It's is possible to assign test case execution of same test case to several users.
This has been design to be consider an OR mode assignment.
Example
Testers: Nick Fury, Professor X, Captain Kirk
You assign execution Task for: Test Case Z-00
On: Test Plan PLAN-A , Build 01 (Test Plan + Build = Execution Context).
To: Nick Fury, Captain Kirk (any of them can execute, but TestLink does not force both to execute the test case)
If Nick Fury access the execution features and set filter 'Assigned To me': he will get Test Case Z-00
Same happens to Captain Kirk.
If Captain Kirk executes, any report that display effective tester (who has written the result) will show Captain Kirk.
If Nick Fury re-execute the same test case , report will show him as effective tester.
Key concept is EXECUTION CONTEXT
Exec context is composed by: TEST PLAN, BUILD & PLATFORM (if any has been assigned to Test Plan).
An execution instance is created for each Execution context, that's why when you use Platforms (say you have 3) you can EXECUTE SAME TEST CASE
and display 3 indipendent results.
This is not going to happen when you assign multiple testers to a test case.
Only way to display execution done by Nick Fury & Captain Kirk as different and 'same category execution' on a Test Plan are:
1. create a build for each User
2. create a Platform for each user
an then you have to assign ONLY ONE USER for test execution on a test case