  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 for several
kinds of $\omega$-regular objectives 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. We show that this
problem is fixed-parameter tractable for games in which objectives are all
reachability, safety, B\"uchi, co-B\"uchi, Boolean B\"uchi, parity, Muller,
Streett or Rabin objectives. We also show that this problem is
NEXPTIME-complete except for the cases of B\"uchi objectives for which it is
NP-complete and co-B\"uchi objectives for which it is in NEXPTIME and NP-hard.
The problem is already NP-complete in the simple case of reachability
objectives and graphs that are trees.
