  Evolutionary game dynamics of two players with two strategies has been
studied in great detail. These games have been used to model many biologically
relevant scenarios, ranging from social dilemmas in mammals to microbial
diversity. Some of these games may in fact take place between a number of
individuals and not just between two. Here, we address one-shot games with
multiple players. As long as we have only two strategies, many results from two
player games can be generalized to multiple players. For games with multiple
players and more than two strategies, we show that statements derived for
pairwise interactions do no longer hold. For two player games with any number
of strategies there can be at most one isolated internal equilibrium. For any
number of players $\boldsymbol{d}$ with any number of strategies n, there can
be at most (d-1)^(n-1) isolated internal equilibria. Multiplayer games show a
great dynamical complexity that cannot be captured based on pairwise
interactions. Our results hold for any game and can easily be applied for
specific cases, e.g. public goods games or multiplayer stag hunts.
