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Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are…
Wealthy individuals may be less tempted to defect than those with comparatively low payoffs. To take this into consideration, we introduce coevolutionary success-driven multigames in structured populations. While the core game is always the…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
Strategies aimed at reducing the negative effects of long-term uncertainty and risk are common in biology, game theory, and finance, even if they entail a cost in terms of mean benefit. Here, we focus on the single mutant's invasion of a…
Trusting in others and reciprocating that trust with trustworthy actions are crucial to successful and prosperous societies. The Trust Game has been widely used to quantitatively study trust and trustworthiness, involving a sequential…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
The dynamical mechanisms that can stabilize the coexistence of species (or strategies) are of substantial interest for the maintenance of biodiversity and in sociobehavioural dynamics. We investigate the mean extinction time in the…
Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a…
Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation…
In this paper we study the minority game in the presence of evolution. In particular, we examine the behavior in games in which the dimension of the strategy space, m, is the same for all agents and fixed for all time. We find that for all…
Mutation rate is a key determinant of the pace as well as outcome of evolution, and variability in this rate has been shown in different scenarios to play a key role in evolutionary adaptation and resistance evolution under stress caused by…
We continue our study of evolution in minority games by examining games in which agents with poorly performing strategies can trade in their strategies for new ones from a different strategy space. In the context of the games discussed in…
The literature on evolutionary game theory suggests that pure strategies that are strictly dominated by other pure strategies always become extinct under imitative game dynamics, but they can survive under innovative dynamics. As we…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
This paper investigates the evolution of strategic play where players drawn from a finite well-mixed population are offered the opportunity to play in a public goods game. All players accept the offer. However, due to the possibility of…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…