All parties have their own interests that partly overlap.
The Taliban is interested in shifting the pro-Western political government and the establishment of pro-Islamic rule. The US for the Taliban is an enemy who consistently destroys identity. UAV strikes on Taliban positions also contribute to the escalation of violence, as the majority of the victims of these attacks are from the civilian population, including women and children.
The Pakistani authorities want to protect their own regime and allow the Taliban to refocus its activities, including in neighboring Afghanistan.
In Afghanistan, the situation is complicated by the activity of the organization of Jalaluddin Haqqani, known as the Haqqani network. It considers the United States to be a terrorist organization. The Haqqani Network is actively cooperating with the Taliban. The Afghan government is interested in solving this dilemma, but also suffers from excessive pressure from Washington.
China is interested in the establishment of safe corridors - gas and oil pipelines, as well as railway lines, which will be part of the infrastructure project "One belt, one road." Of particular interest to Beijing is a transit route from Gwadar port to the north of Pakistan (Chinese border).
The US pretends that they want to establish a peace process. In fact, for Washington it is advantageous to control the weak government in Afghanistan and Pakistan, so that they follow the will of the White House.
Earlier attempts to settle relations with the Taliban ended in failure, and instead of the peace agreement, a Taliban spring offensive began in several provinces. The security forces had to respond with a counter-attack and reprisals.
The main problem is the presence of representatives of the United States at the negotiating table. The US is interested in strengthening its position in the Rimland, to which Washington will resort to using any measures, including an escalation in tensions. The best option will be the exclusion of US from the negotiation process, as the rest of the parties will not be subjected to pressure from the outside and can come to a common consensus.