Stackelberg-Pareto综合（扩展版）
Stackelberg-Pareto Synthesis (Extended Version)
摘要：
我们研究了两个玩家的Stackelberg游戏的框架，在图中，玩家0宣布一个战略和玩家1合理的响应与战略，是一个最佳的反应。虽然通常假设参与人1只有一个目标，但我们在这里考虑一个新的设置，他有几个目标。在这种情况下，在用他的策略做出回应后，参与人1得到了一个对应于他满意的目标的布尔向量形式的回报。参与人1的理性表现为，在参与人0的策略下，他的反应必须产生帕累托最优收益.我们研究了几种$ω$ -正则目标的Stackelberg-Pareto合成问题，该问题询问参与人0是否可以宣布一个满足他的目标的策略，无论参与人1的理性反应如何。我们发现，这个问题是固定参数的游戏，其中的目标都是可达性，安全性，Büchi，合作Büchi，布尔Büchi，奇偶校验，穆勒，斯特里特或拉宾目标的易处理。我们还表明，这个问题是NEXPTIME-完全的，除了Büchi目标的情况下，它是NP-完全的和合作Büchi目标，它是在NEXPTIME和NP-难。在可达性目标和图是树的简单情况下，这个问题已经是NP完全的。
英文摘要：
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 $ω$-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, Büchi, co-Büchi, Boolean Büchi, parity, Muller, Streett or Rabin objectives. We also show that this problem is NEXPTIME-complete except for the cases of Büchi objectives for which it is NP-complete and co-Büchi 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.
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