Stability and Chaos in the Network Replicator Dynamics
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
Time: 2:30pm - 3:30pm