Encourage cooperative games

Yes a lot of them. Played in Orcs Must Die 2 ? =] There's also a coop.

Well, here at a huge variety of options in Terraria can be a cooperative to play, Don't Starve too.. but among the three-dimensional games you (or you) should try Portal 2. If you do not know, there is co-op campaign, and very good.

Arma 3 Apex
Arma 2
Gears of War 4
SC Chaos Theory

Divinity Original SIn recommend)
You can even Dead space 3

A Series Of Dark Souls.

Half Life 2 Synergy

Checkers, chess, dominoes, cards (thousands of them). MtG, if you are fabulously rich, TIC-TAC-toe, if you only own a land and stick.

ARK Survival

Craft The World