Evolutionary branching points are a paradigmatic feature of adaptive dynamics, because they are potential starting points for adaptive diversification. The antithesis to evolutionary branching points are continuously stable strategies (CSS's), which are convergent stable and evolutionarily stable equilibrium points of the adaptive dynamics and hence are thought to represent endpoints of adaptiv...

In this paper we study the notion of the Evolutionary Stable Strategies (ESS) in evolutionary games and we demonstrate their qualitative difference from the Nash Equilibria, by showing that a random evolutionary game has on average exponentially less number of ESS than the number of Nash Equilibria in the underlying symmetric 2-person game with random payoffs.

Evolutionary stable strategies (ESSs) are often used to explain the behaviors of individuals and species. The analysis of ESSs determines which, if any, combinations of behaviors cannot be invaded by alternative strategies. However, two of the assumptions required to generate ESSs, an infinite population and payoffs described only on the average, are not particularly realistic in natural situat...

Currently, many socially responsible governments adopt economic incentives and deterrents to manage environmental impacts of electricity suppliers. Considering the Stackelberg leadership of the government, the government’s role in the competition of power plants in an electricity market is investigated. A one-population evolutionary game model of power plants is developed to study how their pro...

The analysis of models of evolutionary games requires explicit consideration of both evolutionary game rules and mutants which infinitesimally break these rules. For example, the Scotch Auction is an evolutionary game which lacks both a rule-obeying evolutionarily stable strategy and an asymptotically stable polymorphism of rule-obeying strategies. However, an infinitesimal rule-breaking, or ch...

ABSTRACT. An important question in the study of the evolution of dispersal is what kind of dispersal strategies are evolutionary stable. This work is motivated by recent work of Cosner et al. [9], in which they introduced a class of ideal free dispersal kernels and found conditions suggesting that they determine evolutionarily stable dispersal strategies. The goals of this paper are to introduc...

Game theory has been successfully applied in biology as a method for studying evolution. However, biologists approached game theory in a different way as economists have done. In the introduction to his influential book, John Maynard Smith (1982) states the differences between evolutionary game theory —the application of game theory to biology— and the traditional economic approach to game theo...