Contracting with a Mechanism Designer
Tian Bai, Yiding Feng, Yaohao Liu, Mengfan Ma, Mingyu Xiao
TL;DR
This paper introduces a three-party model for crowdsourcing markets, capturing the economic interplay between a principal, an intermediary, and agents under a two-stage Stackelberg framework. It shows that the intermediary’s optimal mechanism reduces to a Bayesian revenue-maximizing (virtual welfare) design parameterized by the principal’s contract, and that linear contracts are optimal when reward distributions are identical across agents; with identical reward and cost distributions, the problem further maps to virtual value pricing. The authors quantify the efficiency loss from delegation using PoDM and PoA, deriving tight bounds under regular and MHR distributions and showing the intermediary’s impact diminishes as market size grows, while also analyzing anonymous-pricing and unknown-market-size variants. The work connects contract design with auction theory, providing a tractable, auction-theoretic lens on crowdsourcing platforms and offering guidance on when intermediation improves or hurts principal utility in large-scale markets. It contributes novel theoretical tools (virtual value pricing in a contract-downstream mechanism setting) and insights into how platform fees and information asymmetries shape welfare and revenue in modern crowdsourcing ecosystems.
Abstract
This paper explores the economic interactions within modern crowdsourcing markets. In these markets, employers issue requests for tasks, platforms facilitate the recruitment of crowd workers, and workers complete tasks for monetary rewards. Recognizing that these roles serve distinct functions within the ecosystem, we introduce a three-party model that distinguishes among the principal (the requester), the intermediary (the platform), and the pool of agents (the workers). The principal, unable to directly engage with agents, relies on the intermediary to recruit and incentivize them. This interaction unfolds in two stages: first, the principal designs a profit-sharing contract with the intermediary; second, the intermediary implements a mechanism to select an agent to complete the delegated task. We analyze the proposed model as an extensive-form Stackelberg game. Our contributions are threefold. First, we fully characterize the subgame perfect equilibrium of our model. In particular, the principal's contract design problem can be represented as virtual value pricing, a novel auction-theoretic formulation. We identify the optimality of linear contracts, even when the task has multiple outcomes and agents' cost distributions are asymmetric. Second, to quantify the principal's utility loss from delegation and information asymmetry, we introduce the price of double marginalization (PoDM) and the classical price of anarchy (PoA). We derive tight or nearly tight bounds on both ratios under regular and monotone hazard rate distributions. Finally, we extend our analysis to two natural variants of the base model: (i) the intermediary is restricted to anonymous pricing mechanisms, and (ii) the principal lacks precise information about the market size.