Multi-party dialogue machine reading comprehension (MRC) brings tremendous challenge since it involves multiple speakers at one dialogue, resulting in intricate speaker information flows and noisy dialogue contexts. To alleviate such difficulties, previous models focus on how to incorporate these information using complex graph-based modules and additional manually labeled data, which is usually rare in real scenarios. In this paper, we design two labour-free self- and pseudo-self-supervised prediction tasks on speaker and key-utterance to implicitly model the speaker information flows, and capture salient clues in a long dialogue. Experimental results on two benchmark datasets have justified the effectiveness of our method over competitive baselines and current state-of-the-art models.