The defense mechanism is based on the information extracted from messages in the buffer, potential threat (PT) messages, and fuzzy logic. Fuzziness aids the system in being adaptive by modeling the character of nodes as either benign or malicious. It provides the network with the ability to judge the character of nodes based on relationships between different parameters instead of basing this decision on fixed conditions. FuzzyPT is observed to reduce erroneous decision‐making and decrease the number of false positives and false negatives in the system. An evolutionary game theoretic model is applied, which analyzes the decision‐making ability of relays in choosing varied strategies while forwarding messages. The evolutionary stable state is computed for the protocol, which verifies the proposition that a majority of the relays will cooperate by forwarding messages. The efficiency of the protocol is judged on various grounds such as delivery probability, network overhead ratio, packets dropped, and transmission latency. It is observed that the proposed game theoretic protocol outperforms an existing acknowledge and evolutionary game theory–based security protocol in terms of all the aforementioned performance characteristics.

Stochastic and information-thermodynamic structures of population dynamics in a fluctuating environment.

Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more proactive decision making, in which environmental information is sensed and exploited more actively and effectively. Understanding the fundamental relation between fitness and information is therefore crucial to clarify the limits and universal properties of adaptation. In this work, we elucidate the underlying stochastic and information-thermodynamic structure in this process, by deriving causal fluctuation relations (FRs) of fitness and information. Combined with a duality between phenotypic and environmental dynamics, the FRs reveal the limit of fitness gain, the relation of time reversibility with the achievability of the limit, and the possibility and condition for gaining excess fitness due to environmental fluctuation. The loss of fitness due to causal constraints and the limited capacity of real organisms is shown to be the difference between time-forward and time-backward path probabilities of phenotypic and environmental dynamics. Furthermore, the FRs generalize the concept of the evolutionary stable state (ESS) for fluctuating environment by giving the probability that the optimal strategy on average can be invaded by a suboptimal one owing to rare environmental fluctuation. These results clarify the information-thermodynamic structures in adaptation and evolution.

A Graphical Evolutionary Game Approach to Social Learning

In this work, we study the social learning problem, in which agents of a networked system collaborate to detect the state of the nature based on their private signals. A novel distributed graphical evolutionary game theoretic learning method is proposed. In the proposed game-theoretic method, agents only need to communicate their binary decisions rather than the real-valued beliefs with their neighbors, which endows the method with low communication complexity. Under mean field approximations, we theoretically analyze the steady state equilibria of the game and show that the evolutionarily stable states (ESSs) coincide with the decisions of the benchmark centralized detector. Numerical experiments are implemented to confirm the effectiveness of the proposed game-theoretic learning method.

Stability properties of nonlinear dynamical systems and evolutionary stable states

In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.

Evolutionary Game Analysis of Financial Regulation and Innovation Under Asymmetric Conditions

The loose financial supervision and excessive financial innovation will lead the country to heavy losses in financial crisis. So how to balance the relationship between financial supervision and financial innovation and make financial supervision and financial innovation to achieve complementary has become a hot issue. The financial supervision and financial institutions are a process of repeated game, but the research on them is still in a superficial stage. Therefore, this paper uses evolutionary game theory and method to analyze the dynamic replication system of asymmetric evolutionary game of two groups of financial institutions and regulators in China. And the evolutionary stable state of the system under different conditions is analyzed. The conclusion is that under different parameter values, the other side adopts different strategies, and the system will tend to different equilibrium states.

Strategy evolution of information diffusion under time-varying user behavior in generalized networks

Modern generalized networks, where physical devices and social players are combined to support seamless and more flexible services, are strongly driven by user behavior and its evolution. A typical example of behavior-affected processes is the information diffusion by users in generalized networks. In this paper, we focus on user strategy selection with respect to information diffusion in generalized networks, and study its evolutionary dynamics and their benefits, as user behavior/interests change over the course of time. We model information diffusion in generalized networks through graphical evolutionary game theory (graphical EGT) and analyze the evolution of the system and its Evolutionary Stable States (ESS) for time-varying fitness values due to time-varying user interests. We perform extensive evaluations based on numerical and simulation results, and study the impact of several parameters on the derived ESS curves (i.e., ESS points over time). Such parameters involve user interests and their fitness values, and the degree distributions and network type of the layers of the generalized network. We thoroughly evaluate via numerical analysis and appropriate examples the existence of ESS loci for the system dynamics depending on the associated parameters. Also, we discuss the relation between (graphical) EGT-based information diffusion analysis and the epidemics-based information diffusion modeling and analysis that is frequently applied in the literature. Our modeling and evaluations can be used to predict the evolution of the cumulative behavior, allowing for efficient design and control of information campaigns.

Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games

Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper, we investigate a new methodology to compute evolutionary stable states based on the level- ${k}$ equilibrium, a new refinement of Nash equilibrium in repeated games. A level- ${k}$ equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level- ${k}$ equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of ${n}$ -player symmetric games. Three games, including the iterated prisoner’s dilemma, are analyzed by means of the proposed methodology.

Evolutionary Information Diffusion over Heterogeneous Social Networks

A huge amount of information, created and forwarded by millions of people with various characteristics, is propagating through the online social networks every day. Understanding the mechanisms of the information diffusion over the social networks is critical to various applications including online advertisement and website management. Different from most of the existing works, we investigate the information diffusion from an evolutionary game-theoretic perspective and try to reveal the underlying principles dominating the complex information diffusion process over the heterogeneous social networks. Modeling the interactions among the heterogeneous users as a graphical evolutionary game, we derive the evolutionary dynamics and the evolutionarily stable states (ESSs) of the diffusion. The different payoffs of the heterogeneous users lead to different diffusion dynamics and ESSs among them, in accordance with the heterogeneity observed in real-world datasets. The theoretical results are confirmed by simulations. We also test the theory on Twitter hashtag dataset. We observe that the derived evolutionary dynamics fit the data well and can predict the future diffusion data.

Evolutionary Game-Based Trust Strategy Adjustment among Nodes in Wireless Sensor Networks

Wireless sensor networks (WSNs) provide network services through the cooperation of sensor nodes, while the basis of cooperation depends on the trust relationships among the nodes. In this paper, we construct an evolutionary game-based trust strategy model among the nodes in WSNs, and we subsequently introduce a strategy adjustment mechanism into the process of game evolution to make up for the deficiency that the replicator dynamic model cannot reflect the requirement of individual strategy adjustments. Afterward, we derive theorems and inferences in terms of the evolutionary stable state through dynamic analyses, providing a theoretical basis for WSN trust management. Furthermore, we verify the theorems and inferences with different parameter values, especially the trust incentive and the upper limit of data retransmission after packets are lost, and both of them are closely related to the evolutionary stable state. The experiments demonstrated that, under certain conditions, the involved nodes can finally reach a stable state of the system by constantly adjusting their trust strategy. At the same time, the speed of evolution of our strategy adjustment mechanism in achieving the stable state is much faster than that of the usual replicator dynamic evolution method.

Social norms, costly punishment and the evolution of cooperation

Within a co-evolutionary framework of reputations, strategies and social norms, we study the role of punishment in the promotion of cooperation. Norms differ according to whether they allow or do not allow the punishment action to be a part of the strategies, and, in the case of the former, they further differ in terms of whether they encourage or do not encourage the punishment action. In such a framework, depending on the applied social norm, players are first given different reputations based on their employed strategies. Players then update their strategies accordingly after they observe the payoff differences among different strategies. Finally, over a longer horizon, the evolution of the social norms may be driven by the average payoffs of all members of the society. The strategy dynamics are articulated under different social norms. It is found that costly punishment does contribute to the evolution toward cooperation. Not only does the attraction basin of the cooperative evolutionary stable state become larger, but the speed of convergence to the CESS also becomes faster. These two properties are further enhanced if the punishment action is encouraged by the social norm.

Financial Payoff in Patent Alliance: Evolutionary Dynamic Modeling

Originating from the strategic management theory, resource-based view of firm believes that firms rely on bundles of resources which enable them to gain competitive advantage. Patent, as an integral part of intellectual capital, is an important resource for organizations building capabilities. With the heterogeneous in nature and imperfectly mobile, patent and its management becomes increasingly crucial for organizations facing globalization, information transparency, and intensified competition in developing a sustainable competitive advantage. Drawing upon the literature on strategic alliance, resource-based view, and patent management, we study how sharing patents can create sharing value added and synergy value added that enable participants in the patent alliance to obtain better financial payoff. Specifically, in this paper, we use the evolutionary stable strategy and replicator dynamic from evolutionary game theory to model the synergy effects in patent alliance. Our evolutionary dynamic modeling shows that an evolutionary stable state converges when organizations share patents, and supports that both patent sharing value added and synergy value added from patent alliance would be financially beneficial to organizations.