Daniel invited Nick to his house for a party, which turned out to be a sales pitch for the fitness equipment line that Daniel had recently started selling. Nick didn't need any fitness equipment, but since he was already at Daniel's house and enjoying the complimentary food and drink, he felt obligated to purchase something. Daniel is using the:

rule of reciprocity.

Explanation:

The rule of reciprocity refers to the social norm in which you feel obligated to do something for the person in response to what that person has done something for you. The concept of rule of reciprocation was developed by Robert Cialdini in his book titled "Influence: Psychology of Persuasion."

According to this principle, it is a universal habit in humans that one feels obligated to reciprocate to an act of generosity that has been offered by others either in a form of a material gift or a good deed. The rule of reciprocation is also used as a tool to persuade.

In the given case, Daniel has used the principle of reciprocity. Daniel invited Nick for a party which was nothing but a sales pitch. He offered him complimentary food and in response, Nick felt obligated to reciprocate buy a product from Daniel.

So, the correct answer is the rule of reciprocity.