Braess's Paradox of Generative AI

TL;DR

This paper initiates the study of GenAI's long-term social impact resulting from the weakening network effect of human-based platforms like Stack Overflow and presents an analog to Braess's paradox in which all users would be better off without GenAI.

Abstract

ChatGPT has established Generative AI (GenAI) as a significant technological advancement. However, GenAI's intricate relationship with competing platforms and its downstream impact on users remains under-explored. This paper initiates the study of GenAI's long-term social impact resulting from the weakening network effect of human-based platforms like Stack Overflow. First, we study GenAI's revenue-maximization optimization problem. We develop an approximately optimal solution and show that the optimal solution has a non-cyclic structure. Then, we analyze the social impact, showing that GenAI could be socially harmful. Specifically, we present an analog to Braess's paradox in which all users would be better off without GenAI. Finally, we develop necessary and sufficient conditions for a regulator with incomplete information to ensure that GenAI is socially beneficial.

Figures (2)

• Figure 1: Social welfare over time in Example \ref{['example']}. The schemes $\bm x^0$, $\bm x^r$, and $\bm x^w$ are the no-training, revenue-maximizing, and welfare-maximizing schemes, respectively. The counterfactual welfare is the welfare users obtain in a world without GenAI.
• Figure 2: The two sub-figures showcase contraction and expansion of long-term proportions with varying initial proportions $p_1$. In Figure \ref{['fig:subfig1']}, strong contraction applies. The proportion $p_3$ for $t=3$ is almost invariant to $p_1$. In Figure \ref{['fig:subfig2']}, the initial proportion determines whether the long-term proportion converges to 0 or 1. This showcases that even an $\varepsilon$-close estimate can be unfruitful to the regulator.

Theorems & Definitions (56)

• Theorem 1: Braess's paradox of generative AI
• Example 1
• Proposition 1
• Definition 1: $k-cyclic$ training scheme
• Proposition 2
• Corollary 1
• Theorem 2
• proof : Proof sketch of \ref{['thm not cyclic']}
• Definition 2: Socially beneficial scheme
• Proposition 3