Altruism, Collectivism and Egalitarianism: On a Variety of Prosocial Behaviors in Binary Networked Public Goods Games

Binary Networked public goods (BNPG) game consists of a network 𝐺 = (𝑉 , 𝐸) with n players residing as nodes in a network and making a YES/NO decision to invest a public project. Examples of such public projects include face mask wearing during a pandemic, crime reporting and vaccination, etc. Most of the conventional modes of BNPG games solely posit egoism as the motivation of players: they only care about their own benefits. However, a series of real-world examples show that people have a wide range of prosocial behaviors in making decisions. To address this property, we introduce a novel extension of BNPG games to account for three kinds of prosocial motivations: altruism, collectivism, and egalitarianism. We revise utility functions to reflect different prosocial motivations with respect to the welfare of others, mediated by a prosocial graph. We develop computational complexity results to decide the existence of pure strategy Nash equilibrium in these models, for cases where the prosocial graph is a tree, a clique or a general network. We further discuss the Prosocial Network Modification (PNM) problem, in which a principal can change the network structure within a budget constraint, to induce a given strategy profile with respect to an equilibrium. For all three types of PNM problems, we completely characterize their corresponding computational complexity results.