  In this paper, we study the framework of two-player Stackelberg games played
on graphs in which Player 0 announces a strategy and Player 1 responds
rationally with a strategy that is an optimal response. While it is usually
assumed that Player 1 has a single objective, we consider here the new setting
where he has several. In this context, after responding with his strategy,
Player 1 gets a payoff in the form of a vector of Booleans corresponding to his
satisfied objectives. Rationality of Player 1 is encoded by the fact that his
response must produce a Pareto-optimal payoff given the strategy of Player 0.
We study the Stackelberg-Pareto Synthesis problem which asks whether Player 0
can announce a strategy which satisfies his objective, whatever the rational
response of Player 1. For games in which objectives are either all parity or
all reachability objectives, we show that this problem is fixed-parameter
tractable and NEXPTIME-complete. This problem is already NP-complete in the
simple case of reachability objectives and graphs that are trees.
