Martí-Franquès COFUND Fellowship Programme


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Engineering and Architecture

Supervisor name and surname:

Alex Arenas

Supervisor email:

Supervisor short biography

PhD programme:

Computer Science and Mathematics of Security

Title of the research project:

Higher-order dynamical processes on networks

Description of the research project:

We aim at studying how higher-order interactions influence the state of cooperation of a structured population by analyzing the evolutionary dynamics of the public goods game, a n-player social dilemma, on different simple hypergraphs. The phenomenon of cooperation drives and shapes - and often makes even possible - the existence of many real systems, ranging from genomes to human societies. In behavioral terms, cooperation is the providing of some benefit to another individual at some cost for the provider. Therefore, in absence of any special sustaining mechanism, we expect natural selection to wipe out any cooperative behavior in favor of selfish ones, as predicted by the classical approaches of evolutionary game theory. Thus, the complexity of biological and social systems- both animal’s and human’s ones- brought scientists to define and test several mechanisms to explain the ubiquity of cooperation: inclusive fitness, direct reciprocity, reputation, punishment, (cultural) group selection etc. (clearly, those requiring substantial cognitive demands, apply only to human’s social systems).
Among those mechanisms, we focus on the so-called network reciprocity. Apart of its fascinating theoretical character, network reciprocity is regarded as one of the most important and interesting of the mechanisms from an application point of view. It is in fact usually easier to control and redesign the interaction network rather than individuals’ behavior.
The use of networks (mono- and multilayer) to formalize the topology of interactions within a system, tacitly assumes that all the interactions that occur in the system are essentially pairwise. This would not be a satisfactory approximation for those real systems exhibiting higher-order interactions to which more than two entities participate together and which are not reducible to combinations of lower-order ones. In other words, a network may be only a less-informative projection of a better higher-order representation of a real system. Examples of higher-order interactions include triadic closures, which are known to be fundamental building blocks of social networks, cliques in scientific co-authorship networks, spatial coexistence relations between species in an ecosystem and trigenic interactions in gene regulatory networks. Explicitly referring to human societies, one can think of how the behavior of a person changes when relates or makes decisions within a group rather than when does so facing only another person.
The step forward we set out to do with this work, tries to bring network reciprocity closer to reality. We investigate the effect of considering higher-order interactions on the evolution of cooperation when the population of individuals possesses some spatial correlations. Thus, we refer to evolutionary game theory on one hand, and to hypergraph theory on the other. Hypergraphs allow to distinguish the dynamics on a m-clique, in which each of the vertices interacts separately, in pair, with each of the other m−1 vertices, from the dynamics on a hyperedge of cardinality m, in which the m vertices interact all at once in an intrinsically different way (a very recent work made use of hypergraphs as well). We aim at confirm the hypothesis here that the mechanism of network reciprocity can be successfully extended to higher-order structures and that, in fact, it becomes reinforced.
Ethics: This project does not involve ethical aspects.

Workplace location: Campus Sescelades, Tarragona

Gross anual salary:

27103.20 €


Full time

Working hours:

37.5 hours a week

Expected start date:

15 March 2021

European union This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 945413