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Abstract

Evolutionary game theory has become one of the most diverse and far reaching
theories in biology. Applications of this theory range from cell dynamics to social evolution.
However, many applications make it clear that inherent non-linearities of natural systems
need to be taken into account. One way of introducing such non-linearities into evolutionary
games is by the inclusion of multiple players. An example are social dilemmas, where group
benefits could e.g. increase less than linear with the number of cooperators. Such multiplayer
games can be introduced in all the fields where evolutionary game theory is already well
established. However, the inclusion of non-linearities can help to advance the analysis of
systems which are known to be complex, e.g. in the case of non-Mendelian inheritance.
We review the diachronic theory and applications of multiplayer evolutionary games and
present the current state of the field. Our aim is a summary of the theoretical results from
well-mixed populations in infinite as well as finite populations. We also discuss examples
from three fields where the theory has been successfully applied, ecology, social sciences
and population genetics. In closing, we probe certain future directions which can be explored
using the complexity of multiplayer games while preserving the promise of simplicity of
evolutionary games.