This usage is quite natural and grammatically valid. To encourage something among a group is to attempt to persuade the members of the group to adopt the thought or behavior in question.
Some examples:
- To encourage cooperation among the member states in all fields and to recommend related policies to the Supreme Council for approval.
from The GCC and the International Relations of the Gulf by Matteo Legrenzi (2015)
- In 1987, the European Council produced a resolution to encourage cooperation among member states in the field of civil protection. This was followed by a series of Council resolutions and decisions ...
from Explaining EU Internal Security Cooperation by Mark Rhinard and Raphael Bossong (2017)
- Parents encourage cooperation among their offspring, who are siblings of one another. For the same reason, grandparents encourage cooperation among their grandchildren, who include cousins of one another.
from Supernatural and Natural Selection: Religion and ... by
Lyle B. Steadman and Craig T. Palmer (2015)
- ... communicate high expectations was implemented with significantly higher frequency than other principles, and encourage cooperation among students and encourage student-faculty contact were least frequently practiced.
from *The Perfect Online Course: Best Practices for Designing and ...*by Michael Simonson, Terry L. Hudgins, Anymir Orellana (2009) p 97.
- to encourage cooperation among participating states and to facilitate their integration into European structures members
from The CIA World Factbook 2009 - Page 761
- ... non cooperative behavior of peers by adding incentive schemes that discourage the existence of free-riders and encourage cooperation among nodes to share resources in order to increase the total capacity of the P2P system.
from Advances in Communication Systems and Electrical Engineering by He Huang and Yuh-Shyan Chen (2008) p 53
All Examples taken from the results of a Google Books search for "encourage cooperation among", which an Ngram shows as the most frequent result for "encpurage * among".
The OP asks in a comment:
Are there differences between using encourage to and encourage among in this case? –
There is no magic difference, nor is the difference very laege. Let's cconsider some examples:
- (1) I will encourage John to communicate more.
- (2) I will encourage more communication between John and Susan,
- (3) I will encourage more communication among the children
- (4) I will encourage Fred to cooperate more.
- (5) I will encourage more cooperation between Fred and Joan.
- (6) I will encourage more cooperation among the Staff
In (1) the encouragement is directed only at John, and he is being encourages to communicate with anyone.
In (2) the encouragement is directed at both John and Susan, and each i encouraged to communicate with the other.
In (3) all of "the children" are being encouraged, and each is being encouraged to communicate with all of the others.
(4), (5), and (5) correspond closely to (1), (2), and (3).