Nope. A transformer is much more general than that. A GPT predicts the next token.

I don't think this is true. LLM training data almost certainly contains accounts of competitions and other events unfolding. In fact, depending on how the data was filtered, there might be more data of competitions and price wars unfolding than data about game theory.

I would challenge the author to actually task a frontier LLM with simulating a price war and see if it fails, rather than assuming it would. In fact, that would be my feedback on many of these "LLMs can't do X" articles, because often the best models can in fact do X.