How AI Agents Follow the Herd of AI? Network Effects, History, and Machine Optimism¶

🕒 Published (v1): 2025-12-12 12:14 UTC · Source: Arxiv · link

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TL;DR¶

This paper studies how LLM-based agents behave in network-effect games (where payoffs depend on peer participation) under different historical data structures. A novel multi-agent workflow injects price-participation trajectories as in-context history, revealing that temporal ordering of history—not just its presence—governs whether agents converge to game-theoretic equilibria. A key failure mode, "AI optimism," causes agents to persistently overestimate participation under strong network effects regardless of contradictory evidence.

Problem¶

Classical game theory assumes agents can compute fulfilled-expectation equilibria (FEE) in network-effect games, but LLMs lack the recursive reasoning capacity to do this without external scaffolding. Prior multi-agent LLM research has focused on static games (Prisoner's Dilemma, negotiation); network-effect games—where value is collectively determined—are underexplored. The gap is understanding how history structure (not just history presence) shapes LLM strategic coordination.

Method¶

Six LLM agents (Qwen-max, Qwen-turbo, Qwen-2.5-1.5B) play a repeated conference-attendance game with network-effect utility: U(θ) = θ + βN − p ≥ 0, where β ∈ {0.25, 0.75} controls network-effect strength. A manager agent controls price p and feeds agents only aggregate historical participation counts. The workflow tests four price trajectory types—fixed, ascending, descending, randomized—each repeated 10 times. Agents form expectations about peer attendance N before observing actual choices, mirroring real-world partial observability. Static (no history) and dynamic (iterative history) conditions are compared against the theoretical FEE baseline.

Key Contributions¶

Demonstrates that LLM agents cannot infer equilibrium from scratch (no history → high dispersion, no convergence to FEE).
Shows that ordered historical sequences (ascending/descending prices) enable partial convergence under weak network effects (β=0.25).
Identifies "AI optimism": under strong network effects (β=0.75), agents persistently overestimate participation even with contradictory historical evidence.
Proves that randomized price history destroys convergence entirely, establishing that temporal coherence is a prerequisite for LLM in-context learning in strategic settings.
Frames history curation as a new strategic variable in AI-mediated systems—impossible to exploit in purely human systems.

Results¶

Static game (no history): All models show high expectation dispersion with no correlation to FEE across both β=0.25 and β=0.75.
Fixed price, weak β: Agents converge to N=6 and N=4 within ~3 rounds; N=2 equilibrium shows persistent residual optimism.
Fixed price, strong β: Convergence fails entirely; expectations inflate above FEE even after many rounds of contradictory payoff signals.
Ascending prices, weak β: Mean expectations slope downward with prices, aligning with FEE trend; alignment breaks under strong β (at p=5.99, FEE predicts N=1 but agents expect N≈4).
Descending prices: Convergence improves as prices fall; strong β produces apparent convergence at low prices, but confounded by coinciding incentives rather than rational learning.
Random prices: Convergence fails under both weak and strong β; confirms temporal coherence is necessary.
Qwen-max results consistent with Qwen-turbo (not shown in main text).

Limitations¶

Fixed agent roles only; no hybrid human-AI interaction tested.
Uses only Qwen-family models; generalizability to other LLM families (GPT, Claude, Llama) is unverified.
Controlled synthetic game—real-world data noise and messier payoff structures not evaluated.
Ascending/descending price convergence under weak β conflates history effects with favorable price-incentive alignment; causality is difficult to isolate.
Small game size (n=6 agents) may not scale to realistic network sizes.

Relevance to Harnesses / Meta-Harnesses¶

The paper's core contribution is a workflow harness that structures how historical context is encoded and injected into LLM agents—directly analogous to meta-harness design choices about what state to feed agents and in what order. The finding that temporal ordering of injected history determines agent behavior is critical for any orchestration harness: the sequencing and curation of context passed to sub-agents is not neutral but actively shapes their reasoning and outputs. The "history-as-strategic-variable" framing implies harness designers must treat context injection as a first-class design decision, not a passive relay of facts.