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We study a complementarity game as a systematic tool for the investigation of the interplay between individual optimization and population effects and for the comparison of different strategy and learning schemes. The game randomly pairs…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…
This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance).…
We examine kinetic symmetry breaking phenomena in an evolutionary political game in which voters, inhabiting a multidimensional ideological space, cast ballots via selection mechanisms subject to the competing forces of conformity and…
In binary decision-making, individuals often choose either the rare or the common action. In the framework of evolutionary game theory, the best-response update rule can be used to model this dichotomy. Those who prefer the common action…
A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage…
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 $d$-dimensional integer lattice is occupied by a player who is characterized by one…
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…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
This chapter focuses on the derivation of a doubly nonlocal Fisher-KPP model, which is a macroscopic nonlocal evolution equation describing population dynamics in the large population limit. The derivation starts from a microscopic…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
In a laboratory experiment, round by round, individual interactions should lead to the social evolutionary rotation in population strategy state space. Successive switching the incentive parameter should lead to successive change of the…
How humans make decisions in non-cooperative strategic interactions is a challenging question. For the fundamental model system of Rock-Paper-Scissors (RPS) game, classic game theory of infinite rationality predicts the Nash equilibrium…
Moran or Wright-Fisher processes are probably the most well known model to study the evolution of a population under various effects. Our object of study will be the Simpson index which measures the level of diversity of the population, one…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
Forcing finite state mean field games by a relevant form of common noise is a subtle issue, which has been addressed only recently. Among others, one possible way is to subject the simplex valued dynamics of an equilibrium by a so-called…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…