Delegating Decisions in Strategic Settings

In this article, we formalise and investigate the following problem. A number of decisions must be delegated to a collection of agents; once the decisions are delegated, the agents to whom the decisions are delegated will then make these decisions rationally and independently, in pursuit of their own preferences. A principal is able to determine how decisions will be delegated, and seeks to do so in such a way that, when the decisions are ultimately made, some overall goal is satisfied. The principal delegation problem, is then, given such a setting, whether it is possible for the principal to delegate decisions in such a way that, if all the agents to whom decisions have been delegated then make their respective decisions rationally, the principal’s goal will be achieved in equilibrium. We also distinguish the distributed allocation problem where the agents can delegate decisions among themselves. Here we not only require that the principal’s goal will be achieved in equilibrium, but moreover that the allocation to the agents is stable, in the sense that no coalition of agents can redistribute the decisions delegated to them among themselves so as to be better positioned to satisfy their individual goals in equilibrium. We formalise these problems using Boolean games, which provides a very natural framework within which to capture the delegation problem: decisions are directly represented as Boolean variables, which the principal assigns to agents. After motivating and formally defining the principal and distributed delegation problems, we investigate these computational complexity of several varieties of these problems, along with some issues surrounding it. Impact Statement: Our research concerns the ubiquitous problem of how to incentivise agents to decide on courses of action that are simultaneously desirable from the global perspective and rational from a local game-theoretic perspective. The design of mechanisms so as to achieve this is through steering the strategic capabilities of interested agents by delegating decisions to them in specific ways. We distinguish the cases in which the delegation is effectuated by a principal and where the agents are delegating decisions among one another. Our reliance on the mathematical framework of Boolean games to formalise the principal and distributed delegation problems offers valuable insights into the computational complexity of these problems. The delegation problem touches on many important applications, not only in everyday life, but also in Artificial Intelligence, in particular Multi-Agent Systems