
Constrained existence problem for weak subgame perfect equilibria with omegaregular Boolean objectives
We study multiplayer turnbased games played on a finite directed graph ...
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We study multiplayer turnbased games played on a finite directed graph ...
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Constrained existence problem for weak subgame perfect equilibria with omegaregular Boolean objectives (full version)
We study multiplayer turnbased games played on a finite directed graph such that each player aims at satisfying an omegaregular Boolean objective. Instead of the wellknown 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 Pcomplete for Explicit Muller objectives, NPcomplete for CoBüchi, Parity, Muller, Rabin, and Streett objectives, and PSPACEcomplete for Reachability and Safety objectives (we only prove NPmembership 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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