  We investigate the existence of certain types of equilibria (Nash,
$\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect,
Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use
two fundamental approaches: one requires strong topological restrictions on the
games, but produces very strong existence results. The other merely requires
some very basic determinacy properties to still obtain some existence results.
Both results are transfer results: starting with the existence of some
equilibria for a small class of games, they allow us to conclude the existence
of some type of equilibria for a larger class.
  To make the abstract results more concrete, we investigate as a special case
infinite sequential games with real-valued payoff functions. Depending on the
class of payoff functions (continuous, upper semi-continuous, Borel) and
whether the game is zero-sum, we obtain various existence results for
equilibria.
  Our results hold for games with two or up to countably many players.
