In the classical Binary Networked Public Goods (BNPG) game, a player can either invest in a public project or decide not to invest. Based on the decisions of all the players, each player receives a reward as per his/her utility function. However, classical models of BNPG game do not consider altruism, which players often exhibit and can significantly affect equilibrium behavior. Yu et al. [24] extended the classical BNPG game to capture the altruistic aspect of the players. We, in this paper, first study the problem of deciding the existence of a Pure Strategy Nash Equilibrium (PSNE) in a BNPG game with altruism. This problem is already known to be NP-complete. We complement this hardness result by showing that the problem admits efficient algorithms when the input network is either a tree or a complete graph. We further study the Altruistic Network Modification problem, where the task is to compute if a target strategy profile can be made a PSNE by adding or deleting a few edges. This problem is also known to be NP-complete. We strengthen this hardness result by exhibiting intractability results even for trees. A perhaps surprising finding of our work is that the above problem remains NP-hard even for bounded degree graphs when the altruism network is undirected, but becomes polynomial-time solvable when the altruism network is directed. We also show some results on computing an MSNE and some parameterized complexity results. In summary, our results show that it is much easier to predict how the players in a BNPG game will behave compared to how the players in a BNPG game can be made to behave in a desirable way.
翻译:在经典的二进制网络公益物( BNPG) 游戏中, 玩家可以投资公共项目, 或者决定不投资。 根据所有玩家的决定, 每个玩家都会按自己的工具功能获得奖赏。 但是, BNPG 游戏的经典模式不会考虑利他主义, 玩家通常会表现出来, 并且会大大影响平衡行为。 Yu 等人 [24] 扩展了经典的 BNPG 游戏, 以捕捉玩玩家的利他主义方面。 我们在本文件中, 首先研究在 BNPG 游戏中, 确定一个纯战略 Nash Equilibrium (PSNE) 存在的复杂性问题。 这个问题在使用利他( PNPG 游戏) 游戏中, 每个玩家都以利他( PNPG) 游戏得到奖赏。 这个问题已经众所周知, 这个问题已经是NP- NP 游戏游戏中的奖赏。 我们通过显示输入网络的硬性算法, 我们的游戏结果在B- NPNP 上, 也可以在显示直观的图像上展示结果时, 继续显示, 直观, 。 在显示B 直观的游戏中, 直观上显示, 直观的结果在显示, 直观上, 直观的结果在显示, 直观上, 直观 直观上, 直达 。