The Y'Ing High Command will want to induce the Y'Ang to not attack. After all, you can't lose the fights that you don't engage in and the best wars are the ones where you don't have to fight. That said, the price of this war will be trillions of deaths and the destruction of entire star systems. There are four options for how this Cold War will end: It will continue as it is, it will detente without bloodshed, it will escalate and burn the galaxy, or the two empires decide that it's easier to just merge.
- Preserve political autonomy
- Preserve population
- Preserve industrial capacity
- Remove political autonomy from the Y'Ing.
- Preserve population
- Preserve industrial capacity
This could turn into a Dune-style War of Assassins where there need be no bloodshed of the common people but a lot of the empire leadership dies. Given the extreme costs of open conflict, empire leadership may decide that this is the best course. For the lives of the quadrillions of citizens of each empire, I hope they choose this path.
Establish screening pickets along the border and significantly above and below the galactic plane (don't want the Y'Ang to cheat and just go off-plane to avoid detection) There's enough population and industrial capacity to completely saturate all space with redundant detection posts. Extend these listening posts into Y'Ang territory as well. Replace listening posts as the Y'Ang detect and destroy them.
Saturate the Y'Ang Political and Military Organization with Spies/Informants
Knowing when a Y'Ang fleet departs from dry dock is a significant advantage when planning counter-movements. Any kind of positional information on enemy fleet or troop dispositions will help immensely.
Develop a "Nuclear" Triad
Develop the equivalent of nuclear submarines, bombers and ICBMs (heh, they'd be IGBMs, Inter-Galactic Ballistic Missiles). The threat of overwhelming force should make the Y'Ang think twice before launching an attack.
IGBMs - Position autonomous "nuclear" warheads near strategic targets. With the industrial capacity of the Y'Ing, it's possible to build thousands or IGBMs for each target.
Bombers - Position significant attack resources off the galactic plane with orders that if war broke out, they are to attack their targets.
Submarines - highly capable but small fleets of attack ships, each ship capable of glassing a planet, that constantly patrol through Y'Ang space without making threatening moves against any particular Space is huge so catching these patrols will be incredibly difficult.
Command and Control Structures
Trying to manage a naval fleet containing one billion Super Star Destroyers plus billions of support craft can't be done by one human. This many SSDs is only two orders of magnitude away from the number of cells in the human brain. Including support craft, the number of ships in the navy is the number of brain cells in the human brain.
The only solution to this is to automate everything about fleet command and logistics. I can't imagine the compute or storage resources required to do this but it's going to make the combined might of AWS, Google Compute Platform and Microsoft Azure seem like pet projects that junior engineers do as warmup projects.
But, luckily, the Y'Ing and the Y'Ang have had centuries to advance their distributed computing prowess and Strong AI. It's entirely possible that there will be no human commanders at all, just AIs.
Pour as much money as possible into FTL Interdiction fields. Mobility is the key to winning most any conflict. If you deny your enemy the ability to move, you make them that much easier to find and to kill. Without interdiction fields, there's nothing to stop an IGBM from popping out of FTL right on top of your industrial bases and political centers with zero warning.
Make it in the best interests of the Y'Ang businesses not to attack the Y'Ing
If your business depends heavily on trade with the opposing empire, you'll be highly motivated to pressure your politicians to avoid armed conflict. The greater the financial and business relationships between the two empires the greater the resistance to any conflict that will disrupt those relationships.
As the Y'Ang chief executive will find, (s)he won't stay in power long if many major trade unions withdraw their support or start to actively undermine your administration.
Two billion known systems. All systems are known to both sides. All major planetary industrial centers known. Significant mobilized orbital industry.
Ring shaped battlefield, no one goes through the center.
Each battleship has a crew of ~50,000. Assuming that support staff is 8x the ship crews (assumes higher because of the greater complexity of space fleets.) This means that there are 50 trillion sailors in the Y'Ing navy on just the Super Star Destroyers. The naval support staff is 400 trillion people. Earth's infantry requires between 5x and 6x people for each infantryman.
USA military is about 1.8 million compared to 318 million. 0.5% of population is in the military. Estimated population of the Y'Ing empire is 1e+16 people or 1 quadrillion people. 1 quadrillion people.
Imperfect information game state, no one knows everything about all the pieces.
Mixed Industrial Mobility - Most planetside industrial capacity will be static. Reasonable to assume that orbital industrial facilities can be moved, given that there are a billion 1.6Km long battleships on each side.
First, this is unthinkably huge industrial capacity. On Earth in WW2, the US made approximately 47 billion bullets. That's only 47 times more things than the number of kilometer long battleships this civilization has made. Their bullet making capacity is in the quadrillions of bullets, easily.