  We study a complementarity game with multiple populations whose members'
offered contributions are put together towards some common aim. When the sum of
the players' offers reaches or exceeds some threshold K, they each receive K
minus their own offers. Else, they all receive nothing. Each player tries to
offer as little as possible, hoping that the sum of the contributions still
reaches K, however. The game is symmetric at the individual level, but has many
equilibria that are more or less favorable to the members of certain
populations. In particular, it is possible that the members of one or several
populations do not contribute anything, a behavior called defecting, while the
others still contribute enough to reach the threshold. Which of these
equilibria then is attained is decided by the dynamics at the population level
that in turn depends on the strategic options the players possess. We find that
defecting occurs when more than 3 populations participate in the game, even
when the strategy scheme employed is very simple, if certain conditions for the
system parameters are satisfied. The results are obtained through systematic
simulations.
