2 research outputs found
Constrained Existence Problem for Weak Subgame Perfect Equilibria with -Regular Boolean Objectives
We study multiplayer turn-based games played on a finite directed graph such
that each player aims at satisfying an omega-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-B\"uchi, Parity, Muller, Rabin, and Streett
objectives, and PSPACE-complete for Reachability and Safety objectives (we only
prove NP-membership for B\"uchi 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.Comment: In Proceedings GandALF 2018, arXiv:1809.02416. arXiv admin note:
substantial text overlap with arXiv:1806.0554
Constrained existence problem for weak subgame perfect equilibria with omega-regular Boolean objectives (full version)
We study multiplayer turn-based games played on a finite directed graph such
that each player aims at satisfying an omega-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-B\"uchi, Parity, Muller, Rabin, and Streett
objectives, and PSPACE-complete for Reachability and Safety objectives (we only
prove NP-membership for B\"uchi 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