Is it possible to automatically assign tickets to agents when I use the play button?
When you use the play button, tickets are not automatically assigned to agents.
When an agent clicks Play, the first available ticket in the view opens. If the agent clicks Skip, no update is made on the ticket.
If the agent makes any update on the ticket, you can use triggers to auto-assign the ticket to that agent.
If you want to report on skipped tickets, see the article: Can I report on skipped tickets in Guided mode in Insights?