Why do they all work against each other? In the book, Edmund betrays his siblings — but they don’t betray him!
Before Edmund’s visit to Narnia, we read, “The others who thought she was telling a lie, and a silly lie too, made her very unhappy. The two elder ones did this without meaning to do it, but Edmund could be spiteful, and on this occasion he was spiteful.”
Before he meets the witch, when he first enters Narnia, Edmund says, “I say, Lu! I’m sorry I didn’t believe you. I see now you were right all along.”
Edmund assumes Lucy is sulking and refusing to accept his policy, and the narrator tells us he doesn’t really like Narnia and he’s about to head back home when he hears the witch’s sled.
He makes his worst choices after being enchanted by the witch’s Turkish Delight, and Peter here reacts to Edmund’s behavior after the enchantment:
“Look here,” said Peter turning on him savagely, “shut up! You’ve been perfectly beastly to Lu ever since she started this nonsense about the wardrobe and now you go playing games with her about it and setting her off again. I believe you did it simply out of spite.”
So, the narrator agrees with Peter’s assessment that Edmund’s actions are motivated by spite.
As Edmund is leaving the Beavers and heading to the White Witch, the narrator has this to say — and I wish I could say as a child that I was insightful enough to figure this out on my own, but Lewis really hands it all to us:
You mustn’t think that even now Edmund was quite so bad that he actually wanted his brother and sisters to be turned into stone. He did want Turkish Delight and to be a Prince (and later a King) and to pay Peter out for calling him a beast. As for what the Witch would do with the others, he didn’t want her to be particularly nice to them—certainly not to put them on the same level as himself—but he managed to believe, or to pretend he believed, that she wouldn’t do anything very bad to them, “Because,” he said to himself, “all these people who say nasty things about her are her enemies and probably half of it isn’t true. She was jolly nice to me, anyway, much nicer than they are. I expect she is the rightful Queen really. Anyway, she’ll be better than that awful Aslan!” At least, that was the excuse he made in his own mind for what he was doing. It wasn’t a very good excuse, however, for deep down inside him he really knew that the White Witch was bad and cruel.
Edmund is surprised by Peter’s savagery, which indicates that it wasn’t typical. Peter is responding to the post-enchantment actions of his brother. As we see, Edmund is at last briefly willing to apologize and reconcile with Lucy when he sees Narnia for himself, in those brief moments before the Witch gets to him. You are right that Lucy also turns on the others, though of course she doesn’t betray them. We see that Peter and Susan are always on the same side, which of course makes the final problem of Susan much more shocking. (Full disclosure — I haven’t read the final book myself.)
In this game (which ties into the the 2005 LWW adaptation) Aslan will come to everyone’s rescue, and the White Witch and her wolves are threats to everyone. Each sibling has a couple of powers that affect their game play — Lucy can add points to any player’s roll, Edmund can challenge another player’s use of an action card and make them draw another card. With our pawns all clustered on the start square, the four of us naturally made choices that benefitted the whole group, but as our player tokens got separated on the board, we had to put some players in more danger than others.
Playing as Peter, whose special power makes wolves much easier to defeat, I unthinkingly sent a wolf in the direction of Edmund — not really thinking of the wolf as a threat. Edmund, feeling singled out, then challenged Peter, but the cards and dice fell in my favor, and I ended up coming from behind and winning as a direct consequence of the Edmund character turning on the Peter character. (Poor Edmund!)
By contrast, the game Pandemic is designed so that all players are on the same side, against the pandemic. There’s no benefit in Pandemic to acting selfishly.