Related papers: From fixation probabilities to d-player games: an …
To be the fittest is central to proliferation in evolutionary games. Individuals thus adopt the strategies of better performing players in the hope of successful reproduction. In structured populations the array of those that are eligible…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here,…
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 graph theory (EGT) studies the effect of population structure on evolutionary dynamics. The vertices of the graph represent the $N$ individuals. The edges denote interactions for competitive replacement. Two standard update…
Evolutionary game theory assumes that players replicate a highly scored player's strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someone's strategy just by observing the…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
The multi-population replicator dynamics (RD) can be considered a dynamic approach to the study of multi-player games, where it was shown to be related to Cross' learning, as well as of systems of coevolving populations. However, not all of…
We consider learning by fictitious play in a large population of agents engaged in single-play, two-person rounds of a symmetric game, and derive a mean-filed type model for the corresponding stochastic process. Using this model, we…
Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study…
How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a…
We consider ordinary differential equations on the unit simplex of $\RR^n$ that naturally occur in population games, models of learning and self reinforced random processes. Generalizing and relying on an idea introduced in \cite{DF11}, we…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
Population games can be regarded as a tool to study the strategic interaction of a population of players. Although several attention has been given to such field, most of the available works have focused only on the unconstrained case. That…
Fisher's fundamental theorem of natural selection states that the rate of change in a population's mean fitness equals its additive genetic variance in fitness. This implies that mean fitness should not decline in a constant environment,…
One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats…
Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and…
Adaptive populations such as those in financial markets and distributed control can be modeled by the Minority Game. We consider how their dynamics depends on the agents' initial preferences of strategies, when the agents use linear or…
Evolutionary game theory classically investigates which behavioral patterns are evolutionarily successful in a single game. More recently, a number of contributions have studied the evolution of preferences instead: which subjective…
Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept…