In the context of natural disasters, human responses inevitably intertwine
with natural factors. The COVID-19 pandemic, as a significant stress factor,
has brought to light profound variations among different countries in terms of
their adaptive dynamics in addressing the spread of infection outbreaks across
different regions. This emphasizes the crucial role of cultural characteristics
in natural disaster analysis. The theoretical understanding of large-scale
epidemics primarily relies on mean-field kinetic models. However, conventional
SIR-like models failed to fully explain the observed phenomena at the onset of
the COVID-19 outbreak. These phenomena included the unexpected cessation of
exponential growth, the reaching of plateaus, and the occurrence of multi-wave
dynamics. In situations where an outbreak of a highly virulent and unfamiliar
infection arises, it becomes crucial to respond swiftly at a non-medical level
to mitigate the negative socio-economic impact. Here we present a theoretical
examination of the first wave of the epidemic based on a simple SIRSS model
(SIR with Social Stress). We conduct an analysis of the socio-cultural features
of na\"ive population behaviors across various countries worldwide. The unique
characteristics of each country/territory are encapsulated in only a few
constants within our model, derived from the fitted COVID-19 statistics. These
constants also reflect the societal response dynamics to the external stress
factor, underscoring the importance of studying the mutual behavior of humanity
and natural factors during global social disasters. Based on these distinctive
characteristics of specific regions, local authorities can optimize their
strategies to effectively combat epidemics until vaccines are developed.

在自然灾害的背景下，人类的反应不可避免地与自然因素交织在一起。COVID-19 大流行作为一个重要的压力因素，揭示了不同国家在应对不同地区感染爆发蔓延方面适应动力的深刻差异，突显了文化特征在自然灾害分析中的关键作用。

探讨社会压力对 COVID-19 的适应动态的影响：揭示面对流行病的未知人群行为

Exploring the impact of social stress on the adaptive dynamics of  COVID-19: Typing the behavior of naïve populations faced with epidemics

We study the query complexity of approximate notions of Nash equilibrium in
games with a large number of players $n$. Our main result states that for
$n$-player binary-action games and for constant $\varepsilon$, the query
complexity of an $\varepsilon$-well-supported Nash equilibrium is exponential
in $n$. One of the consequences of this result is an exponential lower bound on
the rate of convergence of adaptive dynamics to approxiamte Nash equilibrium.

在大量玩家的二元行动博弈中，查询复杂度与 ε- 支持纳什均衡的关系是指数级的，并导致自适应动态收敛到近似纳什均衡的速度指数级下降。

近似纳什均衡的查询复杂度

Query Complexity of Approximate Nash Equilibria

Except for special classes of games, there is no systematic framework for
analyzing the dynamical properties of multi-agent strategic interactions.
Potential games are one such special but restrictive class of games that allow
for tractable dynamic analysis. Intuitively, games that are "close" to a
potential game should share similar properties. In this paper, we formalize and
develop this idea by quantifying to what extent the dynamic features of
potential games extend to "near-potential" games. We study convergence of three
commonly studied classes of adaptive dynamics: discrete-time better/best
response, logit response, and discrete-time fictitious play dynamics. For
better/best response dynamics, we focus on the evolution of the sequence of
pure strategy profiles and show that this sequence converges to a (pure)
approximate equilibrium set, whose size is a function of the "distance" from a
close potential game. We then study logit response dynamics and provide a
characterization of the stationary distribution of this update rule in terms of
the distance of the game from a close potential game and the corresponding
potential function. We further show that the stochastically stable strategy
profiles are pure approximate equilibria. Finally, we turn attention to
fictitious play, and establish that the sequence of empirical frequencies of
player actions converges to a neighborhood of (mixed) equilibria of the game,
where the size of the neighborhood increases with distance of the game to a
potential game. Thus, our results suggest that games that are close to a
potential game inherit the dynamical properties of potential games. Since a
close potential game to a given game can be found by solving a convex
optimization problem, our approach also provides a systematic framework for
studying convergence behavior of adaptive learning dynamics in arbitrary finite
strategic form games.

本文量化了潜在博弈动态特征的传播，证明了接近潜在博弈的游戏在学习动态上具有类似的特性，同时提出了一个系统的框架来研究有限策略博弈中适应性学习动态的收敛行为。