k-level LP feasibility is Σ^p_{k-1}-complete for k≥2, polynomial for k≤4 without coupling and unbounded variables but Σ^p_{k-1}-complete for k≥5; optimal value is FΔ^p_k-complete for k≥2 even without coupling.
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Price of Coupling in Multilevel Linear Programming
k-level LP feasibility is Σ^p_{k-1}-complete for k≥2, polynomial for k≤4 without coupling and unbounded variables but Σ^p_{k-1}-complete for k≥5; optimal value is FΔ^p_k-complete for k≥2 even without coupling.