Persistent Partners Raise Prices Among Learning Agents

Paul-Peter Arslan, Yubin Kim, Xiao Xiao

When pricing agents meet repeatedly on a platform, the platform decides who faces whom. We ask whether that choice moves the prices the agents learn, and whether a rise comes with learned punishment. In a pre-registered randomised experiment in the Bertrand duopoly of Calvano et al., each agent's price is set by a tabular Q-learning module, not by the small language model attached to it, and we randomise whether each agent keeps its partner, sees its rival's prices and can send messages. Keeping the same partner raises the level of profits, averaged over training, by 0.27 of the gap between competitive and monopoly profit (95% CI 0.20 to 0.35, all twenty paired runs positive), our registered primary result, and the resting price by 0.17 of the Nash-to-monopoly range (post hoc). A plain tabular learner reproduces the effect in all 25 further blocks, and there one permanent partner raises the level more than about three do (+0.23 against +0.05, exploratory). Where rival prices are hidden, the price-setting module cannot see a cut, so cannot punish it, yet the resting price rises as much and the rise lasts to the end of training, while with visible rivals it shrinks with longer…