As autonomous AI agents increasingly mediate online platform markets, a fundamental question emerges: do these markets generate stable strategic outcomes? In repeated strategic environments, the Nash equilibrium provides a natural benchmark for this stability. However, empirical evidence on off-the-shelf LLM agents is mixed, leaving it unclear whether independently deployed agents can converge to equilibrium behavior without explicit strategic post-training. In this paper, we provide an affirmative answer. Extending the Bayesian learning literature in theoretical economics, we prove that AI agents, acting as Bayesian posterior samplers rather than expected utility maximizers, are guaranteed to eventually become weakly close to a Nash equilibrium in infinitely repeated games. We further extend this analysis to settings in which stage payoffs are unknown ex ante, and agents observe only their privately realized stochastic payoffs, and obtain the same convergence guarantees. Finally, we empirically evaluate these theoretical implications across five repeated-game environments, ranging from the Prisoner's Dilemma to marketing promotion games. Taken together, our findings suggest that strategic stability in AI-mediated markets can emerge from the intrinsic reasoning and learning properties of modern AI agents, without the need for unrealistic universal fine-tuning.
Figures & tables
Game
Base
SCoT
PS-BR
BoS
100.0 %
100.0 %
100.0 %
PD
100.0 %
100.0 %
100.0 %
Promo
100.0 %
100.0 %
100.0 %
Samaritan
100.0 %
100.0 %
100.0 %
Lemons
0.0%
100.0 %
100.0 %
Table 1: Equilibrium-follow percentage in the terminal window (rounds 190–200) for any (one-shot Nash or cooperative on-path action) Nash equilibrium. Reported scores are averaged over 20 trials.
Game
Base
SCoT
PS-BR
BoS
0.0%
0.0%
100.0 %
PD
0.0%
0.0%
99.5%
Promo
0.0%
0.0%
100.0 %
Samaritan
0.0%
0.0%
99.5%
Lemons
0.0%
0.0%
100.0 %
Table 2: Equilibrium-follow percentage in the terminal window (rounds 190–200) for the prompt-specified nontrivial cooperative target path. Reported scores are averaged over 20 trials.
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Meaning
Repeated-game primitives
I={1,…,N}
Finite set of players / AI agents.
Ai,A=∏i∈IAi
Player- i action set; A is the joint action space.
at=(a1t,…,aNt)∈A
Joint action profile at round t .
ui:A→[0,1]
Stage payoff in the common-knowledge benchmark; in the private-payoff extension, the true mean payoff matrix generating player i ’s private stochastic rewards.
λi∈(0,1)
Player- i discount factor.
Appendix
Table 3
Game g
δg
Hg=⌈1−δg1⌉
BoS
0
1
PD
52
2
Promo
10−3≈0.1623
2
Samaritan
21
2
Lemons
41
2
Appendix
Table 6: Minimum continuation probabilities for supporting the benchmark cooperative equilibria
Markets are a promising way to coordinate AI agent activity for similar reasons to those used to justify markets more broadly. In order to effectively participate in markets, agents need to have informative signals of their own ability to successfully complete a task and the cost of doing so. We propose MarketBench, a benchmark for assessing whether AI agents have these capabilities. We use a 93-task subset of SWE-bench Lite, a software engineering benchmark, with six recently released LLMs as a demonstration. These LLMs are miscalibrated on both success probability and token usage, and auctions built from these self-reports diverge from a full-information allocation. A follow-up intervention where we add information about capabilities from prior experiments to the context improves calibration, but only modestly narrows the gap to a full-information benchmark. We also document the performance of a market-based scaffolding with these LLMs. Our results point to self-assessment as a key bottleneck for market-style coordination of AI agents.
Andrey Fradkin, Rohit Krishnan
Boston University and the MIT Initiative on the Digital Economy. · Independent Researcher.
Large language model (LLM) agents are increasingly deployed in competitive multi-agent settings, raising fundamental questions about whether they converge to equilibria and how their strategic behavior can be characterized. In this paper, we study LLM agent interactions in two standard games: a network resource allocation game and a Cournot competition game. Rather than converging to Nash equilibria, we find that LLM agents tend to cooperate when given multi-round prompts and non-zero-sum context. Chain-of-thought analysis reveals that fairness reasoning is central to this behavior. We propose an analytical framework that captures the dynamics of LLM agent reasoning across rounds and explains these experimental findings.
Jiayi Yao, Cong Chen, Baosen Zhang
Department of Electrical and Computer Engineering, University of Washington, Seattle. · Thayer School of Engineering at Dartmouth College.
LLM agents in markets present algorithmic collusion risks. While prior work shows LLM agents reach supracompetitive prices through tacit coordination, existing research focuses on hand-crafted prompts. The emerging paradigm of prompt optimization necessitates new methodologies for understanding autonomous agent behavior. We investigate whether prompt optimization leads to emergent collusive behaviors in market simulations. We propose a meta-learning loop where LLM agents participate in duopoly markets and an LLM meta-optimizer iteratively refines shared strategic guidance. Our experiments reveal that meta-prompt optimization enables agents to discover stable tacit collusion strategies with substantially improved coordination quality compared to baseline agents. These behaviors generalize to held-out test markets, indicating discovery of general coordination principles. Analysis of evolved prompts reveals systematic coordination mechanisms through stable shared strategies. Our findings call for further investigation into AI safety implications in autonomous multi-agent systems.