Information and Randomness in Dynamic Games

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.