Static network structure cannot stabilize cooperation among Large Language Model agents

TL;DR

This study examines networked interactions where agents repeatedly engage in the Prisoner’s Dilemma within both well-mixed and structured network configurations, aiming to identify parallels in cooperative behavior between LLMs and humans.

Abstract

Large language models (LLMs) are increasingly used to model human social behavior, with recent research exploring their ability to simulate social dynamics. Here, we test whether LLMs mirror human behavior in social dilemmas, where individual and collective interests conflict. Humans generally cooperate more than expected in laboratory settings, showing less cooperation in well-mixed populations but more in fixed networks. In contrast, LLMs tend to exhibit greater cooperation in well-mixed settings. This raises a key question: Are LLMs about to emulate human behavior in cooperative dilemmas on networks? In this study, we examine networked interactions where agents repeatedly engage in the Prisoner's Dilemma within both well-mixed and structured network configurations, aiming to identify parallels in cooperative behavior between LLMs and humans. Our findings indicate critical distinctions: while humans tend to cooperate more within structured networks, LLMs display increased cooperation mainly in well-mixed environments, with limited adjustment to networked contexts. Notably, LLM cooperation also varies across model types, illustrating the complexities of replicating human-like social adaptability in artificial agents. These results highlight a crucial gap: LLMs struggle to emulate the nuanced, adaptive social strategies humans deploy in fixed networks. Unlike human participants, LLMs do not alter their cooperative behavior in response to network structures or evolving social contexts, missing the reciprocity norms that humans adaptively employ. This limitation points to a fundamental need in future LLM design -- to integrate a deeper comprehension of social norms, enabling more authentic modeling of human-like cooperation and adaptability in networked environments.

Figures (7)

• Figure 1: Illustrating the networked interactions in an eight-node network, with the degrees $k=2,4,6$ in panels A, B, and C, respectively. The convention of using so-called circulant graphs to represent static networks follows Ref. rand.
• Figure 2: Two example experiments with GPT-3.5. The parameter settings are $k=2$ and $b/c=6$. The position around the circle corresponds to the identity of the node. In panel A, the interactions are well-mixed. In panel B, neighbors along the perimeter interact with each other.
• Figure 3: Comparing networked and well-mixed topologies for humans (panel A, adapted from Ref. rand2014static), GPT-3.5 (panel B), and GPT-4 (panel C). All AI values are averaged over five independent runs of the experiments. The shaded regions represent the one-standard error confidence bands.
• Figure 4: Average cooperation levels for GPT-3.5 (panels A, B, and C) and GPT-4 (panels D, E, and F). A and D give our results for the sparsest networks ($k=2$), B and E show results for $k=4$, and C and F give results for $k=6$. The shaded regions represent one-standard-error confidence bands. The AI curves are averaged over 25 players and 5 realizations of the experiments. The human curves involve, on average, $24.2$ players.
• Figure 5: Cooperation level after 15 rounds as reported in Ref. rand2014static for humans A, compared to AI: GPT-3.5 and GPT-4, respectively. The colors represent the three theoretically distinct classes $b/c< k$, $b/c= k$, $b/c> k$, respectively. The first number on the bars indicates $b/c$, whereas the second number represents $k$ (so $2<4$ means $b/c=2$ and $k=4$).