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Collective Upkeep

Erik Madsen, Eran Shmaya

TL;DR

The paper develops a dynamic mechanism-design framework for maintaining a long-run public good via in-kind contributions, motivated by crowd-based recommender systems. It analyzes a first-best benchmark and then introduces participation constraints and private information, deriving a robust result: at most two membership tiers suffice at the optimum, with a threshold-based structure that concentrates contributions on low-cost types while potentially excluding others. Through fluid (long-lived agents) and sequential (short-lived agents) microfoundations, the authors connect the model to crowdsourced platforms and incentivized exploration, offering practical guidance such as simple two-setting menus for recommender configurations. The work contributes a tractable, duality-based analysis that links physical uptime constraints to economic incentives, highlighting how redistribution, screening, and participation interact in steady-state public-good provision with in-kind contributions. The findings have actionable implications for platform design, suggesting that a small menu of user-adjustable settings can substantially improve welfare without transfers, while clarifying when and how participation constraints bind.

Abstract

We design mechanisms for maintaining public goods which require periodic in-kind contributions, motivated by incentives problems facing crowd-sourced recommender systems. Utilitarian welfare is maximized by redistributive policies which are infeasible when group members can leave or misreport their preferences. An optimal mechanism reduces contributions for group members with low benefit-cost ratios to encourage participation; and pairs reduced contributions with restricted access to the good to ensure truthful reporting. At most two membership tiers are offered at the optimum, indicating that ecommerce and digital content platforms may benefit substantially from offering simple user-adjustable recommendation settings.

Collective Upkeep

TL;DR

The paper develops a dynamic mechanism-design framework for maintaining a long-run public good via in-kind contributions, motivated by crowd-based recommender systems. It analyzes a first-best benchmark and then introduces participation constraints and private information, deriving a robust result: at most two membership tiers suffice at the optimum, with a threshold-based structure that concentrates contributions on low-cost types while potentially excluding others. Through fluid (long-lived agents) and sequential (short-lived agents) microfoundations, the authors connect the model to crowdsourced platforms and incentivized exploration, offering practical guidance such as simple two-setting menus for recommender configurations. The work contributes a tractable, duality-based analysis that links physical uptime constraints to economic incentives, highlighting how redistribution, screening, and participation interact in steady-state public-good provision with in-kind contributions. The findings have actionable implications for platform design, suggesting that a small menu of user-adjustable settings can substantially improve welfare without transfers, while clarifying when and how participation constraints bind.

Abstract

We design mechanisms for maintaining public goods which require periodic in-kind contributions, motivated by incentives problems facing crowd-sourced recommender systems. Utilitarian welfare is maximized by redistributive policies which are infeasible when group members can leave or misreport their preferences. An optimal mechanism reduces contributions for group members with low benefit-cost ratios to encourage participation; and pairs reduced contributions with restricted access to the good to ensure truthful reporting. At most two membership tiers are offered at the optimum, indicating that ecommerce and digital content platforms may benefit substantially from offering simple user-adjustable recommendation settings.
Paper Structure (37 sections, 14 theorems, 70 equations)

This paper contains 37 sections, 14 theorems, 70 equations.

Key Result

Proposition 1

Let $y^\mathrm{fb}$ be the unique $y$ solving and let $W^\mathrm{fb}$ be the common value in yfb evaluated at $y^{FB}$. Then the mechanism $(P^\mathrm{fb},Q^\mathrm{fb})$ defined by solves the first-best problem and yields welfare $W^\mathrm{fb}$.

Theorems & Definitions (26)

  • Proposition 1
  • Corollary
  • proof
  • Corollary
  • proof
  • Theorem 1
  • Example
  • Definition 1
  • Proposition 2
  • Proposition 3
  • ...and 16 more