We propose a coordinated random access scheme for industrial internet-of-things (IIoT) scenarios, with machine-type devices (MTDs) generating sporadic correlated traffic. This occurs, e.g., when external events trigger data generation at multiple MTDs simultaneously. Time is divided into frames, each split into slots and each MTD randomly selects one slot for (re)transmission, with probability density functions (PDFs) specific of both the MTD and the number of the current retransmission. PDFs are locally optimized to minimize the probability of packet collision. The optimization problem is modeled as a repeated Markov game with incomplete information, and the linear reward-inaction algorithm is used at each MTD, which provably converges to a deterministic (suboptimal) slot assignment. We compare our solution with both the slotted ALOHA and the min-max pairwise correlation random access schemes, showing that our approach achieves a higher network throughput with moderate traffic intensity.