Assignment flows are smooth dynamical systems for data labeling on graphs. Although they exhibit structural similarities with the well-studied class of replicator dynamics, it is nontrivial to apply existing tools their analysis. We propose an embedding underlying assignment manifold into interior a single probability simplex. Under this embedding, large pushed much higher-dimensional dynamics....

Evolutionary conflict between the sexes has been studied in various taxa and in various contexts. When the sexes are in conflict over mating rates, natural selection favors both males that induce higher mating rates and females that are more successful at resisting mating attempts. Such sexual conflict may result in an escalating coevolutionary arms race between males and females. In this artic...

The public goods game represents a straightforward generalization of the prisoner's dilemma to an arbitrary number of players. Since the dominant strategy is to defect, both classical and evolutionary game theory predict the asocial outcome that no player contributes to the public goods. In contrast to the compulsory public goods game, optional participation provides a natural way to avoid dead...

In this thesis we establish a theory of evolutionary dynamics that accounts for the following requirements. 1. The evolutionary process is considered in a coevolutionary context. 2. The theory describes the full dynamics of the coevolutionary process. 3. The coevolutionary dynamics are derived from the underlying population dynamics. 4. The theory accounts for the stochastic aspects of the evol...

where K is the set of pure strategies, ∆ = ∆(K) is the set of mixed strategies (the simplex on K), e is the k unit vector in ∆, xt ∈ ∆ is the composition of the population at time t with x k t denoting the frequency of strategy k. It was introduced by Taylor and Jonker [25] as the basic selection dynamics for the evolutionary games of Maynard Smith [20], see Hofbauer and Sigmund [16] for a summ...

We study adaptive dynamics in games where players abandon the population at a given rate and are replaced by naive players characterized by a prior distribution over the admitted strategies. We demonstrate how such a process leads macroscopically to a variant of the replicator equation, with an additional term accounting for player turnover. We study how Nash equilibria and the dynamics of the ...

This short note proposes some ideas for considering evolutionary game theory in the area of membrane computing.

There are games with a unique Nash equilibrium but such that, for almost all initial conditions, all strategies in the support of this equilibrium are eliminated by the replicator dynamics and the bestreply dynamics. MSC classification. Primary: 91A22 ; Secondary: 34A34, 34A60.

Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe co-evolution of strategic actions a population individuals and state surrounding environment; correspondingly range interesting dynamic behaviors have reported. In this paper, we provide new theoretical insight such discuss control options. Instead standard replicator dynam...

This paper investigates the properties of the most common form of reinforcement learning (the “basic model” of Erev and Roth, American Economic Review, 88, 848-881, 1998). Stochastic approximation theory has been used to analyse the local stability of fixed points under this learning process. However, as we show, when such points are on the boundary of the state space, for example, pure strateg...