Related papers: Mixing times in evolutionary game dynamics
Game dynamics in which three or more strategies are cyclically competitive, as represented by the rock-scissors-paper game, have attracted practical and theoretical interests. In evolutionary dynamics, cyclic competition results in…
The paper deals with the problem of long-time asymptotic behaviour of solutions for classes of ODEs and PDEs, perturbed by stationary noises. The latter are not assumed to be $\delta$-correlated in time, so that the evolution in question is…
We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
Studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics. In the former case, individuals imitate the strategy of a more successful peer.…
We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…
We consider games of strategic substitutes and strategic complements on networks. We introduce two different evolutionary dynamics in order to refine their multiplicity of equilibria, and we analyse the system through a mean field approach.…
Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…
Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several…
The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…
In bi-matrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initial quantum states…
Game theory deals with strategic interactions among players and evolutionary game dynamics tracks the fate of the players' populations under selection. In this paper, we consider the replicator equation for two-player-two-strategy games…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
Static stability in economic models means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been…
We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two…