In an ultimatum game, the responder must decide between pursuing self‐interest and insisting on fairness, and these choices are affected by the intentions of the proposer. However, the time course of this social decision‐making process is unclear. Representational similarity analysis (RSA) is a useful technique for linking brain activity with rich behavioral data sets. In this study, electroencephalography (EEG) was used to measure the time course of neural responses to proposed allocation schemes with different intentions. Twenty‐eight participants played an ultimatum game as responders. They had to choose between accepting and rejecting the fair or unfair money allocation schemes of proposers. The schemes were offered based on the proposer's selfish intention (monetary gain), altruistic intention (donation to charity), or ambiguous intention (unknown to the responder). We used a spatiotemporal RSA and inter‐subject RSA (IS‐RSA) to explore the connections between event‐related potentials (ERPs) after offer presentation and intention presentation with four types of behavioral data (acceptance, response time, fairness ratings, and pleasantness ratings). The spatiotemporal RSA results revealed that only response time variation was linked with the difference in ERPs at 432–592 ms after offer presentation on the posterior parietal and prefrontal regions. Meanwhile, the IS‐RSA results found a significant association between inter‐individual differences in response time and differences in ERP activity at 596–812 ms after the presentation of ambiguous intention, particularly in the prefrontal region. This study expands the intention‐based reciprocal model to the third‐party context and demonstrates that brain activity can represent response time differences in social decision‐making.