Delegating Decisions in Strategic Settings

We formalise and investigate the following problem. A principal must delegate a number of decisions to a collection of agents. Once the decisions are delegated, the agents to whom the decisions are delegated will act selfishly, rationally, and independently in pursuit of their own preferences. The principal himself is assumed to be self-interested, and has some goal that he desires to be achieved. The delegation problem is then, given such a setting, is it possible for the principal to delegate decisions in such a way that, if all the agents to whom decisions have been delegated then make decisions rationally, the principal's goal will be achieved in equilibrium. We formalise this problem 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 delegation problem, we investigate the computational complexity of the problem, and some issues surrounding it.