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

我们讨论了子集和问题的博弈论变体，其中两个玩家竞争以背包代表的公共资源。每个玩家拥有一组私人物品，玩家交替包装物品，每个玩家都希望最大化自己装在背包中的物品的总重量，或最小化另一位玩家的物品的总重量。我们表明，找到针对敌对或自私对手的最佳包装策略是PSPACE完全的，并且针对这些对手，对于玩家而言，最佳可达到的物品重量不能在任何恒定因子内估算（除非P = NP）。当对手短视并贪婪地玩游戏时，游戏变得更加容易：在较弱的意义上，找到针对贪婪的对手的最佳打包策略是NP完全的。