Kantian imperatives in public goods networks

Abstract

To maximize aggregate effort, a principal allocates agents to a given graph of roles where each agent’s reward is exogenously fixed and increases in the aggregate effort of their immediate neighbourhood. Effort is costly for individual agents, thus forming a local public goods game. Agents can be selfish or stubborn (following Kantian imperatives that maximize agent welfare). For regular graphs, we provide conditions under which Kantians are located in clusters or are far apart. When Kantian and isolated-selfish efforts are close, the principal’s optimal allocation also maximizes agent welfare. We discuss difficulties surrounding the notion of Kantian imperatives on non-regular graphs and solve the principal’s problem on graphs where roles are entirely based on degree. Our results show that, compared to standard public goods games over complete networks, organizations with Kantian agents suffer from both over- and under-provision of public goods when the underlying graph becomes relevant.