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Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
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,…
In this paper, we focus on studying the passivity properties of different versions of replicator dynamics (RD). RD is an important class of evolutionary dynamics in evolutionary game theory. Evolutionary dynamics describe how the population…
A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters…
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner's Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
The sampling of interaction partners depends on often implicit modelling assumptions, yet has marked effects on the dynamics in evolutionary games. One particularly important aspect is whether or not competitors also interact. Population…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The emergence of cooperation among self-interested agents has been a key concern of the multi-agent systems community for decades. With the increased importance of network-mediated interaction, researchers have shifted the attention on the…
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…
Phylogenetics is the study of the evolutionary relationships between organisms. One of the main challenges in the field is to take biological data for a group of organisms and to infer an evolutionary tree, a graph that represents these…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
Reputation plays a crucial role in social interactions by affecting the fitness of individuals during an evolutionary process. Previous works have extensively studied the result of imitation dynamics without focusing on potential irrational…
Dynamics of evolutionary games strongly depend on underlying networks. We study the coevolutionary prisoner's dilemma in which players change their local networks as well as strategies (i.e., cooperate or defect). This topic has been…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…