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Register a new userHerd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach
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The recent COVID-19 pandemic has led to an increasing interest in the modeling and analysis of infectious diseases. The pandemic has made a significant impact on the way we behave and interact in our daily life. The past year has witnessed a strong interplay between human behaviors and epidemic spreading. In this paper, we propose an evolutionary game-theoretic framework to study the coupled evolutions of herd behaviors and epidemics. Our framework extends the classical degree-based mean-field epidemic model over complex networks by coupling it with the evolutionary game dynamics. The statistically equivalent individuals in a population choose their social activity intensities based on the fitness or the payoffs that depend on the state of the epidemics. Meanwhile, the spreading of the infectious disease over the complex network is reciprocally influenced by the players social activities. We analyze the coupled dynamics by studying the stationary properties of the epidemic for a given herd behavior and the structural properties of the game for a given epidemic process. The decisions of the herd turn out to be strategic substitutes. We formulate an equivalent finite-player game and an equivalent network to represent the interactions among the finite populations. We develop structure-preserving approximation techniques to study time-dependent properties of the joint evolution of the behavioral and epidemic dynamics. The resemblance between the simulated coupled dynamics and the real COVID-19 statistics in the numerical experiments indicates the predictive power of our framework.
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Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of `topological stability to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context.
Regret has been established as a foundational concept in online learning, and likewise has important applications in the analysis of learning dynamics in games. Regret quantifies the difference between a learners performance against a baseline in hindsight. It is well-known that regret-minimizing algorithms converge to certain classes of equilibria in games; however, traditional forms of regret used in game theory predominantly consider baselines that permit deviations to deterministic actions or strategies. In this paper, we revisit our understanding of regret from the perspective of deviations over partitions of the full emph{mixed} strategy space (i.e., probability distributions over pure strategies), under the lens of the previously-established $Phi$-regret framework, which provides a continuum of stronger regret measures. Importantly, $Phi$-regret enables learning agents to consider deviations from and to mixed strategies, generalizing several existing notions of regret such as external, internal, and swap regret, and thus broadening the insights gained from regret-based analysis of learning algorithms. We prove here that the well-studied evolutionary learning algorithm of replicator dynamics (RD) seamlessly minimizes the strongest possible form of $Phi$-regret in generic $2 times 2$ games, without any modification of the underlying algorithm itself. We subsequently conduct experiments validating our theoretical results in a suite of 144 $2 times 2$ games wherein RD exhibits a diverse set of behaviors. We conclude by providing empirical evidence of $Phi$-regret minimization by RD in some larger games, hinting at further opportunity for $Phi$-regret based study of such algorithms from both a theoretical and empirical perspective.
We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be represented as a Markov process with substantially reduced number of states with explicitly computable probabilities. For any payoff, the finiteness of the number of states is proved. Interesting features of an extensive random variable, called aggregated demand, viz. its strong inhomogeneity and presence of patterns in time, can be easily interpreted. Using Markov theory and quenched disorder approach, we can explain important macroscopic characteristics of the game: behavior of variance per capita and predictability of the aggregated demand. We prove that in case of linear payoff many attractors in the state space are possible.
This paper is concerned with a family of Reaction-Diffusion systems that we introduced in [15], and that generalizes the SIR type models from epidemiology. Such systems are now also used to describe collective behaviors.In this paper, we propose a modeling approach for these apparently diverse phenomena through the example of the dynamics of social unrest. The model involves two quantities: the level of social unrest, or more generally activity, u, and a field of social tension v, which play asymmetric roles. We think of u as the actually observed or explicit quantity while v is an ambiant, sometimes implicit, field of susceptibility that modulates the dynamics of u. In this article, we explore this class of model and prove several theoretical results based on the framework developed in [15], of which the present work is a companion paper. We particularly emphasize here two subclasses of systems: tension inhibiting and tension enhancing. These are characterized by respectively a negative or a positivefeedback of the unrest on social tension. We establish several properties for these classes and also study some extensions. In particular, we describe the behavior of the system following an initial surge of activity. We show that the model can give rise to many diverse qualitative dynamics. We also provide a variety of numerical simulations to illustrate our results and to reveal further properties and open questions.
We investigate the herd behavior of returns for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution $P(R)$ of returns $R$ satisfies the power-law behavior $P(R) simeq R^{-beta}$ with the exponents $ beta=3.11$(the time interval $tau=$ one minute) and 3.36($tau=$ one day). The informational cascade regime appears in the herding parameter $Hge 2.33$ at $tau=$ one minute, while it occurs no herding at $tau=$ one day. Especially, we find that the distribution of normalized returns shows a crossover to a Gaussian distribution at one time step $Delta t=1$ day.
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