On differences between fractional and integer order differential equations for dynamical games

Abstract

We argue that fractional order (FO) differential equations are more suitable to model complex adaptive systems (CAS). Hence they are applied in replicator equations for non-cooperative game. Rock-Scissors-Paper game is discussed. It is known that its integer order model does not have a stable equilibrium. Its fractional order model is shown to have a locally asymptotically stable internal solution. A FO asymmetric game is shown to have a locally asymptotically stable internal solution. This is not the case for its integer order counterpart.