Computational Science and Engineering, UC Davis
Speaker: James Crutchfield
I will show how to model multiagent systems using dynamical systems theory by deriving a class of macroscopic differential equations that describe mutual adaptation in agent collectives, starting from a discrete-time stochastic (microscopic) model. The resulting dynamical systems show that the agents’ adaptation is a dynamic balance between optimization of actions that achieve the highest rewards (exploitation) and randomization that chooses locally suboptimal, but novel actions (exploration). It turns out that, although individual agents interact with their environment and other agents in a purely self-interested way without sharing knowledge and ignorant of a context larger than immediate interaction, a strategic dynamic emerges naturally between agents. Under suitable assumptions, the strategic interactions can be interpreted as a game. Overall, though, the emergent strategies are determined by environment-mediated interactions and agents’ local reinforcement schemes and so are not amenable to game-theoretic techniques. Application to several familiar, explicitly game-theoretic interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors, including stable limit cycles, quasiperiodicity, intermittency, and deterministic chaos. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in multiagent systems.
(Source: YouTube | Bill Broadley)