  In general, finite concurrent two-player reachability games are only
determined in a weak sense: the supremum probability to win can be approached
via stochastic strategies, but cannot be realized.
  We introduce a class of concurrent games that are determined in a much
stronger sense, and in a way, it is the larger class with this property. To
this end, we introduce the notion of \emph{local interaction} at a state of a
graph game: it is a \emph{game form} whose outcomes (i.e. a table whose
entries) are the next states, which depend on the concurrent actions of the
players. By definition, a game form is \emph{determined} iff it always yields
games that are determined via deterministic strategies when used as a local
interaction in a Nature-free, one-shot reachability game. We show that if all
the local interactions of a graph game with Borel objective are determined game
forms, the game itself is determined: if Nature does not play, one player has a
winning strategy; if Nature plays, both players have deterministic strategies
that maximize the probability to win. This constitutes a clear-cut separation:
either a game form behaves poorly already when used alone with basic
objectives, or it behaves well even when used together with other well-behaved
game forms and complex objectives.
  Existing results for positional and finite-memory determinacy in turn-based
games are extended this way to concurrent games with determined local
interactions (CG-DLI).
