Weak Subgame Perfect Equilibria and their Application to Quantitative Reachability

Brihaye, Thomas; Bruyère, Véronique; Meunier, Noémie; Raskin, Jean-François

doi:10.4230/lipics.csl.2015.504

Cited by 2 publications

(9 citation statements)

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“…We recall two classical concepts of equilibria: Nash equilibrium and subgame perfect equilibrium (see [20]). We also recall weak variants of these equilibria as proposed in [7,11]. We conclude the section by the constrained existence problem that is studied in this paper.…”

Section: Preliminariesmentioning

confidence: 97%

“…We also observe that our results on Reachabilty and Safety objectives transfer from weak SPEs to SPEs: the constrained existence problem for SPEs is PSPACE-complete for those objectives. Quantitative Reachability objectives are investigated in [7] where it is proved that the constrained existence problem for weak SPEs and SPEs is decidable, but its exact complexity is left open. In [7,11,17], the existence of (weak) SPEs in graph games is established using a construction based on a fixpoint.…”

Section: Related Work and Additional Contributionsmentioning

confidence: 99%

“…Quantitative Reachability objectives are investigated in [7] where it is proved that the constrained existence problem for weak SPEs and SPEs is decidable, but its exact complexity is left open. In [7,11,17], the existence of (weak) SPEs in graph games is established using a construction based on a fixpoint. Our fixpoint algorithm is mainly inspired by the fixpoint technique of [11].…”

Section: Related Work and Additional Contributionsmentioning

confidence: 99%

“…In [7], the notion of weak subgame perfect equilibrium (weak SPE) is introduced, and it is shown how it can be used to study the existence SPEs (possibly with contraints) in quantitative reachability games. While an SPE must be resistant to any unilateral deviation of one player, a weak SPE must be resistant to deviations restricted to deviating strategies that differ from the original one on a finite number of histories only.…”

Section: Introductionmentioning

confidence: 99%

“…Weak SPEs are also easier to characterize and to manipulate algorithmically. We refer the interested reader to [7,11] for further justifications of their interest, as well as for related work on NEs and SPEs.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Constrained Existence Problem for Weak Subgame Perfect Equilibria with ω-Regular Boolean Objectives

Brihaye

Bruyère

Goeminne

et al. 2018

Electron. Proc. Theor. Comput. Sci.

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We study multiplayer turn-based games played on a finite directed graph such that each player aims at satisfying an ω-regular Boolean objective. Instead of the well-known notions of Nash equilibrium (NE) and subgame perfect equilibrium (SPE), we focus on the recent notion of weak subgame perfect equilibrium (weak SPE), a refinement of SPE. In this setting, players who deviate can only use the subclass of strategies that differ from the original one on a finite number of histories. We are interested in the constrained existence problem for weak SPEs. We provide a complete characterization of the computational complexity of this problem: it is P-complete for Explicit Muller objectives, NP-complete for Co-Büchi, Parity, Muller, Rabin, and Streett objectives, and PSPACE-complete for Reachability and Safety objectives (we only prove NP-membership for Büchi objectives). We also show that the constrained existence problem is fixed parameter tractable and is polynomial when the number of players is fixed. All these results are based on a fine analysis of a fixpoint algorithm that computes the set of possible payoff profiles underlying weak SPEs.

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Section: Preliminariesmentioning

confidence: 97%

Section: Related Work and Additional Contributionsmentioning

confidence: 99%

Section: Related Work and Additional Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Constrained Existence Problem for Weak Subgame Perfect Equilibria with ω-Regular Boolean Objectives

Brihaye

Bruyère

Goeminne

et al. 2018

Electron. Proc. Theor. Comput. Sci.

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Synthesis of equilibria in infinite-duration games on graphs

Bruyère

2021

ACM SIGLOG News

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In this survey, we propose a comprehensive introduction to game theory applied to computer-aided synthesis. We study multi-player turn-based infinite-duration games played on a finite directed graph such that each player aims at maximizing a payoff function. We present the well-known notions of Nash equilibrium and subgame perfect equilibrium, as well as interesting strategy profiles of players as response to the strategy announced by a specific player. We provide classical and recent results about the related threshold synthesis problem.

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Weak Subgame Perfect Equilibria and their Application to Quantitative Reachability

Cited by 2 publications

References 0 publications

Constrained Existence Problem for Weak Subgame Perfect Equilibria with ω-Regular Boolean Objectives

Constrained Existence Problem for Weak Subgame Perfect Equilibria with ω-Regular Boolean Objectives

Synthesis of equilibria in infinite-duration games on graphs

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