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Achieving Equilibrium
Dragon Editorial
by Steve Winter

Dungeons & Dragons is a funny type of game. It has aspects of a traditional game. Players take turns, evaluate strategies, and manage resources. There's randomness in the form of dice rolls. The rules are complex for a leisure/recreational game, yet there's no question that that's what it is.

Seen from another angle, D&D doesn't look like a game at all but more like a structured activity. It's as if someone walked into a room, dumped a bucket of wooden blocks onto the table, and told everyone to build a tower. The tower is a goal; there are no rules for building it, just a bunch of people sorting and stacking blocks. There will be chaos, false starts, maybe even a few fights, but eventually a tower will emergeā€”or a dragon will be slain, or the owlbear's cave located and looted.

One of the more interesting concepts in game theory is that of equilibrium. In a competitive game, everyone follows a strategy that gives them the best chance to win. Equilibrium occurs when all the players are making all the right moves. Because everyone is playing perfect strategy and no one has any reason to let up, no one is getting any closer to victory. As long as no one makes a mistake, the game stalemates.*

In some circumstances, the best way to break the deadlock is for players to take actions which individually are not optimal for them but which nevertheless lead to the best outcome for the group. Here's where it gets interesting. No one player acting on his own can bring about that best-for-all solution. All of the players must participate in pursuing what they know to be the second-best strategy in order for it to pay off for everyone. This isn't just some dry, academic exercise; the "Nash Equilibrium" and others like it have been used to model behavior from economic interaction to war. Equilibrium is a powerful tool for analyzing complex interactions.

Unlike a competitive game, D&D doesn't stalemate when no one makes a mistake. It's still possible, however, for what seems to be the best individual strategy to lead to less-than-optimal group results.

Most characters are built with an eye toward maximizing their effectiveness in a particular role, a particular situation, or even a specific attack routine. As we all know, sometimes in a D&D combat, the action that contributes the most to winning the battle might not be the action that the character is optimized for. A soft-skinned leader or controller might need to step into the danger zone to set up a flank so the striker can get the most out of her daily attack. The striker might need to forego that devastating daily attack or use it in a less-than-ideal way (attacking only one target instead of three, for example) in order to lock an enemy into a vulnerable location so that someone else can trigger a more important effect. There's an element of trust in doing this. The druid with the lousy Armor Class risks stepping next to the ogre because he trusts that the rogue will kill it if he has combat advantage. If the rogue doesn't follow through, then the druid player is right to wonder why he's taking so much risk for others.

This idea that what's best for the individual isn't always best for the group is part of what makes D&D a compelling game. It creates dramatic tension within the players and the group. Sometimes it even leads to tragedy when a character pays 'the ultimate price' for the good of others. You won't find that in Uno or Parcheesi.

Before wrapping up, I want to mention something that we're adding to Dragon articles in conjunction with Organized Play. Starting with last month's compilation, you'll notice little icons in some articles indicating one or more D&D rulebooks. These indicate what D&D product an article is more closely related to. If an Organized Play event is limited to, say, Essentials-only characters, then Dragon magazine content which comes with an Essentials icon (for now, those are Heroes of the Fallen Lands and Heroes of the Forgotten Kingdoms) can also be used at that event.

As always, send any thoughts or comments on Dragon magazine to dndinsider@wizards.com.

* If you've watched the film A Beautiful Mind, then you saw a whimsical explanation of this principle in a parable about a group of men, each trying to get a date with the most beautiful girl in the room. If all of the men talk only to her, she'll turn them all down and no one gets a date with anyone. If all of the men talk only to her friends, they'll all get dates, although none will be with the most beautiful girl. You really ought to watch the film. It's not about math.