  We consider games played on finite graphs, whose goal is to obtain a trace
belonging to a given set of winning traces. We focus on those states from which
Player 1 cannot force a win. We explore and compare several criteria for
establishing what is the preferable behavior of Player 1 from those states.
  Along the way, we prove several results of theoretical and practical
interest, such as a characterization of admissible strategies, which also
provides a simple algorithm for computing such strategies for various common
goals, and the equivalence between the existence of positional winning
strategies and the existence of positional subgame perfect strategies.
