Can More LLM Users Reduce the Welfare Cost of Selfish Advice?

Large language models (LLMs) increasingly guide decisions whose consequences extend beyond their users. We study a shared LLM *advisor* that learns from user feedback while other players follow no regret learning in the *volunteer's dilemma*, a multiplayer public good game. We compare a **selfish** LLM benchmark that optimizes its users' expected payoffs with a **selfless** benchmark that optimizes total expected welfare. Our central quantity is the social welfare gap, the selfless benchmark's total welfare minus the selfish benchmark's at the same adoption level. To analyze this gap, we first establish convergence of the other players' response and the advisor's mean learning dynamics. When the other players continue volunteering, both objectives select the same policy, so the gap is zero. When LLM users alone supply the public good, this gap has a unique maximum as adoption varies. When the maximum is interior, the gap first widens and then narrows. Broader adoption brings more of those who benefit from the public good into the selfish objective. Higher contribution costs relative to the benefit each player receives increase the gap and move an interior maximum toward lower adoption. Our experiments on Qwen3 8B reveal action probabilities close to theoretical predictions and generally smaller average welfare gaps at higher adoption levels. These findings suggest that wider LLM adoption can reduce the welfare cost of serving users alone, so losses at limited adoption need not persist as more users join.