  This work introduces the concept of Variable Size Game Theory (VSGT), in
which the number of players in a game is a strategic decision made by the
players themselves. We start by discussing the main examples in game theory:
dominance, coexistence, and coordination. We show that the same set of pay-offs
can result in coordination-like or coexistence-like games depending on the
strategic decision of each player type. We also solve an inverse problem to
find a $d$-player game that reproduces the same fixation pattern of the VSGT.
In the sequel, we consider a game involving prosocial and antisocial players,
i.e., individuals who tend to play with large groups and small groups,
respectively. In this game, a certain task should be performed, that will
benefit one of the participants at the expense of the other players. We show
that individuals able to gather large groups to perform the task may prevail,
even if this task is costly, providing a possible scenario for the evolution of
eusociality. The next example shows that different strategies regarding game
size may lead to spontaneous separation of different types, a possible scenario
for speciation without physical separation (sympatric speciation). In the last
example, we generalize to three types of populations from the previous analysis
and study compartmental epidemic models: in particular, we recast the SIRS
model into the VSGT framework: Susceptibles play 2-player games, while
Infectious and Removed play a 1-player game. The SIRS epidemic model is then
obtained as the replicator equation of the VSGT. We finish with possible
applications of VSGT to be addressed in the future.
