Here's a quick list of inexpensive games I think your kids could enjoy. All of these are shared screen games and I've played (almost) all of these with my kid who is around the same age. All of these run great on my Steam Deck.

• BattleBlock Theater $15 on Steam
• Broforce $15 on Steam
• Castle Crashers $15 on Steam
• Cuphead $20 on Steam
• Duck Game $13 on Steam
• Earth Defense Force 5 $60 on Steam (currently on sale for $15, ends Sept 1)
• Earth Defense Force: World Brothers $40 on Steam (currently on sale for $10, ends Sept 1)
• Just Shapes and Beats $20 on Steam (currently on sale for $12, ends Sept 7)
• Left 4 Dead 2 $10 on Steam
• Lovers in a Dangerous Spacetime $15 on Steam
• Overcooked $17 on Steam
• Portal $10 on Steam
• Rabbit and Steel $15 on Steam
• Screencheat $15 on Steam
• Stardew Valley $15 on Steam
• Unrailed $20 on Steam
• Wizard of Legend $16 on Steam

All costs are in USD, so they should all fall below the 20 EUR mark.

Of these games, I would absolutely grab EDF 5 while it's on sale. It's just plain, stupid, fun and at $15 it's a steal. Saw EDF World Brothers is on sale as well, though I haven't played that one, it looks like it's the same dumb fun as the others.

Sure. Get two controllers and Retroarch and they're set on games for life.

Overcooked is one of the most popular co-op games of the last few years, simple concept but fun, frantic gameplay. It's pretty cheap at base price but goes on sale pretty regularly too.

Would have to get it through Steam I believe.

• A Hat in Time - $30 USD
• Caveblazers - $10
• Unravel Two - $20
• Alien Hominid Invasion - $20
• Magicka 2 - $15
• Jamestown - $10
• Ship of Fools - $22
• Pixeljunk Shooter - $9
• River City Girls - $30
• Degrees of Separation - $20
• Speedrunners - $15
• Blanc - $15
• Cat Quest 2 - $15
• Potion Party - $10
• Double Dragon Gaiden - $25
• Biped - $15
• Guacamelee 1 + 2 - $15 & $20
• KeyWe - $25

All of these are full price, so if you wait for a sale (like I do), you can usually find each of these for $10 or less.

Any of the Worms games

Ordered by amount of "potential" replayability, vaguely

I've played all these through and am confident it'd be ok for 13 yos

If they like silly chaos and cooking games, $20 PlateUp!

If they like absolute madness and precise button inputs to make pretty food, $20 Cook, Serve, Delicious! 3?!

Rock of ages series I think all have local multiplayer, but I think $30 > on sale for $3 till sept 1 rn Rock of Ages 3: Make & Break is the only one you can do the actual story mode together (which is very fun) instead of just versus. describing this one is hard uh. Both a tower defense as well as a reverse tower defense where you play as a boulder smashing things. historical art humour themed. very silly. highly recommend this series.

$15 Tricky towers is competitive tetris with balancing physics

$14 Neurovoider is a straightforward / small scope game, robot piece-swapping twin stick shooter, very arcadey

$20 Ember knights is in the same vein as neurovoider but with flamey dudes and more fantasy / magic theme

I love worms Armageddon when I was a kid.

Basically all the Lego games (although 13y olds might already find them too child-like, depends...).
They all have split screen, so are suitable for couch (or desk) coop.
Also the slightly older ones are quite inexpensive when buying them during sales (a few €).

Special recommendation: Lego City Undercover.

Another fun couch-coop-capable game would be SuperTux, a Super-Mario-Cart like game.
This one is OSS and therefore completely free!

If you are ok with emulation dolphin is pretty great. You can still find wiimotes for cheap and don't need the sensor bar ( use two candle instead ). With that the entire wii games library is yours.

If you want natives games I would recomend indie couch games ( overcook, moving out, etc... ).

Off the top of my head.

Peak

Sunderfolk, needs a tablet or phone as a controller, though.

Brothers: A Tale of Two Suns

Sunderered

It Takes Two

Split Fiction

Rayman Origins

Definitely recommend It Takes 2 when it's on sale.

SuperTuxKart is fun

Stardew valley

• Lethal League (and the sequel, but I liked LL1 better tbh)
• Mega Knockdown
• Panel Attack (FOSS)
• Petal Crash
• Streets of Rage 4
• Them's Fightin' Herds

Heroes of Might and Magic 3. Great strategy game, on steam or gog, can't remember which one has the expansion packs, but they're not necessary anyway for the first year. I played it for hundreds of hours with my sister as a kid. Has a lot of replayability. Works really well with two players with hot seat mode. More players and you will want to use the network capability.

Boomerang-Fu ?

Depends on their tastes I guess. Stardew Valley is cheap, you can put hundreds of hours in and it does "couch co-op" off a single PC. It also doesn't require very good hardware either.

lego games and on sale?

Goat simulator still exists?

My nephews loved it

Atomic Tanks. Old school 2D hot seat fun. Nuke your friends and family.

I mean, I can basically advise the same list as I do for anybody.

• Mindustry
• OpenTTD
• Luanti (especially MT-Game, I actually dislike MineClonia)
• Endless Sky
• Shattered Pixel Dungeon
• FreeCiv
• YGO Omega & EDOPro

If you're open to buying and/or piracy, I can also suggest the following:

• OpenRCT2 (get both RCT Deluxe and RCT2)
• OpenXCom (get both X-COM: UFO Defense and Terror From the Deep)
• CorsixTH (Theme Hospital)

If you're okay with more violent games, any Doom sourceport (like GZDoom) with FreeDoom phases 1 & 2. There's also OpenQuake, but I don't do 3D much.

I think Children of Morta can be played in coop on a single PC.

SuperTuxKart? Also, emulation of retro consoles as others have suggested.

Civ5 and earlier installments in the Civ franchise are also pretty good if they like virtual board games, although recent decisions at TakeTwo corporate might be a turnoff.

Ultimate chicken horse

Boomerang Fu maybe, haven't played it myself but looks cute and funny from what I've seen. 14.79 rn

I played an ungodly amount of Tapan Kaikki 3 with my brother.

Best game ever.

Lego Batman 2. Probably all the other Lego games as well. But I know that this one can be played on one keyboard.

Nidhogg 2

It's hilarious, and easy to learn.

Kerbal Space Program.

(The original!!)

Brotato

ShellShock Live

https://store.steampowered.com/search/?maxprice=20&supportedlang=english&category2=39&ndl=1

It takes two

Horizon Chase

Overcooked (part one is better than two, get the second only if you finish the first and want more)

Unrailed