The subset sum game revisited

Abstract We discuss a game theoretic variant of the subset sum problem, in which two players compete for common resource represented by knapsack. Each player owns private set items, pack items alternately, and each either wants to maximize total weight his own packed into knapsack or minimize other player. show that finding best packing strategy against hostile selfish adversary is PSPACE-complete, these adversaries optimal reachable item cannot be approximated within any constant factor (unless P=NP). The becomes easier when short-sighted plays greedily: greedy NP-complete weak sense. This forms one rare examples pseudo-polynomially solvable problems have PTAS, but do not allow an FPTAS