Brihaye, Thomas and Bruyère, Véronique and Goeminne, Aline and Raskin, Jean-François and Bogaard, Marie van den - The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games

lmcs:5966 - Logical Methods in Computer Science, November 5, 2020, Volume 16, Issue 4 - https://doi.org/10.23638/LMCS-16(4:8)2020
The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games

Authors: Brihaye, Thomas and Bruyère, Véronique and Goeminne, Aline and Raskin, Jean-François and Bogaard, Marie van den

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.


Volume: Volume 16, Issue 4
Published on: November 5, 2020
Submitted on: December 11, 2019
Keywords: Computer Science - Computer Science and Game Theory,Computer Science - Logic in Computer Science


Share

Consultation statistics

This page has been seen 144 times.
This article's PDF has been downloaded 83 times.