Stability and Chaos in the Network Replicator Dynamics

Logic, Games, and Graphs Seminar

Meeting Details

For more information about this meeting, contact Stephanie Zerby, Andrew Belmonte, Jan Reimann, Linda Westrick, Kristin Berrigan, Christopher Griffin.

Speaker: Christopher Griffin, Applied Research Laboratory, Penn State University

Abstract: We provide a simple motivation and derivation of an evolution equation for game theory dynamics on a network (the network replicator), and completely characterize its fixed points on arbitrary graph structures for 2 X 2 symmetric games. We show that the N-dimensional phase portrait admits no circulation, and consequently complex dynamics cannot emerge for 2 X 2 games, independent of underlying network structure. Our results rely on a surprising combinatoric property of independent vertex sets in graphs. By contrast, we show that chaotic behavior emerges in the network replicator on the three cycle, when playing Rock-Paper-Scissors. These dynamics satisfy Liouville's theorem and admit a generalized Hamiltonian formulation; we demonstrate the existence of foliated manifolds in phase space, coexistant with Poincare tangles.

Room Reservation Information

Room Number: 114 McAllister

Date: 09/04/2019

Time: 2:30pm - 3:30pm