This brief discusses evolutionary game theory as a powerful and unified
mathematical tool to study evolution of collective behaviours. It summarises
some of my recent research directions using evolutionary game theory methods,
which include i) the analysis of statistical properties of the number of
(stable) equilibria in a random evolutionary game, and ii) the modelling of
safety behaviours' evolution and the risk posed by advanced Artificial
Intelligence technologies in a technology development race. Finally, it
includes an outlook and some suggestions for future researchers.

本文讨论了进化博弈理论作为一种强大而统一的数学工具，用于研究集体行为的演化，总结了作者最近通过进化博弈理论方法所涉及的一些研究方向，包括：i）随机进化博弈中（稳定）均衡数量的统计性质分析，以及 ii）在技术发展竞赛中建模安全行为的演化及先进人工智能技术带来的风险。最后，对未来研究者提出了展望和一些建议。

进化博弈论：进化与集体行为的数学

Evolutionary game theory: the mathematics of evolution and collective  behaviours

The mechanisms of emergence and evolution of collective behaviours in
dynamical Multi-Agent Systems (MAS) of multiple interacting agents, with
diverse behavioral strategies in co-presence, have been undergoing mathematical
study via Evolutionary Game Theory (EGT). Their systematic study also resorts
to agent-based modelling and simulation (ABM) techniques, thus enabling the
study of aforesaid mechanisms under a variety of conditions, parameters, and
alternative virtual games. This paper summarises some main research directions
and challenges tackled in our group, using methods from EGT and ABM. These
range from the introduction of cognitive and emotional mechanisms into agents'
implementation in an evolving MAS, to the cost-efficient interference for
promoting prosocial behaviours in complex networks, to the regulation and
governance of AI safety development ecology, and to the equilibrium analysis of
random evolutionary multi-player games. This brief aims to sensitize the reader
to EGT based issues, results and prospects, which are accruing in importance
for the modeling of minds with machines and the engineering of prosocial
behaviours in dynamical MAS, with impact on our understanding of the emergence
and stability of collective behaviours. In all cases, important open problems
in MAS research as viewed or prioritised by the group are described.

本文通过进化博弈理论和基于代理的建模和仿真技术，对在多智能体系统中通过多个交互者的存在和互动的多种行为策略下涌现和演变的集体行为机制的主要研究方向和挑战进行了总结，包括将认知和情感机制引入智能体的实现、在复杂网络中促进亲社会行为的成本效益干预、AI 安全发展生态的监管和治理以及随机演化多人游戏的平衡分析。总之，本文描述了该小组视图或优先考虑的 MAS 研究中的重要开放问题。

多智能体系统中的演化博弈理论对新兴行为的理解

Understanding Emergent Behaviours in Multi-Agent Systems with Evolutionary Game Theory

Complex networks have become the main paradigm for modelling the dynamics of
interacting systems. However, networks are intrinsically limited to describing
pairwise interactions, whereas real-world systems are often characterized by
higher-order interactions involving groups of three or more units. Higher-order
structures, such as hypergraphs and simplicial complexes, are therefore a
better tool to map the real organization of many social, biological and
man-made systems. Here, we highlight recent evidence of collective behaviours
induced by higher-order interactions, and we outline three key challenges for
the physics of higher-order systems.

用复杂网络建模相互作用系统的动态已成为主要范例，但现实系统的高阶相互作用往往涉及三个或更多单元的团体，因此更好的工具是高阶结构，如超图和单形复合体，本文概述了高阶相互作用引发的集体行为及高阶系统物理面临的三个关键挑战。