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.

中文翻译：

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Stackelberg-Pareto综合

在本文中，我们研究了在图表上玩的两人Stackelberg游戏的框架，其中玩家0宣布策略，而玩家1用最佳响应策略做出合理响应。通常假设玩家1有一个目标，但在这里我们考虑他拥有多个目标的新设置。在这种情况下，玩家1响应自己的策略后，将获得布尔值向量形式的回报，该布尔值向量对应于其满意的目标。给定玩家0的策略，玩家1的反应必须产生帕累托最优收益这一事实对玩家1的合理性进行了编码。我们研究了Stackelberg-Pareto综合问题，该问题询问玩家0是否可以宣布满足其目标的策略，无论玩家1的理性反应 对于目标要么都是奇偶目标，要么是所有可达性目标的游戏，我们证明此问题是固定参数可处理的并且NEXPTIME完全。在可达性目标和树形图的简单情况下，此问题已经是NP完全的。