Not Giving Kids a Birthday Party??

So two years ago my ex and I separated. He's still super bitter and refuses to communicate unless it's through a lawyer. So anyways, the past two years come birthday time we both have been having individual parties for our kids.

However I feel its unnecessary and this year, I attempted to communicate and ask my ex husband what his plans were concerning a party for our oldest, and he never replied. I assumed he wouldn't be doing much, and went ahead and told my daughter she could have a movie and popcorn party at the theater with 6 friends. It was fun, but expensive! Easily $500 not including her gift.

So, two weeks later, my ex throws my daughter ANOTHER party. Which is fine, EXCEPT he told her to invite her WHOLE CLASS. Yes, he knew about the party I threw. So now my kid is known as some sort of double dipper gift grabber and both her parents look stupid. Not only did he invite the whole class (even the kids invited to the last one), he ordered a custom cake and special venue, bouncy castles, face painting, the works! Easily a $2000 party.

I feel as though my ex always tries to compete and show me up, whether it be birthdays or Christmas or whatever. So I'm thinking...

Instead of playing games, I can let him "win" and throw the big parties and I won't do any parties. Instead it would be a family dinner, a gift and a mommy and me date.

Would this be cruel? Would my kids resent me for being the "cheap" parent?? I'm just tired of constantly dropping money and watching my kids become increasingly spoiled.