Information and Randomness in Dynamic Games

合作构成了从蚂蚁到人类的所有成功的社会物种的基石。然而，生物和社会系统中出现的合作和公平是一个巨大的谜团。当自然选择本质上是不公平的时，人类怎么会经常寻求公平的结果呢？进化博弈论是一种捕捉决策动态的数学框架，它提供了一些答案。这一理论在经济学、军事战略和生物学中都有应用。这个项目开发了更广泛的分布式社会学习和新兴群体动力学理论，将进化博弈论的各个方面与统计力学和机器学习相结合，以解释合作、公平和其他不适合传统方法的社会动力学的出现。所开发的数学框架可以应用于进化心理学和人工智能中的问题。特别是，一些结果可能有助于让政策制定者了解不同社会中不同行为的起源。研究生从事该项目的研究。该项目开发了一个关于分布式社会学习和复杂系统中的紧急群体现象的连贯理论，将进化博弈论的各个方面与统计力学和机器学习相结合。以公共物品博弈和最后通牒博弈为基础，研究了有限种群的进化动力学，这些种群的相遇是用简单的参数化规则和随机相互作用来描述的。这些演化系统的一个方面是收敛到非Nash不动点，包括对初始条件和实现的样本路径的敏感依赖。利用拓扑数据分析技术对这些固定点的吸引盆地进行了表征。利用统计力学的观点，导出了势布居数不动点的分布，并与动力系统中的信息量有关；在这里，空间相互作用的速度起着类似于相互作用粒子气体中的温度的作用。对这些动力系统中可能的平衡态进行了分类，并给出了相应的平衡点分布。量化相互作用或移动的代理之间的信息传输是该项目的另一个目标。确定商品化信息对均衡分布和收敛的影响，无论是有益的还是有害的，也是如此。研究生从事该项目的研究。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Cooperation forms the cornerstone for all successful social species from ants to humans. Yet the emergence of cooperation and fairness in biological and social systems is one of the great puzzles. How did it arise that humans often seek fair outcomes, when natural selection is inherently unfair? Evolutionary game theory, a mathematical framework to capture the dynamics of decisions, provides some answers. The theory finds applications in economics, military strategy, and biology. This project develops a more extensive theory of distributed social learning and emergent group dynamics, combining aspects of evolutionary game theory with statistical mechanics and machine learning to explain the emergence of cooperation, fairness, and other social dynamics that do not fit well into traditional approaches. The mathematical framework developed can be applied to problems in evolutionary psychology and artificial intelligence. In particular, some results may help to inform policy makers on the origins of differing behaviors in different societies. Graduate students are engaged in the research of the project.This project develops a coherent theory of distributed social learning and emergent group phenomena in complex systems, merging aspects of evolutionary game theory with statistical mechanics and machine learning. Using public goods games and ultimatum style games as a foundation, the investigators study the evolutionary dynamics of finite populations whose encounters are described in game-theoretic terms using simple parameterized rules and random interactions. An aspect of these evolutionary systems is convergence to non-Nash fixed points, including a sensitive dependence on initial conditions and sample paths realized. Basins of attraction for these fixed points are characterized using techniques from topological data analysis. Using insights from statistical mechanics, the distributions of potential population fixed points are derived and related to the information content in the dynamical system; here the speed of spatial interactions plays a role analogous to that of temperature in a gas of interacting particles. Possible equilibrium states in these dynamical systems are categorized, along with the corresponding equilibrium point distributions. Quantifying information transfer among interacting or moving agents is an additional goal of the project. So also is determining the impact of commoditized information, whether beneficial or harmful, on equilibrium distributions and convergence. Graduate students are engaged in the research of the project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.