First things first: the AI has a clear double-standard in this game.  It's very quick to ally with other AI's, but it takes a lot of time and effort for the human player to achieve the same thing.  As a result, particularly on these kinds of small maps, the game very quickly turns into "all the AI's against the human".  Not to say that it's impossible to win a 2v1, but that's basically what the situation is going to become.  I personally play with locked teams.

Secondly: avoid hangers, they're practically worthless for Advent (at least on small maps like these).  The problem is that you need tactical upgrades on each planet you want to place hangers, which just gets way too pricy.  If you need to beat back siege frigates, use scouts.  You'll have to use a few command points, but it's way less expensive than hangers.

Your first priority should be to capture those two nearby asteroids and start grabbing the neutral extractors.  The planet next to your homeworld is of random type.  If it's an ice or volcanic, you're probably best to ignore it.  Not worth getting two labs just to access one planet, better to shore up your fleet and push your enemies.  Given that this is a free for all scenario, you'll probably want to get a second capital ship relatively early to keep one on the offensive and one on the defensive.

My approach to this map would be to get a Progenitor as my first capital ship.  I'd clear my initial asteroid, then send it clockwise towards the nearest enemy's asteroid to grab this early.  While my Progen gets to work, I'd send a few disciples and a missionary to grab my own second asteroid.  I'd put up two labs to access repair bays and start grabbing neutrals, but otherwise at this point I'd hunker down for a while to get a second capital ship and illuminators.  If the enemy gets strike craft, I'd also add flaks.

Make a decisive push, and I'd imagine you could get enough momentum to defeat both AI's.  Once the first one falls, you can just pincer the second for a very quick kill.

i'll give you my start off for a defencive formation :

Halcyon, Radiance, 3 hostilitys (scuttle cap fact for the third on hw), illum research, repair bay research, missionary

go for roid colonise, defend, slaughtr, build illum spam ^^

all that aint in order but thats almost all ^^

Holding those asteroids is a top priority.  However, I'm surprised the AI was attacking you before you had the desert locked down.  The AI is usually very slow to start attacking.

Yeah, 2 turrets, placed adjoining (touching) both sides of a roid, is an very effective (and adequate) defense against the AI's seige attacks.

I too, initially had trouble with this map, and discussed detailed steps to winning it in an old thread about Centrifuge.  I am sure that you will find helpful information there, but remember this discussion was befor Quick Start, and other upgrades.

The 49% loyalty means you must have hurt (killed) one the TEC's ships (a scout?).  Avoid attacking a potential ally at all cost.  You need the ally to win this map.  Correcting that simple mistake, may be all it takes to win.  Suprisingly, sometimes a slower/weaker start will give you a better chance of allying.  Because the AI's veiw you as less of a threat! 

Good Luck.

I, like almost all multiplayer gamers, play on random maps.  I have to analyze the map immediately as I scout it to determine what my strategy will be.  One of the first things I do is look for the distance to my nearest enemy, and this dictates how much I should spend on military tech.

This is more of a guideline rather than a rule.  If I'm 2 jumps from an enemy, but the planet between us is a desert with massive amounts of militia, that's probably going to prevent an early rush.  On the other hand, a chain of three asteroids between us might give a 4-jump distance, but the massive priority of those asteroids is going to force me to play extremely aggressively.

With that disclaimer, here's my guideline:

1-2 jumps:  All military, don't spend a penny on anything that isn't going to have an immediate impact on the fight.  Unless you're specifically pursuing a double-cap strategy, you should scuttle your capital ship factory after you're done with it.  Every penny counts.  You do not have time to colonize planets other than asteroids in this very dangerous situation.

3-4 jumps:  You should be putting the vast majority of your income into military tech.  You do have some leeway for non-military investment, but it should make up only a tiny fraction of your total expenditure.  Building civic labs to access ice/volcanic planets is a major risk here; it can pay off, but you have to be very careful when doing this since you won't have repair bays or higher tech units for some time.

5-6 jumps:  This is a reasonable distance where you can realistically pursue an economic strategy.  However, you have to be aware of your enemy and be prepared to defend yourself.  That means identifying and claiming choke points early, and also keeping active scouts in between your empires to know if he's heading towards you.  You're still close enough to rush, so you need to be ready with a military or at very least the capacity to produce one on very short order.

7-8 jumps:  In these positions, it's very difficult to rush and chances are an economic lead is the important thing to build here.  You can very safely pursue civic labs and try to colonize a large number of planets.  However you must be conscious of where your enemy is and when he intends to strike.  Any rush is going to be delayed just by distance, but it's still entirely feasible for an enemy to attack early on and hit you before you're ready.  In fact, many players are all the more vulnerable because they think it's safe to go all-out on their economy, and then have nothing to stop an attacker.

9+ jumps: This is an extremely rare scenario, but at these distances it's practically impossible to rush.  It's safe to go straight for economic techs and build up a stronger foundation.  You always have to be cautious of the enemy trying an aggressive ploy, but he's going to have a lot of trouble getting in position to do this early on.  Chances are he won't try that (at least until later...) and instead will focus on building up himself.  The one thing to be careful about is that in this scenario it's actually very easy to have heavy cruisers ready for the first major fight, so you have to scout and know what's coming so you have the counters researched.

As has already been mentioned, the AI has a double-standard when it comes to making friends with other AI's or the player.  On smaller maps in particular, this can quickly become a case of "everyone gang beat the player".  Basically, you need strategies on how to handle a 2v1 situation, not on how to deal with the map configuration (though some maps are easier to handle 2v1's on than others).

My approach to this kind of situation would probably be to starbase one side of my empire (asteroids work best) then throw all my fleet on the other side to try and kill that neighbour, then try to keep some momentum and wipe out each in succession.

I had a battle against 7 unfairs on "Grindstone" over the course of the week, and this was pretty much my strategy.  I rushed my nearest opponent and wiped him out, then swung around and beat the guy who'd snuck up behind me, captured a planet from him and starbased it (creating a nice choke) and then turned around and cleared every remaining player in succession.