The struggle for existence occurs through the vital rates of population growth. This basic fact demonstrates the tight connection between ecology and evolution that defines the emerging field of eco-evolutionary dynamics. An effective synthesis of the interdependencies between ecology and evolution is grounded in six principles. The mechanics of evolution specifies the origin and rules governin...

This paper investigates the long-term behavior of an interacting particle system of interest in the hot topic of evolutionary game theory. Each site of the ddimensional integer lattice is occupied by a player who is characterized by one of two possible strategies. Following the traditional modeling approach of spatial games, the configuration is turned into a payoff landscape that assigns a pay...

We study potential games with continuous player sets, a class of games characterized by an externality symmetry condition arising naturally in models of network congestion. We offer a simple description of equilibria which are locally stable under a broad class of evolutionary dynamics, and prove that behavior converges to equilibrium from all initial conditions. We propose a subclass of potent...

We consider stability properties of equilibria in stochastic evolutionary dynamics. In particular, we study the stability of mixed equilibria in strategic form games. In these games, when the populations are small, all strategies may be stable. We prove that when the populations are large, the unique stable outcome of best-reply dynamics in 2 × 2 games with a unique Nash equilibrium that is com...

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. ...

This paper develops an evolutionary trade network game (TNG) that combines evolutionary game play with endogenous partner selection. Successive generations of resource-constrained buyers and sellers choose and refuse trade partners on the basis of continually updated expected payo®s. Trade partner selection takes place in accordance with a modi ̄ed Gale-Shapley matching mechanism, and trades are...

The projection dynamic is an evolutionary dynamic for population games. It is derived from a model of individual choice in which agents abandon their current strategies at rates inversely proportional to the strategies’ current levels of use. The dynamic admits a simple geometric definition, its rest points coincide with the Nash equilibria of the underlying game, and it converges globally to N...