Rival and non excludable products
To continue the example of the street performer: 

Suppose there are two people offering the performer money, but in exchange they want her to perform different songs. Person A prefers song A while person B prefers song B. Whoever offers the higher sum gets their wish. In this case there is rivalry between the consumers. Yet there is also non-excludability: Even if someone loses the bidding war, they can listen to the song chosen by the other person.

Note that the rivalry results in higher profits than if both people preferred song A played, because then they would have had no incentive to bid against each other due to non-excludability.