Information and Randomness in Dynamic Games

从蚂蚁到人类，合作是所有成功的社会物种的基石。 然而，生物和社会系统中合作与公平的出现是最大的难题之一。 当自然选择本质上是不公平的时候，人类是如何经常寻求公平的结果的？ 进化博弈论，一个捕捉决策动态的数学框架，提供了一些答案。 该理论在经济学、军事战略和生物学中得到应用。 该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。 开发的数学框架可以应用于进化心理学和人工智能的问题。 特别是，一些结果可能有助于告知政策制定者在不同的社会中不同行为的起源。 研究生参与了该项目的研究。该项目将进化博弈论与统计力学和机器学习相结合，发展了复杂系统中分布式社会学习和涌现群体现象的连贯理论。 以公共产品博弈和最后通牒式博弈为基础，研究人员研究了有限种群的进化动力学，这些种群的遭遇是使用简单的参数化规则和随机相互作用在博弈论术语中描述的。 这些进化系统的一个方面是收敛到非纳什不动点，包括对初始条件和实现的样本路径的敏感依赖。 这些固定点的吸引力盆地的特点是使用拓扑数据分析技术。 利用统计力学的见解，潜在的人口不动点的分布推导和相关的动力系统中的信息内容;在这里，空间相互作用的速度起着类似于相互作用粒子的气体中的温度的作用。 在这些动力学系统中可能的平衡状态进行分类，沿着，与相应的平衡点分布。 量化交互或移动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趋同的影响，无论是有益的还是有害的，也是如此。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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.