We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between two-player and multi-player games. In particular, we construct examples which exhibit a novel behavior not found in two-player games.

This paper studies how a matching rule affects the evolution of fairness in an ultimatum mini game. Gale et al. [1995] show that only selfish behaviour survives in the deterministic replicator dynamics under the random matching rule. In contrast, this paper shows that, under an assortative matching rule, the fair behaviour may survive at an asymptotically stable state.

Many real-world scenarios can be modelled as multi-agent systems, where multiple autonomous decision makers interact in a single environment. The complex and dynamic nature of such interactions prevents hand-crafting solutions for all possible scenarios, hence learning is crucial. Studying the dynamics of multi-agent learning is imperative in selecting and tuning the right learning algorithm fo...

Evolutionary games have been introduced by Maynard Smith and Price [1973] in the early 70’s with the aim to study the stability of populations in time. In the general model, a population consists of finitely many different types that interact randomly with each other, where each interaction leads to fitness payoffs for each of the types involved. Consequently, the population distribution over t...

Knowledge Discovery and Data Mining A Replicator Dynamics Approach to Collective Feature Engineering in Random Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Khaled Fawgreh, Mohamed Medhat Gaber and Eyad Elyan A Directed Acyclic Graph Based Approach to Multi-Class Ensemble Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Esra’a Alshda...

There are many different models—both continuous and discrete— used to describe gene mutation fixation. In particular, the Moran process, the Kimura equation and the replicator dynamics are all well known models, that might lead to different conclusions. We present a discussion of a unified framework to embrace all these models, in the large population regime.

Standard oneand two-population models for evolutionary games are the limit cases of a uniparametric family combining intraand intergroup interactions. Our setup interpolates between both extremes with a coupling parameter κ. For the example of the hawk-dove game, we analyze the replicator dynamics of the coupled model. We confirm the existence of a bifurcation in the dynamics of the system and ...