We begin these lecture notes by a crash course in game theory. In particular, we introduce a fundamental notion of a Nash equilibrium. To address the problem of the equilibrium selection in games with multiple equilibria, we review basic properties of the deterministic replicator dynamics and stochastic dynamics of finite populations. We show the almost global asymptotic stability of an efficie...

Swarm intelligence has been successfully applied in various domains, e.g., path planning, resource allocation and data mining. Despite its wide use, a theoretical framework in which the behavior of swarm intelligence can be formally understood is still lacking. This article starts by formally deriving the evolutionary dynamics of ant colony optimization, an important swarm intelligence algorith...

The application of reinforcement learning algorithms to multiagent domains may cause complex non-convergent dynamics. The replicator dynamics, commonly used in evolutionary game theory, proved to be effective for modeling the learning dynamics in normal form games. Nonetheless, it is often interesting to study the robustness of the learning dynamics when either learning or structural parameters...

A replicator equation with mutation processes is studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the attractors. A mutation introduces some new aspects: the emergence of structurally stable attractors, and chaotic itinerant behavior. In addition, it is reported that a neutr...

We consider the general properties of the replicator dynamical system from the standpoint of its evolution and stability. Vector field analysis as well as spectral properties of such system has been studied. Lyaponuv function for investigation of system evolution has been proposed. The generalization of the replicator dynamics for the case of multi-agent systems has been introduced. We propose ...

Evolutionary game-theoretic models and, in particular, the so-called replicator equations have recently proven to be remarkably effective at approximately solving the maximum clique and related problems. The approach is centered around a classic result from graph theory that formulates the maximum clique problem as a standard (continuous) quadratic program and exploits the dynamical properties ...

In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell proliferation is governed by a non-negative, unimodal, symmetric response function f (h), where the field h summarizes the effect of the network on a single clone. We show that by transforming into ...

In this paper we focus on agent society and its indirect control. For the purpose we deal with the norm game as a material and introduce replicator dynamics (RD) of norm game. The norm game was introduced by R. Axelrod to explain how norm collapse [1]. We reformulate the norm game as a weak coupling model between two 1 dimensional RD. The one represents population dynamics of alternatives {C,D}...