SQLite3 multiple primary key fields with autoincrement (rails project) - mysql

Question

I'm trying to create a SQLite3 database for use with a Rails application.
I have the same database created already in MySQL and am trying to replicate the same in SQLite3.
The create syntax for MySQL is
CREATE TABLE `leaderboard_A` (
`league` tinyint(1) NOT NULL,
`id` bigint(10) NOT NULL,
`cut` tinyint(1) NOT NULL,
`wd` tinyint(1) NOT NULL,
`tie` tinyint(1) NOT NULL,
`pos` int(4) NOT NULL,
`pos_s` varchar(10) COLLATE utf8_unicode_ci NOT NULL,
`name` varchar(128) COLLATE utf8_unicode_ci NOT NULL,
`to_par` smallint(3) NOT NULL,
`to_par_s` varchar(5) COLLATE utf8_unicode_ci NOT NULL,
`hole` varchar(8) COLLATE utf8_unicode_ci NOT NULL,
`round` smallint(6) NOT NULL,
`round_s` varchar(8) COLLATE utf8_unicode_ci NOT NULL,
`round_1` int(11) NOT NULL,
`round_2` int(11) NOT NULL,
`round_3` int(11) NOT NULL,
`round_4` int(11) NOT NULL,
`total` smallint(4) NOT NULL,
`tournament_id` varchar(13) COLLATE utf8_unicode_ci NOT NULL,
`tournament_name` varchar(255) COLLATE utf8_unicode_ci NOT NULL,
`year` smallint(4) NOT NULL,
PRIMARY KEY (`league`,`id`,`tournament_id`),
KEY `pos` (`pos`),
KEY `player_key` (`name`,`tournament_name`,`year`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 COLLATE=utf8_unicode_ci;
I believe I need to have an ID column added in for my SQLite3 schema.
Is it possible to have an autoincrement column in my SQLite3 aswell as making other columns primary too?
I have some SQLite3 SQL written already with just a slightly different column setup as below.
CREATE TABLE IF NOT EXISTS Leaderboard (
id INTEGER,
current_position TEXT,
current_round INTEGER,
country TEXT,
is_amateur BOOLEAN,
first_name TEXT,
last_name TEXT,
name TEXT,
player_id INTEGER,
round1 INTEGER,
round2 INTEGER,
round3 INTEGER,
round4 INTEGER,
start_position TEXT,
status TEXT,
thru INTEGER,
today INTEGER,
total INTEGER,
tournament_name TEXT,
tournament_id INTEGER,
start_date datetime,
end_date datetime,
year INTEGER,
PRIMARY KEY (id, player_id, tournament_id, year)
)
My eventual solution is to read in a JSON record and update the details if it exists and if not create the record using the SQL below
INSERT OR REPLACE INTO Leaderboard (
current_position, current_round, country, is_amateur, first_name, last_name, name, player_id, round1, round2, round3, round4, start_position, status, thru, today, total, tournament_name, tournament_id, start_date, end_date, year)
VALUES
('1','4','USA','false','Jordan','Spieth','Spieth, Jordan','34046','68','67','71','69','T1','active','18','-1','-78','US Open','026','2015-06-18','2015-06-21','2015')
Any feedback, suggestions or fixes would be appreciated. New to working all this out. :)