There are times to fight. No great startup has been built without getting one's knuckles bloody at times. This is especially true because incumbents now know how much is at stake when they let a startup get a huge head start in a market.
So if you're in a battle, if you're right, if you feel confident you can win -- and, importantly, if the prize for winning is worth the fight -- then go for it. But you should feel confident that all of these conditions are met before fighting, and you should try hard to make your fight as unemotional as possible.
There are times to give in and compromise -- even when you feel you're right.
Perhaps the costs of "winning" the battle aren't worth the consequences. This happens sometimes in lawsuits, where as unpleasant as it sometimes is, you have to chalk up some situations as "not worth fighting." I have seen this in cases where a fight would take the CEO's time and attention away from important business dealings, or where the cost of not settling is huge (like when you can't raise more capital until the dispute is resolved).
It might be that you assess the situation and realize you couldn't win if you were to carry on the fight. This sucks because even when you feel "wronged," there are times where you still aren't going to win if you engage in battle. I've had this at times in dealing with big companies like Facebook and Apple, where we realized that going against the machine was going to be counterproductive. It's a Hobbesian world, and the sooner you realize this the better equipped you are to know how you fit into it.
The key in life and business is to know the difference of when to fight and when not to and not to confuse situations due to emotions or self-righteousness.
I like to tell people: "If somebody has wronged you and you let it eat you up, then you lose twice."
If you decide that your current situation isn't worth fighting, then I recommend you come to emotional peace with that and move on. When you decide give in, do so graciously. Take the high road. Act and feel zen.
Back when I ran my first company I fought a lot. It seemed the world was always on fire and there was some skirmish to be had. I fought with landlords (when the real estate market crashed), venture debt providers (who wouldn't take a haircut when everybody else had to), the board (over compensation), our competitors (over everything) and any service provider who didn't live up to our perceived contract (recruiters, accountants, sales lead companies, web hosting companies).
The longer I was CEO and the more skirmishes I had been through, the more I realized that finding common ground is often better than fighting. My scarcest resource was time and it was important to put my time against the most productive activities. You don't need to sub-optimize your results, but if you can find solutions you should try.
If you give in or compromise and then feel miserable about the outcome and it sours you emotionally, then you've lost twice. Don't get less than you deserve and beat yourself up about it! You can only lose twice if you let yourself give in to anger or resentment.
Also, if you do need to compromise to accommodate somebody you think is acting inappropriately, it's very tempting to fold your cards but then swipe back by saying or writing things you'll regret. If you compromise but then display "sour grapes" to the other party, then you not only didn't get the result you wanted but you've also created ill will with other people -- and you lose twice.
This also applies to internal company decisions. Let's say a senior member of your team demanded a pay increase (cash or equity) and you didn't like the way he or she approached you. Sometimes the right thing is to firmly but politely resist the increase. Sometimes the right thing to do is to give in completely. And sometimes the right thing to do is to compromise. If you do decide to compromise, then don't be snide or mean-spirited about it after the fact. If you're going to give him a victory, then lavish praise on him as you meet his request. There's nothing worse than consenting to the increase and having him feel pissed off about it. You lose twice.
There are many times in life where taking the wrong path causes you to lose twice. Know the difference between fighting (and enjoying it) or giving in, letting go of the angst, and choosing to be zen. So in business when it's time to fight , fight. When it's time to concede or compromise , do so graciously.
But never lose twice.