Dynamics with expectations.

摘要

The study of dynamics with expectations is relevant whenever the entities or "agents" comprising a complex system take into account possible future states when making decisions in the present. Goal-seeking agents form plans to achieve their ends based on their knowledge of causes, their memory of the past, their predictions for the future, as well as on their biases and their beliefs. A dynamical formulation of agent interactions requires a different approach when the behavior of the entities depends on their beliefs and knowledge as well as on the rules governing the evolution of the system. The agents' predictions for the future must enter explicitly into the dynamical rules governing the evolution of the system.; This thesis examines the behavior of two dynamical systems in particular. The first, referred to as a computational ecosystem, is composed of a collection of processes, or agents, that compete among themselves for limited resources. The analytical tools of nonlinear dynamics and the modern-day aid of numerical integration via computer are employed to map out the behavioral regimes of the system first when the external environment changes over time, and second when the individual agents incorporate expectations about the future into their decisions.; In the second part, a system composed of interacting agents whose individual goals conflict with the overall good of the group is studied both analytically and through computer simulations. It is shown how spontaneous cooperation can be achieved if the agents take into account their expectations about the future when making their choices in the present. Further, the system can remain trapped in a metastable state for long periods of time; eventually, rare large fluctuations occur due to uncertain information that can cause a transition to the global equilibrium. The effects of ultrametric group structure and diversity on the dynamics of cooperation are also elucidated. Specifically, it is seen how the interplay between evolving group structure and the number of agents cooperating introduces new dynamical pathways to cooperation.