Landscape Dynamics: Models for the Social Sciences

该项目研究了一类新的复杂社会系统模型，基于具有连续策略空间的进化博弈。 这里的当前状态是参与者在策略空间上的分布。 回报函数，称为适应性景观，取决于当前状态。 随着每个参与者不断调整策略，以获得更高的收益，分布发生了变化，因此适应性景观发生了变化，参与者再次调整。 这个调整过程定义了一个非线性偏微分方程，也就是说，一个动力系统的无限维空间的当前状态，与非平凡的动态。 软件将开发，扩展代理基于建模方法的无限维动态系统。 结合纯数学，经济学和计算机科学的方法，该项目将确定自适应景观和回报函数的属性，从而导致动态的重要定性特征。 这些功能将在金融市场的示范模型中实现。 来自其他社会科学的问题，例如，政治，也将被考虑。来自数学和计算机科学的新方法为社会和行为科学的数学建模提供了一个很好的机会。 该项目的目标是这一前沿。 通过示范性的应用程序、可重复使用的软件和在国际会议上的计算机动画演示，该项目将招募年轻学者进行社会科学研究的新方法。 这些新方法似乎是模拟和研究重大社会问题的理想方法。 例如，对金融市场的更深入理解将导致更好的市场运作和更好的政策。 该奖项是作为2004财政年度数学科学优先领域数学社会和行为科学（MSBS）特别竞赛的一部分得到支持的。

The project studies a new class of models for complex social systems, based on evolutionary games with a continuous space of strategies. Here the current state is the distribution of players on the space of strategies. The payoff function, called the adaptive landscape, depends on the current state. As each player adjusts her strategy in continuous time towards higher payoff, the distribution changes, so the adaptive landscape changes, and the players adjust again. This adjustment process defines a nonlinear partial differential equation, that is, a dynamical system on the infinite-dimensional space of current states, with nontrivial dynamics. Software will be developed, extending agent based modeling methods to infinite-dimensional dynamical systems. Combining methods from pure mathematics, economics, and computer science, the project will identify properties of the adaptive landscape and payoff function leading to significant qualitative features of the dynamics. These features will be implemented in an exemplary model of financial markets. Problems from other social sciences, for example, politics, also will be considered.New methods from mathematics and computer science provide a great opportunity for mathematical modeling in the social and behavioral sciences. The project is aimed at this frontier. With exemplary applications, reusable software, and computer animated presentations at international conferences, the project will recruit young scholars to new methods of social science research. The new methods seem ideal for the simulation and study of major social problems. For example, a deeper understanding of financial markets will lead to better functioning markets and better policy. This award was supported as part of the Fiscal Year 2004 Mathematical Sciences priority area special competition on Mathematical Social and Behavioral Sciences (MSBS).