How would you set-up a cooperative (non-competitive) working arrangement between 2 UA Teams?

Put the budget into one pool. Don't even attempt to work with the UA agency. This never works for the simple fact that incentives are not the same.

I have seen this situation in the wild twice as a consultant, and I’d advise you to do whatever you can to AVOID having two teams working on UA for the same app and to consolidate the budget with just one team.

A situation like this is basically unworkable unless each team operates in a distinct set of geographies. Doing that, you’d avoid overlapping targeting, but it’s still not an efficient way to work. In 2019, there is no reason to not have the UA team operating globally (obviously with some specific care taken to localize and culturalize creatives).

Here are some reasons that a configuration like this is difficult to make work:

• As you said, if you are operating in the same geographies, you’ll be competing against each other and driving up the cost of CPMs. You’ll also probably be delivering different creatives to the same people, confusing / muddying your messaging;
• You won’t be able to use view-through attribution in this setup — it simply won’t work;
• If both teams are spending their own money, then both teams will likely be running their own measurement and evaluating the traffic they buy against their own ROAS models. This isn’t a tenable workflow: what do you do if one team is more conservative about payback windows than the other? Or one includes organic contribution into LTV and one doesn’t? This is a disaster;
• If the budgets are dramatically different then you’ll run into performance conflicts. Let’s say Team A has a budget of $50k / month and Team B has a budget of $5MM / month. Team A could buy more profitable traffic in isolation (ie. if their money was the ONLY money buying traffic for the app), but with Team B doing media buying, the cost of traffic for that title is likely to be much higher on average, making Team A’s contribution less meaningful. You have to consider what the incremental impact of both teams’ spend is in the context of the total — if there’s a large differential, it might not make sense for the smaller budget to be deployed separately.