Evolutionary games on graphs and the speed of the evolutionary process

In this paper, we investigate evolutionary games with the invasion process updating rules on three simple non-directed graphs: the star, the circle and the complete graph. Here, we present an analytical approach and derive the exact solutions of the stochastic evolutionary game dynamics. We present formulae for the fixation probability and also for the speed of the evolutionary process, namely for the mean time to absorption (either mutant fixation or extinction) and then the mean time to mutant fixation. Through numerical examples, we compare the different impact of the population size and the fitness of each type of individual on the above quantities on the three different structures. We do this comparison in two specific cases. Firstly, we consider the case where mutants have fixed fitness r and resident individuals have fitness 1. Then, we consider the case where the fitness is not constant but depends on games played among the individuals, and we introduce a ‘hawk–dove’ game as an example

A Hawk-Dove game in kleptoparasitic populations

Kleptoparasitism, the parasitism by theft, is a widespread biological phenomenon. In this paper we extend earlier models to investigate a population of conspecifics involved in foraging and, potentially, kleptoparasitism. We assume that the population is composed of two types of individuals, Hawks and Doves. The types differ according to their strategic choices when faced with an opportunity to steal and to resist a challenge. Hawks use every opportunity to steal and they resist all challenges. Doves never resist and never steal. The fitness of each type of individual depends upon various natural parameters, for example food density, the handling time of a food item, density of the population, as well as the duration of potential fights over the food. We find the Evolutionarily Stable States (ESSs) for all arameter combinations and show that there are three possible ESSs, pure Hawks, pure Doves, and a mixed population of Hawks and Doves. We show that for any set of parameter values there is exactly one ESS. We further investigate the relationship between our findings and the classical Hawk-Dove game as defined in Maynard Smith 1982. We also show how our model extends the classical on

Evolutionary games with sequential decisions and dollar auctions

Conflict occurs throughout the animal world. Such conflicts are often modelled by evolutionary games, where individual animals make a single decision each within the game. These decisions can be sequential, in either order, or simultaneous, and the outcome of the game can depend strongly upon which case is assumed to occur. Real conflicts are generally more complex, however. A fight over a territory, for instance, can involve a succession of different stages and, therefore, choices to be made by the protagonists. In this paper we thus introduce a method of modelling a more complex class of interactions, where each individual can make a sequence of decisions. We show that despite the inherent complexity, under certain assumptions, the resulting game often leads to the case where both animals fight to the fullest extent or where one concedes immediately, thus mirroring the outcomes of simpler single decision games. However, for other cases we see that the outcome is not so simple, and intermediate level contests can occur. This happens principally in cases where the duration of contests is uncertain, and partially governed by external factors which can bring the contest to a sudden end, such as the weather or the appearance of a predator. We thus develop a theory grounded in simple evolutionary models, but extending them in various important ways

Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

The important biological problem of how groups of animals should allocate themselves between different habitats has been modelled extensively. Such habitat selection models have usually involved infinite well-mixed populations. In particular, the model of allocation over a number of food patches when movement is not costly, the ideal free distribution (IFD) model, is well developed. Here we generalize (and solve) a habitat selection game for a finite structured population. We show that habitat selection in such a structured population can have multiple stable solutions (in contrast to the equivalent IFD model where the solution is unique). We also define and study a “predator dilution game” where unlike in the habitat selection game, individuals prefer to aggregate (to avoid being caught by predators due to the dilution effect) and show that this model has a unique solution when movement is unrestricted

The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population

We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology

The Game-Theoretical Model of Using Insecticide-Treated Bed-Nets to Fight Malaria

Malaria infection is a major problem in many countries. The use of the Insecticide-Treated BedNets (ITNs) has been shown to significantly reduce the number of malaria infections; however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease