With this being an economics course one of my favorite examples of a principle comes from the financial sector. A stock broker or any other type of asset manager is a principle with two agents the client and the firm.
The asset manager's job is to increase profits for the firm and increase the return on investment for the client. More often than not these two goals can be accomplished together but there are specific times when the two aims will conflict. Usually when there is a conflict the goal to increase profits for the firm supersedes the needs of the client.
For example, in many brokerage firms the firm makes a profit from the volume of trades brokers are able to produce. This may lead to conflict because the client will lose money for each trade and unlike the firm there are no guarantees that there will be a return. On top of that the broker can justify his actions by claiming that he had the best interest of the client in mind. the broker would fail one agent by focusing too much on the other.
A possible resolution for this conflict is to have the same measure of performance for both principles, and bring any competing incentives inline. So, instead of the firm earning profit from trade volume and the client earning profit from returns, the client and the firm could split the returns and eliminate the fee for each trade. If the firm was only give a percentage of the clients return the goals of the brokers would simply be to increase the return on investment and there would be no conflicting incentives to favor one principle over the other.
I am confident that many brokerage firms would not be willing to have a performance scheme quite like this but there may also be other paths to resolving conflicts. The firm could set limits on trade volume to reduce risks for the clients or provide incentives to its brokers for maximizing client returns and not just trades.