The Complexity of Tournament Fixing: Subset FAS Number and Acyclic Neighborhoods
A major computational puzzle in AI game theory has finally been cracked...
Deep Dive
Researchers have resolved a long-standing open problem in computational game theory regarding the Tournament Fixing Problem (TFP). They proved TFP remains NP-hard even when a key structural parameter (the subset FAS number) is constant, but becomes fixed-parameter tractable (FPT) when both the in-neighbor and out-neighbor subgraphs are acyclic. This settles a question posed in AAAI 2026 and refines the complexity landscape for tournament manipulation, a core problem in AI and multi-agent systems.
Why It Matters
This breakthrough clarifies the fundamental limits of algorithmically manipulating competitive structures, impacting AI strategy design and algorithmic fairness.