On the Hardness of Lying under Egalitarian Social Welfare

Abstract

When it comes to distributing resources among different agents, there are different objectives that can be maximized. In the case of egalitarian social welfare, the goal is to maximize the utility of the least satisfied agent. Unfortunately, this goal can lead to strategic behaviors on the part of the agents: if they lie about their utility functions, then the dealer might grant them more goods than they would be entitled to. In this work, we study the computational complexity of obtaining the optimal lie in this context. We show that although it is extremely easy to obtain the optimal lie when we do not impose any restrictions on the lies used, the problem becomes Σ2P-complete by imposing simple limits on the usable lies. Thus, we prove that we can easily make it hard to lie in the context of egalitarian social welfare.