Tol Barad, the Prisoner's Dilemma, and Cooperation

Introduction

In response to the fact that Tol Barad has turned out to be clearly imbalanced in favor of the defender, Blizzard implemented the following change: winning as the attacker rewards 1800 Honor Points (and winning as the defender still rewards 180). For purposes of this analysis, the only thing you need to know about Tol Barad is that the winner of any match will be the defender in the next match.

I'm going to do some brief game-theoretic analysis to show that the defending side now has a significant incentive to throw the match. When I first read this change, I thought "this creates a perfect Prisoner's dilemma - Wikipedia, the free encyclopedia ." It turns out that that's not the case--as I'll show here, it creates something that incentivizes losing even more than the canonical Prisoner's Dilemma does.

The Prisoner's Dilemma

If you're not at all familiar with the Prisoner's Dilemma, skim the wikipedia article linked in the last paragraph. It's a fundamental game theory problem which has been the subject of extensive literature over the past few decades. Briefly, it concerns a game played between two players, each of whom has two choices: "cooperate" with the other player, or "defect" from him. It is a non-zero sum game, meaning that one player's win is not necessarily the other's loss--the outcome can be simultaneously good or bad for both. In the classic Dilemma, the best total result for both players is if they both cooperate. However, there is a powerful incentive to defect, since doing so can let you claim a large prize at the expense of the other player. But if both players defect, the result is worse than if they both cooperate. For more details, see the wikipedia article.

Tol Barad

I'm going to lay out an analysis of Tol Barad in the following way: there are two sides (Horde and Alliance) who are going to play iterated rounds of the Tol Barad game. Each side has two possible strategies:
Cooperate: Play normally when attacking, intentionally lose when defending.
Defect: Play normally (trying to win) always.

What we need to is compute the expected outcome for both sides under all combinations of cooperating and defecting. As one intermediate step, we need to know the probability that the attacker will win if both sides are trying. Because Blizzard has made the reward for the attacker 10 times are great as that for the defender, they've implicitly assumed that the attacker as a 1/11 chance of winning, so I'm going to go with that.

1) Both sides cooperate: the attacker wins every game. Each side gets 1800 points in alternate rounds, for an average payout of 900 points per game.

2) Both sides defect: the game is played normally. On average, Tol Barad changes hands every 11 games. Therefore, in each set of 22 games, each side can expect to win 1 game as the attacker and 10 as the defender. Each side gets an average payout of 3600 points over 22 games, or 163.6 points per game.

3) One player cooperates and the other defects. Remember this is the case in which one side voluntarily throws all of their defender-side games, seemingly for nothing in return. So whenever they have Tol Barad, they give it away next round, and take an average of 11 rounds to get it bad. In each set of 12 games, the cooperator expects to win 1 game attacking for 1800 points. The defector wins 1 game attacking and 10 games defending, for 3600 points. The average payout is 150 points per game for the cooperator and 300 for the defector.

Summarizing the results in a table:

P1\P2	Cooperate	Defect
Cooperate	900,900	150,300
Defect	300,150	163.6 163.6

(Note that this is not a true Prisoner's Dilemma, since the 900 is greater than the 300. This makes cooperating look overly attractive, which is part of the point of this post).

So the first result is obvious--the two players working together have a strictly dominant strategy in which both cooperate. If the Alliance and Horde on any server can come to an agreement, there is no question that they should agree to perpetually have the defender throw their games.

More likely though, no actual agreement can be reached. The more interesting question is how to behave when you don't know what your opponent will do. If you assume they will defect (because they have not read this post), your are better off defecting (getting 163.6 points per game over 150). However, it is rather notable that the difference is very small--even you expect to get no consideration in return, there is almost no penalty in throwing all your games while defending! And if you think there's even a small chance that your opponent might cooperate (for example, if you spread this information through your server community, so at least the occasional enemy team might cooperate), the balance rapidly tips in favor of cooperating.

Conclusion

So your goal, really, is to find some way to plant a "seed" of cooperation on your server. If you can get over a threshold where even a small portion of Tol Barad groups elect to give up when on defense, the system will snowball towards complete cooperation: that promised land where everyone can get 900 points per game.

Obviously there are practical difficulties in getting something like this to happen in the live community. A substantial fraction of the server community will have to have read this post or something like to understand why they would intentionally lose Tol Barad. But I'd be highly interested if any server (maybe a small one) could ever reach the point where it becomes common practice for Horde and Alliance to alternate TB victories to secure the maximum rewards.