Stackelberg-Pareto Synthesis

Bruyère, Véronique; Raskin, Jean-François; Tamines, Clément

doi:10.4230/lipics.concur.2021.27

Cited by 3 publications

(1 citation statement)

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“…The proof of the NEXPTIME-hardness of the SPS problem for parity objectives provided in[13] is erroneous due to this argument.…”

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confidence: 99%

Stackelberg-Pareto Synthesis (Extended Version)

Bruyère¹,

Fievet²,

Raskin³

et al. 2022

Preprint

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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 -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. CCS Concepts: • Theory of computation → Logic and verification; Solution concepts in game theory; • Software and its engineering → Formal methods.

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“…The proof of the NEXPTIME-hardness of the SPS problem for parity objectives provided in[13] is erroneous due to this argument.…”

mentioning

confidence: 99%

Stackelberg-Pareto Synthesis (Extended Version)

Bruyère¹,

Fievet²,

Raskin³

et al. 2022

Preprint

Self Cite

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Quantitative Reachability Stackelberg-Pareto Synthesis Is NEXPTIME-Complete

Brihaye,

Bruyère,

Reghem

2023

Lecture Notes in Computer Science

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Stackelberg-Pareto Synthesis

Bruyère,

Fievet,

Raskin

et al. 2024

ACM Trans. Comput. Logic

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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 \(\mathsf {NEXPTIME} \) -complete except for the cases of Büchi objectives for which it is \(\mathsf {NP} \) -complete and co-Büchi objectives for which it is in \(\mathsf {NEXPTIME} \) and \(\mathsf {NP} \) -hard. The problem is already \(\mathsf {NP} \) -complete in the simple case of reachability objectives and graphs that are trees.

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Stackelberg-Pareto Synthesis

Cited by 3 publications

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Stackelberg-Pareto Synthesis (Extended Version)

Stackelberg-Pareto Synthesis (Extended Version)

Quantitative Reachability Stackelberg-Pareto Synthesis Is NEXPTIME-Complete

Stackelberg-Pareto Synthesis

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