Yes, in Resources > Reservation process you can configure automatic cancellations either when not enough payments were received within specified time or if not enough participants signed up for a trip (or whatever the resource represents). Below are all the options that must be configured in the resource settings in order for the automatic cancellations to work.

Resources > General info

Resource sharing - set this to Always possible
Number of clients this resource can be shared between - set this to the max. number of participants

Once the general info settings are set correctly, configure the reservation process settings as follows:

Resources > Reservation process

Automatically cancel reservations set to if less than X units were reserved within specified time
...entered by - here you can differentiate between reservations entered by the customers and also reservations made by your agents or administrators, so e.g. you can tell Planyo never to cancel admin-created reservations
Time when reservations are checked for auto-cancellation - this can be relative to the time when the reservation was created but in this case it makes sense to set it to X days before the rental (trip) takes place

Once you have the automatic cancellations configured, it's good to also configure the email/sms notification that will go out to the customers who made the reservation that gets cancelled automatically. As with all other notifications, go to Site settings > Notifications to configure them (see this tutorial for the details). Of course the admins can also receive this notification.