Or team B's army will move from 3 to 2, team's A army at 2 will be dislodged and team A's army will move from 1 to 3

I do not believe units can exchange places without use of a convoy order. Due to this I believe everyone would bump at the boarder and return home.

Barn3tt is right: 3 dislodges 2 and one moves to 3.

Barn#tt is correct. Here's why:

Team B's army move 3 to 2 is successful with support from Army 4 (since Army 4's support is not cut).
Team A's army 2 is dislodged and forced to retreat/disband (and actual "support" of Army 1 move to 3 is unsucessful). However Team A army 1 still succeeds in moving to 3 because that space was voluntarily vacated by Team B.

Yep, Barn3tt is correct. The confusion is people thinking the two moving units were moving against each other, which they are not. 1 is moving to 3 and 3 is moving to 2. 2 is dislodged and can retreat to 1 or any other spot it could have moved to unsupported.

Edit, 2 could only retreat to 1 if 2 and 1 were adjacent. In my head they were, but that was unspecified, sorry.

The dislodged unit from 2 can retreat to any spot that it could have moved unsupported during the movement phase.

Guys, thank you all! It's clear now.

I was hoping this was going to be one that I've wondered about many times. It's only a slight modification to the OP with are 4 being attacked instead of are 3

There are 4 areas: 1,2,3,4, team A occupies 1 and 2, team B - 3 and 4.
Team A moves: Army at 1: move from 1 to 4; Army at 2: support move from 1 to 4 Team B moves: Army at 3: move from 3 to 2; Army at 4: support move from 3 to 2.

In this variation both of the supporting units are being attacked by the other. I see this a lot when I'm grunge to figure out possibilities, but so far the other player hasn't made the moves for me to know for sure.

I think I know what the result would be, but i'd like to hear from the more experienced players.

The possible contradictions are a dislodged unit has no effect, and a unit that is hit has its support broken. In this case, each supporting unit is being double attacked with no support holds, so which rule wins (or is applied first) and what is the outcome?

Are= Area. & grunge=trying

Both supports are cut, so nothing moves.

You can try it out using jDip or realpolitik which you can download from sourceforge.net.

http://sourceforge.net/projects/jdip/
http://sourceforge.net/projects/realpolitik/

Both supports are not cut. A(3)'s support by A(4) remains. So, A(2) is dislodged.

ex: A(Gal) supported into Budapest by A(Rum). A(Bud) supports A(Vie) to Gal.
Result: A(Bud) dislodged. A(Vie) proceeds to now vacated Gal.

By the way, the rulebook on page 9 (http://www.wizards.com/avalonhill/rules/diplomacy.pdf) says:

"A dislodged unit, even with support, has no effect on the province that dislodged it."

and

"A dislodged unit can still cause a standoff in a province different from the one that dislodged it."

So those rules don't really apply to the scenario you put forth.

@Barn3tt, I was responding to philcore's tweaked scenario in which 1 cuts 4 and 2 cuts 3. So both are cut.

For example, A Rum S Gal-Bud and A Bud S Ukr-Rum.

Yup- didn't see that Philcore had a modified questions. Standoff all around.

my bad

Ok that's what I thought. Thanks brn3ttt and alderain.

And thanks for the links, ill have to check those out.