This paper introduces a new model, i.e. state-coupled replicator dynamics, expanding the link between evolutionary game theory and multiagent reinforcement learning to multistate games. More precisely, it extends and improves previous work on piecewise replicator dynamics, a combination of replicators and piecewise models. The contributions of the paper are twofold. One, we identify and explain...

We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be selected in large populations. The expe...

This paper extends the Adaptively Rational Equilibrium Dynamics (ARED) of (Brock and Hommes 1997) by introducing a generalized version of the replicator dynamic of (Sethi and Franke 1995). The Replicator Equilibrium Dynamics (RED) couples the price dynamics of a cobweb model with predictor selection governed by an evolutionary replicator dynamic. We show that the RED supports the main conclusio...

In signaling games the replicator dynamics does not almost always converge to states of perfect communication. A significant portion of the state space converges to components of Nash equilibria that characterize states of partial communication. Since these components consist of non-hyperbolic rest points, the significance of this result will depend on the dynamic behavior of specific perturbat...

The replicator equation is one of the fundamental tools to study evolutionary dynamics in well-mixed populations. This paper contributes to the literature on evolutionary graph theory, providing a version of the replicator equation for a family of connected networks with communities, where nodes in the same community have the same degree. This replicator equation is applied to the study of diff...

Recent work on costly signaling games has identified new Nash equilibria in addition to the standard costly signaling equilibrium as a possible explanation for signaling behavior. These so-called hybrid equilibria are Liapunov stable, but not asymptotically stable for the replicator dynamics. Since some eigenvalues of the hybrid equilibria have zero real part, this result is not structurally st...

A class of autocatalytic reaction networks based on template-dependent replication and specific catalysis is considered. Trimolecular "elementary steps" of simple replicator dynamics are resolved into two consecutive irreversible reactions. The extreme cases, competition for common resources and hypercycle-like cooperative feedback, were analyzed in some detail. Although the dynamics of the ext...

We investigate whether replicator dynamics justify “survival of the fittest” when players inherit pure strategies, mixed strategies, or rules for choosing strategies. A strategy that never is a best reply can survive replicator dynamics if only pure strategies are heritable, but only rationalizable strategies survive if mixed strategies are heritable. Now suppose agents can inherit the rule of ...

Replicator equations have been studied for three decades as a generic dynamical system modelling replication processes. Here we show how they arise naturally in models of self-replicating polymers and discuss some of their basic properties. We then concentrate on a minimal dynamic model of a protocell by coupling replicating polymers with a growing membrane.

Deterministic evolutionary dynamics for games first appeared in the mathematical biology literature, where Taylor and Jonker (1978) introduced the replicator dynamic to provide an explicitly dynamic foundation for the static evolutionary stability concept of Maynard Smith and Price (1973) (see the entry on “Evolutionarily Stable Strategies” in this dictionary). But one can find precursors to th...