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。这里的当前状态是玩家在策略空间上的分布。收益函数，称为适应性景观，取决于当前状态。当每个玩家在连续的时间内调整自己的策略以获得更高的收益时，分配也会发生变化，所以适应性景观也会发生变化，玩家也会再次调整。这一调整过程定义了一个非线性偏微分方程，即在当前状态的无限维空间上的一个具有非平凡动力学的动力系统。将开发软件，将基于智能体的建模方法扩展到无限维动态系统。结合纯数学、经济学和计算机科学的方法，该项目将确定适应性景观和收益函数的属性，从而得出动态的重要定性特征。这些特征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。数学和计算机科学的新方法为社会科学和行为科学中的数学建模提供了巨大的机会。这个项目就是针对这一前沿地区的。通过示范应用、可重用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研究社会科学的新方法。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，对金融市场的深入了解将导致更好的市场运作和更好的政策。该奖项是2004财政年度数学科学优先领域数学社会和行为科学特别竞赛的一部分。

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).