  We study the memory requirements of Nash equilibria in turn-based multiplayer
games on possibly infinite graphs with reachability, shortest path and B\"uchi
objectives.
  We present constructions for finite-memory Nash equilibria in these games
that apply to arbitrary game graphs, bypassing the finite-arena requirement
that is central in existing approaches. We show that, for these three types of
games, from any Nash equilibrium, we can derive another Nash equilibrium where
all strategies are finite-memory such that the same players accomplish their
objective, without increasing their cost for shortest path games.
  Furthermore, we provide memory bounds that are independent of the size of the
game graph for reachability and shortest path games. These bounds depend only
on the number of players.
  To the best of our knowledge, we provide the first results pertaining to
finite-memory constrained Nash equilibria in infinite arenas and the first
arena-independent memory bounds for Nash equilibria.
