The communication burden of payment determination

In the presence of self-interested parties, mechanism designers typically aim to implement some social-choice function in an equilibrium. This paper studies the cost of such equilibrium requirements in terms of communication. While a certain amount of information x needs to be communicated just for computing the outcome of a certain social-choice function, an additional amount of communication may be required for computing the equilibrium-supporting payments (if exist). Our main result shows that the total amount of information required for this task can be greater than x by a factor linear in the number of players n, i.e., n⋅x (under a common normalization assumption). This is the first known lower bound for this problem. In fact, we show that this result holds even in single-parameter domains. On the positive side, we show that certain classic economic domains, namely, single-item auctions and public-good mechanisms, only entail a small overhead. ► How much additional communication is required for computing equilibrium-supporting payments? ► The overhead can be linear in the number of players for some (one-parameter) objective functions. ► The overhead is a small constant for some well-studied objectives.