Long Wang

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Verified

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• PhD
• Professor (Full) at Peking University

In network science, change is good Historically, network science focused on static networks, in which nodes are connected by permanent links. However, in networked systems ranging from protein-protein interactions to social networks, links change. Although it might seem that permanent links would make it easier to control a system, Li et al. demons...

Significance Evolving populations are constantly subjected to changing environmental conditions. The environment can determine how the expression of traits affects the individuals possessing them. Just as important, however, is the fact that the expression of traits can also alter the environment. We model this phenomenon by introducing game transi...

Update rules, which describe how individuals adjust their behavior over time, affect the outcome of social interactions. Theoretical studies have shown that evolutionary outcomes are sensitive to model details when update rules are imitation-based but are robust when update rules are self-evaluation based. However, studies of self-evaluation based...

Cooperation is key to prosperity in human societies. Population structure is well understood as a catalyst for cooperation, where research has focused on pairwise interactions. But cooperative behaviors are not simply dyadic, and they often involve coordinated behavior in larger groups. Here we develop a framework to study the evolution of behavior...

Humans update their social behavior in response to past experiences and changing environments. Behavioral decisions are further complicated by uncertainty in the outcome of social interactions. Faced with uncertainty, some individuals exhibit risk aversion while others seek risk. Attitudes toward risk may depend on socioeconomic status; and individ...

The stability of complex ecosystems, which indicates the ability of the system to recover from perturbations, is profoundly influenced by the environment. Recent findings point out that changing environments with the renewal and decay of resources can alter ecological stability by affecting species abundances and interactions. These changes in turn...

In recent years, along with some ground-breaking advances made by artificial intelligence (AI) in Go, chess, video games, computer vision, natural language processing, and the analysis and prediction of protein struc- tures, the inherent barriers of traditional disciplines are gradually being broken, and a cross-discipline wave is stead- ily underw...

In this paper, the problem of distributively searching the Stackelberg equilibria of aggregative games with bilevel structures is studied. Different from the traditional aggregative games, here the aggregation is determined by the minimizer of the objective function in the inner level, which depends on players' actions in the outer level. Moreover,...

Logical dynamic games (LDGs) are a class of dynamic games that incorporate logical dynamics to describe the evolution of external states. Such games can be found in a wide range of natural and engineered systems, such as the Boolean network of lactose operon in Escherichia coli . However, little attention has been paid to LDGs in the control comm...

Recent empirical studies have revealed that social interactions among agents in realistic networks merely exist intermittently and occur in a particular sequential order. However, it remains unexplored how to theoretically describe evolutionary dynamics of multiple strategies on temporal networks. Herein, we develop a deterministic theory for study...

The stability of complex systems is profoundly affected by underlying structures, which are often modeled as networks where nodes indicate system components and edges indicate pairwise interactions between nodes. However, such networks cannot encode the overall complexity of networked systems with higher-order interactions among more than two nodes...

Direct reciprocity promotes the evolution of cooperation when players are sufficiently equal, such that they have similar influence on each other. In the light of ubiquitous inequality, this raises the question of how reciprocity evolves among unequal players. Existing studies on inequality mainly focus on payoff-driven learning rules, which rely o...

In this paper, the problem of online distributed optimization subject to a convex set is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this problem, an online distributed stochastic mirror descent algorithm is proposed. E...

In stochastic dynamic environments, multi-agent Markov decision processes have emerged as a versatile paradigm for studying sequential decision-making problems of fully cooperative multi-agent systems. However, the optimality of the derived policies is usually sensitive to model parameters, which are typically unknown and required to be estimated f...

In this paper, we investigate the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite-dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponentially fast consensus using a Lyapunov function consisting of...

Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One of the key statistics to summarize temporal patterns is the inter-event time, namely the duration between suc...

In this paper, the problem of online distributed optimization subject to a convex set is studied by employing a network of agents, where the objective functions allocated to agents are nonconvex. Each agent only has access to its own objective function information at the previous time, and can only communicate with its immediate neighbors via a tim...

In this paper, the problem of distributed optimization with nonconvex objective functions is studied by employing a network of agents. Each agent only has access to a noisy estimate on the gradient of its own objective function, and can only communicate with its immediate neighbors via a time-varying directed graph. To handle this problem, a distri...

Population structure is a well-known catalyst for the evolution of cooperation and has traditionally been considered to be static in the course of evolution. Conversely, real-world populations, such as microbiome communities and online social networks, frequently show a progression from tiny, active groups to huge, stable communities, which is insu...

In this paper, online game is studied, where at each time, a group of players aim at selfishly minimizing their own time-varying cost function simultaneously subject to time-varying coupled constraints and local feasible set constraints. Only local cost functions and local constraints are available to individual players, who can share limited infor...

The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to demographic stochasticity—that is, randomness associated with birth and death processes. In nature, individuals who are more fecund tend to have greater variance in the...

This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite-dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponentially fast consensus using a Lyapunov function consisting of a sum...

Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of temporal {\emph{continuous-time}} linear networks from a generic viewpoint, where only the zero-nonzero patterns of s...

Community structure is reported to play a critical role in ecosystem stability, which indicates the ability of a system to return to equilibrium after perturbations. However, current studies rely on the assumption that the community consists of only a single-layer structure. In practice, multi-layer structures are common in ecosystems, e.g. the dis...

Previous studies have shown that the topological properties of a complex network, such as heterogeneity and average degree, affect the evolutionary game dynamics on it. However, traditional numerical simulations are usually time-consuming and demand a lot of computational resources. In this paper, we propose the method of dynamical approximate mast...

The fact that people often have preference rankings for their partners is a distinctive aspect of human behavior. Little is known, however, about how this talent as a powerful force shapes human behavioral traits, including those which should not have been favored by selection, such as cooperation in social dilemma situations. Here we propose a dyn...

In repeated social interactions, humans often have the freedom to opt out and be absent due to unpleasant experiences or low benefits. Yet most studies on direct reciprocity neglect this option of opting out and implicitly assume that repeated interactions are compulsory. Here, we introduce a general framework of repeated optional multiplayer games...

The advent of Zero-Determinant (ZD) strategies has reshaped the study of reciprocity and cooperation in the iterated Prisoner's Dilemma games. The ramification of ZD strategies has been demonstrated through their ability to unilaterally enforce a linear relationship between their own average payoff and that of their co-player. Common practice conve...

We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We rigorously prove that the evolutionary process soon or later either enters a cycle and from then on repeats the c...

The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to noise, arising from environmental or demographic stochasticity. In nature, individuals who are more fecund tend to have greater variance in their offspring number -- so...

The advent of Zero-Determinant (ZD) strategies has reshaped the study of reciprocity and cooperation in the iterated Prisoner's Dilemma games. The ramification of ZD strategies has been demonstrated through their ability to unilaterally enforce a linear relationship between their own average payoff and that of their co-player. Common practice conve...

Several studies have confirmed the existence of zero-determinant (ZD) strategies in repeated social dilemmas since Press and Dyson's ingenious discovery of ZD strategies in iterated prisoner's dilemmas. However, less research studies evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective. Here, we use a sta...

A long-standing debate is whether social influence improves the collective wisdom of a crowd or undermines it. This paper addresses this question based on a naive learning setting in influence systems theory: in our models individuals evolve their estimates of an unknown truth according to the weighted-average opinion dynamics. A formal mathematiza...

‘Personal responsibility’, one of the basic principles of social governance, requires one to be accountable for what one does. However, personal responsibility is far from the only norm ruling human interactions, especially in social and economic activities. In many collective communities such as among enterprise colleagues and family members, one’...

In this work, we study stochastic non-cooperative games, where only noisy black-box function evaluations are available to estimate the cost function for each player. Since each player's cost function depends on both its own decision variables and its rivals' decision variables, local information needs to be exchanged through a center/network in mos...

Distributed dynamic compensators play a key role in the output consensus problem of heterogeneous nonlinear multi-agent systems. The existing distributed dynamic compensators require the compensators' information to be exchanged through communication networks, and to satisfy additional stability conditions in the controller design. This note propos...

Temporal networks provide a general framework to capture time-varying interactions of complex systems. The interevent time (IET), the time interval between two successive interactions, is a common statistic to characterize the structure of temporal networks. Previous findings support that burstiness, the IET distribution to be heavy-tailed, is ubiq...

In this paper, we investigate the interval consensus for a network of agents with flocking dynamics, where each agent imposes an interval constraint on its preferred consensus values. Specifically, we work on two different frameworks, viz., the first one that the node states are constrained in their own constraint intervals and the second one that...

Studies on the evolution of cooperation among a population of individuals are essential in evolutionary dynamics. Population structure is a key factor affecting the evolution of cooperation. Temporal networks with randomly active nodes and edges have been demonstrated to facilitate the evolution of cooperation relative to their static counterparts....

"Personal responsibility", one of the basic principles of modern law, requires one to be responsible for what he did. However, personal responsibility is far from the only norm ruling human interactions, especially in social and economic activities. In many collective communities such as among enterprise colleagues and family members, one's persona...

Since Press and Dyson's ingenious discovery of ZD (zero-determinant) strategy in the repeated Prisoner's Dilemma game, several studies have confirmed the existence of ZD strategy in repeated multiplayer social dilemmas. However, few researches study the evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective...

Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players' payoffs in games, since payoffs are jointly determined by all players. Until recently, a class of so-called zero-det...

Direct reciprocity is a well-known mechanism that could explain how cooperation emerges and prevails in an evolving population. Numerous prior researches have studied the emergence of cooperation in multiplayer games. However, most of them use numerical or experimental methods, not theoretical analysis. This lack of theoretical works on the evoluti...

In this paper, the problem of online distributed optimization with a set constraint is solved by employing a network of agents. Each agent only has access to a local objective function and set constraint, and can only communicate with its neighbours via a digraph which is not necessarily balanced. Moreover, agents do not have prior knowledge of the...

In a population of interacting individuals, the environment for interactions often changes due to individuals' behaviors, which in turn drive the evolution of individuals' behaviors. The interplay between the environment and individuals' behaviors has been demonstrated to remarkably influence the evolutionary outcomes. In reality, in highly cogniti...

In stochastic dynamic environments, team stochastic games have emerged as a versatile paradigm for studying sequential decision-making problems of fully cooperative multi-agent systems. However, the optimality of the derived policies is usually sensitive to the model parameters, which are typically unknown and required to be estimated from noisy da...

Decentralized online learning for seeking generalized Nash equilibrium (GNE) of noncooperative games in dynamic environments is studied in this paper. Each player aims at selfishly minimizing its own time-varying cost function subject to time-varying coupled constraints and local feasible set constraints. Only local cost functions and local constra...

The evolution of fairness is favored by adaptive social structures, yet it is infeasible to give precise solutions of how to adjust social ties to optimize the evolution of fairness. This study establishes linking dynamics by stochastic process for coevolutionary fairness, and introduces a key ratio between the probability of rewiring for accepting...

In this paper, the structural controllability of multi-agent networks defined over directed signed graphs is investigated, where the agents are divided into leaders and followers, and only leaders are manipulated by the external control input directly.The communication digraph contains positive and negative edges, which represent cooperative and an...

This paper studies the evolution of social power in influence networks with stubborn individuals. We formulate two models grounded on the Friedkin-Johnsen opinion dynamics and the reflected appraisal mechanism; the models are defined over issue sequences and over single issue, respectively. The key advance over the original DeGroot-Friedkin dynamic...

In this technical note, we deal with the consensus problem of multiple partial-state coupled linear systems that are neutrally stable. These systems communicate over dynamic undirected networks which change continuously and can be disconnected at any time. We develop an analysis framework from uniform complete observability theory to work out the n...

Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g...

Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g...

Network science provides a powerful methodology to study the evolutionary dynamics in the structured population, however, its current formulation of time-invariant structure does not account for the coevolutionary issue that mainly focuses on structure adaptation in response to the change in the state of nodes. Here we investigate the propagation o...

In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action set. The action sets of all players are coupled through a shared convex inequality constraint. Each player can on...

In this paper, we study the distributed generalized Nashequilibrium seeking problem of non-cooperative games in dynamicenvironments. Each player in the game aims to minimize its own time-varying cost function subject to a local action set. The action sets of allplayers are coupled through a shared convex inequality constraint. Eachplayer can only h...

Most studies on the propagation problem focus mainly on the network without antagonistic interactions. Yet generally, the information propagation is affected by the type of interaction between individuals. In this article, we study the propagation problem over a network with antagonistic interactions, modeled as a signed graph. The sign attached to...

The structure of social networks is a key determinant in fostering cooperation and other altruistic behavior among naturally selfish individuals. However, most real social interactions are temporal, being both finite in duration and spread out over time. This raises the question of whether stable cooperation can form despite an intrinsically fragme...

In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action set. The action sets of all players are coupled through a shared convex inequality constraint. Each player can on...

To promote the implementation of realistic control over various complex networks, recent work has been focusing on analyzing energy cost. Indeed, the energy cost quantifies how much effort is required to drive the system from one state to another when it is fully controllable. A fully controllable system means that the system can be driven by exter...

In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on the switching topologies is imposed, which allows them to be directed and jointly connected. We propose a novel...

Signed network can be used to effectively characterize both collaborative and antagonistic interactions among individuals in networks. In this paper, we consider a setting in which two stubborn agents compete to maximize the expected number of non-stubborn agents adopting their opinions in a signed network. Here, two stubborn agents hold two compet...

Social organizations, especially human society, rely on egalitarian social norm, which can be characterized by high levels of fairness, empathy and collective conformity. Nevertheless, the evolution of egalitarian social norm remains a conundrum, as it suffers the persistent challenge from individual self-interest. To address this issue, we constru...

Distributed dynamic compensators, also known as distributed observer, play a key role in the output consensus problem of heterogeneous nonlinear multi-agent systems. However, most existing distributed dynamic compensators require either the compensators' information to be exchanged through communication networks, or that the controller for each sub...

The existing results on controllability of multiagent systems (MASs) are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous MASs, where the agents are modeled as two types. One type is that the agents have the same high‐order dynamics, and the interconnection topologies of the information flow in different ord...

We propose an analytic model to explore the effect of interaction stochasticity on the evolution of cooperation in spatial public goods game. The results show that whether cooperation can dominate in populations crucially depends on the player's probability of opting-out. Stochastic opting-out enhances cooperation as long as the probability of opti...

This paper investigates controllability and observability of multi-agent systems, in which all the agents adopt identical general linear dynamics and the interconnection topologies are switching. For controllability, criteria are established by virtue of the switching sequence and the constructed subspace sequence, respectively. Furthermore, contro...

To promote the implementation of realistic control over various complex networks, recent work has been focusing on analyzing energy cost. Indeed, the energy cost quantifies how much effort is required to drive the system from one state to another when it is fully controllable. A fully controllable system means that the system can be driven by exter...

In this paper, the mixed equilibrium problem is solved by a multi-agent network. The objective for agents is to cooperatively find a point in a convex set, at which the sum of some local bifunctions with a free variable is non-negative. To address this problem, we propose a distributed extragradient algorithm based on a consensus strategy. By imple...

This brief investigates the controllability of switching signed networks, in which the interconnection topologies are directed, weighted and switched. First, we study the controllability from the union digraph perspective and derive a graph-theoretic sufficient condition. It is shown that a switching signed network can be controllable even if each...

Real networks are not only multi-layered yet also dynamic. The role of coordinated network evolution regarding dynamic multi-layer networks where both network and strategy evolution simultaneously show diverse interdependence by layers remains poorly addressed. Here, we propose a general and simple coevolution framework to analyze how coordination...

How rational individuals make strategic decisions when confronted with the temptation of defection is consistently a longstanding conundrum. Particularly, in a heterogeneous environment incorporating multiple decision rules, little is known about the evolutionary dynamics of networked multi-person games. To address this issue, we propose an origina...

The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continuous change in nature. To model an ever-changing environment, we develop a framework of evolutionary dynamics with stochastic game transitions, where individuals' behaviors together with...

Examining the controllability of complex networks has received much attention recently. The focus of many studies is commonly trained on whether we can steer a system from an arbitrary initial state to any final state within finite time with admissible external inputs. In order to accomplish the control at the minimum cost, we must study how much c...