Below query can be helpful to find users assigned to a specific responsibility
SELECT * FROM ( SELECT DISTINCT user_name , DECODE ( GREATEST (u.start_date , ur.start_date , r.start_date , TO_DATE ('01/01/1000', 'DD/MM/YYYY')) , TO_DATE ('01/01/1000', 'DD/MM/YYYY'), '' , TO_CHAR (GREATEST (u.start_date, ur.start_date, r.start_date))) resp_start_date , DECODE ( LEAST (NVL (u.end_date, TO_DATE ('01/01/4712', 'DD/MM/YYYY')) , NVL (ur.end_date, TO_DATE ('01/01/4712', 'DD/MM/YYYY')) , NVL (r.end_date, TO_DATE ('01/01/4712', 'DD/MM/YYYY'))) , TO_DATE ('01/01/4712', 'DD/MM/YYYY'), '' , TO_CHAR ( LEAST (NVL (u.end_date, NVL (ur.end_date, r.end_date)) , NVL (ur.end_date, NVL (u.end_date, r.end_date)) , NVL (r.end_date, NVL (u.end_date, ur.end_date))))) resp_end_date , s.security_group_name , u.description FROM fnd_user u , fnd_user_resp_groups_all ur , fnd_responsibility r , fnd_security_groups_vl s , fnd_responsibility_tl frt WHERE 1 = 1 AND frt.responsibility_name = :resp_name AND ur.responsibility_application_id = r.application_id AND ur.responsibility_id = r.responsibility_id AND u.user_id = ur.user_id AND ur.security_group_id = s.security_group_id AND frt.responsibility_id = r.responsibility_id AND frt.language = userenv('lang') ) a WHERE Nvl(resp_end_date,sysdate + 1) > sysdate ORDER BY USER_NAME, SECURITY_GROUP_NAME