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Abstract

Evolutionary game theory has been successful in describing phenomena from
bacterial population dynamics to the evolution of social behaviour. However,
it has typically focused on a single game describing the interactions between
individuals. Organisms are simultaneously involved in many intraspecies and
interspecies interactions. Therefore, there is a need to move from single games
to multiple games. However, these interactions in nature involve many
players. Shifting from 2-player games to multiple multiplayer games yield
richer dynamics closer to natural settings. Such a complete picture of multiple
game dynamics (MGD), where multiple players are involved, was lacking.
For multiple multiplayer games—where each game could have an arbitrary
finite number of players and strategies, we provide a replicator equation for
MGD having many players and strategies. We show that if the individual
games involved have more than two strategies, then the combined dynamics
cannot be understood by looking only at individual games. Expected
dynamics from single games is no longer valid, and trajectories can possess
different limiting behaviour. In the case of finite populations, we formulate
and calculate an essential and useful stochastic property, fixation probability.
Our results highlight that studying a set of interactions defined by a single
game can be misleading if we do not take the broader setting of the interactions
into account. Through our results and analysis, we thus discuss and
advocate the development of evolutionary game(s) theory, which will help
us disentangle the complexity of multiple interactions.