This note shows, by means of two simple, three-strategy games, the existence of stable periodic orbits and of multiple, interior steady states in a smooth version of the Best Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, occur under the Logit Dynamics, even for three strategy games. We also sh...

It has been demonstrated how random subspaces can be used to create a Diversified Random Forest, which in turn can lead to better performance in terms of predictive accuracy. Motivated by the fact that each subsforest is built using a set of features that can overlap with those sets of features in other subforests, we hypothesise that using Replicator Dynamics can perform a collective feature e...

In this paper, a well-known evolutionary dynamics, replicator dynamics, is used to model the dynamics of an immune network. A doubly symmetric game is associated to an immune network by this model, which implies some optimal behavior throughout time under replicator dynamics. Stability of an immune network is guaranteed by such dynamics. Two types of immune networks were modeled. In addition, a...

This paper presents the dynamics of multi-agent reinforcement learning in multiple state problems. We extend previous work that formally modelled the relation between reinforcement learning agents and replicator dynamics in stateless multi-agent games. More precisely, in this work we use a combination of replicator dynamics and switching dynamics to model multi-agent learning automata in multi-...

We investigate the relevance of application of game theory to the field of wireless ad-hoc networks. We give distributed algorithms for routing and multihoming in wireless ad-hoc networks. We propose a distributed routing scheme for a broad class of wireless ad-hoc networks which converges (in the Cesaro sense) to the set of Cesaro-Wardrop equilibria. Convergence is established by formulating a...

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly ...