Landscape Dynamics: Models for the Social Sciences

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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).