Which type of agency arrangement allows both parties to have their own agent while employed by the same brokerage?

The correct choice is designated agency, as it refers to a situation in which a brokerage allows different agents to represent the interests of both the buyer and the seller in a transaction. In this arrangement, each party has their own agent within the same brokerage. This is beneficial as it allows for specialized representation and advocacy for each client's interests while still operating under the same brokerage umbrella.

This arrangement is designed to handle conflicts of interest effectively, ensuring that each agent can act in the best interest of their respective clients. By having designated agents, the brokerage can provide personalized service while adhering to legal and ethical obligations to represent each party fairly.

In contrast, dual agency represents a scenario where a single agent acts for both parties in a real estate transaction, which can lead to conflicts of interest since the agent is tasked with advocating for both sides simultaneously. The other options, deed in trust and delivery and acceptance, pertain to different aspects of real estate and contractual processes, rather than representing an arrangement involving agents. Therefore, designated agency is the correct term that accurately describes the arrangement where both the buyer and the seller have their own agents within the same brokerage.