Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

When AI Improves Answers but Slows Knowledge Creation: Matching and Dynamic Knowledge Creation in Digital Public Goods

Keh-Kuan Sun

Abstract

Generative AI helps users solve problems more efficiently, but without leaving a public trace. Fewer discussions and solutions reach public platforms, and the archives that future problem-solvers depend on can shrink. We build a dynamic model of public good provision where agents contribute by solving problems that other agents posted on a public platform, and the accumulated solutions form a depreciating public archive. AI reduces archive creation through two margins that require different instruments. The flow margin: the posted volume of knowledge-enhancing queries declines as AI resolves more problems privately before they reach the platform. The resolution margin: the probability that posted queries are resolved declines as AI raises contributors' outside options, thinning the contributor pool and creating congestion on the platform. The two margins interact through a self-undermining feedback that can generate low-archive traps. The decomposition yields a diagnostic prediction: in the congested regime, a joint decline in posted volume and conditional resolution requires that supply-side pool thinning is quantitatively present, whereas volume decline with stable or rising resolution indicates that private diversion alone is the dominant force. Encouraging public sharing of AI-assisted solutions offsets the decline associated with private diversion but cannot repair participation-driven deterioration in conditional resolution, which requires maintaining contributor engagement directly.

When AI Improves Answers but Slows Knowledge Creation: Matching and Dynamic Knowledge Creation in Digital Public Goods

Abstract

Generative AI helps users solve problems more efficiently, but without leaving a public trace. Fewer discussions and solutions reach public platforms, and the archives that future problem-solvers depend on can shrink. We build a dynamic model of public good provision where agents contribute by solving problems that other agents posted on a public platform, and the accumulated solutions form a depreciating public archive. AI reduces archive creation through two margins that require different instruments. The flow margin: the posted volume of knowledge-enhancing queries declines as AI resolves more problems privately before they reach the platform. The resolution margin: the probability that posted queries are resolved declines as AI raises contributors' outside options, thinning the contributor pool and creating congestion on the platform. The two margins interact through a self-undermining feedback that can generate low-archive traps. The decomposition yields a diagnostic prediction: in the congested regime, a joint decline in posted volume and conditional resolution requires that supply-side pool thinning is quantitatively present, whereas volume decline with stable or rising resolution indicates that private diversion alone is the dominant force. Encouraging public sharing of AI-assisted solutions offsets the decline associated with private diversion but cannot repair participation-driven deterioration in conditional resolution, which requires maintaining contributor engagement directly.

Paper Structure

This paper contains 39 sections, 7 theorems, 50 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Model
  3. Domain and agents
  4. Outside options and participation
  5. Private resolution and endogenous posting
  6. Answering on the public platform
  7. Participation surplus
  8. Knowledge accumulation and timing
  9. Period equilibrium
  10. AI and the Two Margins
  11. Composition of the posted pool
  12. Resolution: composition vs. congestion
  13. Dynamic crowd-out
  14. Dynamic Crowd-Out and the Self-Undermining Feedback
  15. The self-undermining feedback
  16. ...and 24 more sections

Key Result

Lemma 1

Fix $K$. The expected knowledge increment satisfies which is increasing in the ratio $q_H^{e}/q_L^{e}$. Therefore $c^{*,\mathrm{AI}}(K)\ge c^{*,\mathrm{HO}}(K)$ iff the posted pool is weakly more $H$-rich under AI: A sufficient condition, holding escalation probabilities fixed ($m_\theta^{\mathrm{AI}}=m_\theta^{\mathrm{HO}}$ for both $\theta$), is that AI disproportionately resolves routine quer

Figures (2)

  • Figure 1: Average knowledge creation rate under the human-only economy ($\phi^{\mathrm{HO}}$, solid) and the AI economy ($\phi^{\mathrm{AI}}$, dashed) for the parametric example in Appendix \ref{['app:parametric']}, with depreciation rate $\lambda=0.15$ (dotted). AI compresses the stable steady state inward ($K_H^{\mathrm{AI}}\approx 1.55$ vs. $K^{\mathrm{HO}}\approx 2.64$) while the structural minimum viable archive is approximately environment-independent ($K_U^{\mathrm{AI}}\approx 0.15\approx K_U^{\mathrm{HO}}$).
  • Figure 2: Effect of conversion rate $\eta$ on the average knowledge creation rate $\phi^{\mathrm{AI}}(K;\eta)$ for the parametric example in Appendix \ref{['app:parametric']}. Solid: no conversion ($\eta=0$). Dashed: moderate conversion ($\eta'=0.25<\bar{\eta}$). Dash-dotted: high conversion ($\eta"=0.77>\bar{\eta}\approx 0.51$), which eliminates the low-archive basin.

Theorems & Definitions (9)

  • Lemma 1: Composition of the posted pool and the answering cutoff
  • Proposition 1: Resolution: composition vs. congestion
  • Remark 1: Discriminating prediction: supply vs. demand shocks
  • Proposition 2: Dynamic crowd-out and lower archive steady states
  • Corollary 1: Two-margin decomposition of crowd-out
  • Proposition 3: Self-undermining feedback and multiple steady states
  • Proposition 4: Conversion and expansion of the viable region
  • Lemma 2: Sufficient condition for inner-loop uniqueness
  • proof : Proof sketch