The Complexity of SPEs in Mean-payoff Games
L\'eonard Brice, Jean-Fran\c{c}ois Raskin, Marie van den Bogaard
TL;DR
This paper proves that determining subgame perfect equilibrium thresholds in mean-payoff games is NP-complete, resolving an open question about its exact computational complexity.
Contribution
It establishes the NP-completeness of the SPE threshold problem for mean-payoff games, clarifying its computational difficulty.
Findings
SPE threshold problem is NP-complete.
Decidability of the problem was previously known.
Exact complexity was unresolved before this work.
Abstract
We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst case complexity was left open.
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