Joining and filtering two sets of the same table

I guess this is an easy and stupid question. Consider this MySQL purchase table (where p_id is autoincremented):

+---------+-------------+---------------+---------+
|   p_id  |    item_id  |  user_id      | count   | ... 
+---------+-------------+---------------+---------+
|       1 | 4           |             1 |       22|
|       2 | 4           |             2 |        1|
|       3 | 1           |             1 |        1|
|       4 | 0           |             3 |        1|
|       5 | 3           |             1 |      182|
|       6 | 0           |             4 |        1|
|       7 | 3           |             2 |        7|
|       8 | 3           |             2 |       14|
+---------+-------------+---------------+---------+

What’s an appropriate way (query) to get the rows where the users whose ids are 1 and 2 have purchased the same items, and only retrieved their last purchase of those items?
The result should be something like this:

+---------+-------------+---------------+---------+
|    p_id |    item_id  |  user_id      | count   | ... 
+---------+-------------+---------------+---------+
|       1 | 4           |             1 |       22|
|       2 | 4           |             2 |        1|
|       5 | 3           |             1 |      182|
|       8 | 3           |             2 |       14|
+---------+-------------+---------------+---------+

Assuming:

1. p_id is unique
2. ‘last purchase’ is defined by highest p_id

SQL Fiddle

MySQL 5.5.32 Schema Setup:

create table t(p_id integer, item_id integer, user_id integer, cnt integer);

insert into t(p_id, item_id, user_id, cnt) values(1,4,1,22);
insert into t(p_id, item_id, user_id, cnt) values(2,4,2,1);
insert into t(p_id, item_id, user_id, cnt) values(3,1,1,1);
insert into t(p_id, item_id, user_id, cnt) values(4,0,3,1);
insert into t(p_id, item_id, user_id, cnt) values(5,3,1,182);
insert into t(p_id, item_id, user_id, cnt) values(6,0,4,1);
insert into t(p_id, item_id, user_id, cnt) values(7,3,2,7);
insert into t(p_id, item_id, user_id, cnt) values(8,3,2,14);

Query 1:

select *
from( select *
      from t tt
      where user_id=1 and p_id=( select max(p_id)
                                 from t
                                 where user_id=1 and item_id=tt.item_id )
      union all
      select *
      from t tt
      where user_id=2 and p_id=( select max(p_id)
                                 from t
                                 where user_id=2 and item_id=tt.item_id ) ) u
where item_id in(select item_id from t where user_id=1)
      and item_id in(select item_id from t where user_id=2)

Results:

| P_ID | ITEM_ID | USER_ID | CNT |
|------|---------|---------|-----|
|    1 |       4 |       1 |  22 |
|    5 |       3 |       1 | 182 |
|    2 |       4 |       2 |   1 |
|    8 |       3 |       2 |  14 |

For lack of information, I make the same assumptions as @Jack:

1. p_id is unique.
2. ‘last purchase’ is defined by highest p_id.

SELECT t.*
FROM   t
JOIN  (
    SELECT min(p_id) AS p_id1
          ,max(p_id) AS p_id2
    FROM  (
        SELECT user_id, item_id, max(p_id) AS p_id
        FROM   t
        WHERE  user_id IN (1,2)
        GROUP  BY user_id, item_id
        ) sub1
    GROUP  BY item_id
    HAVING count(*) = 2           -- for two user_ids
    ) sub2 ON t.p_id = sub2.p_id1
           OR t.p_id = sub2.p_id2
ORDER  BY t.p_id;

-> SQLfiddle demo.

This form avoids correlated subqueries, which should therefore perform better. It works well for two IDs at a time, but not for more.

Could be much simpler if MySQL supported CTEs or window functions like other modern RDBMS. Or even DISTINCT ON (Postgres specific).

The query that you are looking for, might be similar to this:

SELECT 
    pp1 . *
FROM
    (SELECT 
        *
    FROM
        (SELECT 
        *
    FROM
        purchase
    WHERE
        user_id IN (1 , 2)
    ORDER BY p_id DESC) pp
    GROUP BY pp.user_id , pp.item_id
    ORDER BY pp.p_id) pp1
        INNER JOIN
    (SELECT 
        *
    FROM
        (SELECT 
        *
    FROM
        purchase
    WHERE
        user_id IN (1 , 2)
    ORDER BY p_id DESC) pp
    GROUP BY pp.user_id , pp.item_id
    ORDER BY pp.p_id) pp2 ON pp1.item_id = pp2.item_id
        AND pp1.user_id != pp2.user_id
ORDER BY pp1.p_id;