Paper Info
Title
The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games (full version).
Abstract
We study multiplayer quantitative reachability games played on a finite directed graph, where the objective of each player is to reach his target set of vertices as quickly as possible. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE), a refinement of NE well-suited in the framework of games played on graphs. It is known that there always exists an SPE in quantitative reachability games and that the constrained existence problem is decidable. We here prove that this problem is PSPACE-complete. To obtain this result, we propose a new algorithm that iteratively builds a set of constraints characterizing the set of SPE outcomes in quantitative reachability games. This set of constraints is obtained by iterating an operator that reinforces the constraints up to obtaining a fixpoint. With this fixpoint, the set of SPE outcomes can be represented by a finite graph of size at most exponential. A careful inspection of the computation allows us to establish PSPACE membership.
Year
Venue
DocType
2019
arXiv: Computer Science and Game Theory
Journal
Citations 
PageRank 
References 
0
0.34
0
Authors
5
Name
Order
Citations
PageRank
Thomas Brihaye146035.91
Véronique Bruyère242943.59
Aline Goeminne302.03
Jean-Francois Raskin41157.17
Marie van den Bogaard563.84