We study the allocation of indivisible items to buyers with additive values drawn from independent distributions. The objective is consumer surplus net of burnt payments. We consider artificial-currency mechanisms: buyers receive personalized budgets of a currency worthless outside the mechanism and use them to bid across items. The better of separate selling and artificial-currency mechanisms provides a 3-approximation to optimal consumer surplus. The guarantee holds at every Bayes--Nash equilibrium, without equilibrium selection. Both branches are necessary: either alone may capture only a vanishing share of the optimum. The proof decomposes benchmark surplus into a stable part captured by artificial currency and a variation covered by separate selling.
Paul Dütting, Yingkai Li, Inbal Talgam-Cohen, Jinzhao Wu
原文摘要
In contract design, the principal is often better informed about the project's chances of succeeding than the agents. To incentivize effort, the principal has two main tools: first, to design a contract, sharing part of the project's success among the agents; second, to design a (Bayesian) persuasion scheme, selectively sharing information with the agents. In this work we are interested in the optimal combination of both these tools. We tackle the joint problem through the prism of simplicity vs. optimality, and establish a stark dichotomy: The simple disclosure scheme of full transparency achieves a tight $4/3$-approximation to the optimal combination of information disclosure and team contract, when the team's production function is submodular. In contrast, full transparency can be arbitrarily far from optimal when production is supermodular. The techniques that we develop to bound the gap for submodular functions, also yield a new deterministic polynomial-time approximation algorithm for pure multi-agent contract design, with a significantly improved approximation ratio of $2.311$, and thus a $3.081$-approximation algorithm for the joint information and contracting problem.