A research agreement is a joint science program you create with another friendly civilization.
To unlock this option, first you need to research Education, and then become friends with another player. You (or they) can then offer to enter into a research agreement. To start it, both parties must invest a set amount of Gold based on the era that the more advanced player has reached. After some time, the research is completed and each player receives a bonus to his or her Science output, consisting of an immediate research points boost. The bonus is calculated as 50% of the median Science value for all of the technologies the player can currently research. This bonus can be increased by acquiring the Rationalism Social Policy, or by building the Porcelain Tower Wonder.