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Aggression in Multi-player Games

Jeff Ganong

January, 2002

A Case Against Early Aggression In Multi-player Games Like The Settlers Of Catan.

Die Siedler von CatanImagine that you're playing a game of Settlers and you are the first player. You roll a seven, where do you place the robber?

A couple of months ago several members of the Spielfrieks discussion group argued that it was insanity to not use every opportunity to use the robber to handicap opponents and steal their resources even at the start of the game.

At the early stages of the game I disagree. Here's why:

At the start of the game, all players are equal. If you place the robber on an opponent, you probably have not taken a significant lead with your one additional resource, but the newly-victimized opponent is clearly now in last place. He has lost one resource and more importantly, his ability to get new resources from that hex. On average, this will be 1/6th of his production capacity, but more often then not, an aggressive player will put the robber on the victim's most probable hex. It is likely that the robber will remain there for four turns. If you are playing with the Seafarers expansion, even after another seven is rolled, there is no guarantee that the robber will be moved. This is a significant handicap.

The same probability predicts that the victimized player is likely to roll a seven within 4 turns. Alternatively, he may be so motivated by the loss in production to buy a development card to get a soldier. Whatever the cause, the very next time the victimized player has the opportunity to place the robber, where do you think he will put it?

Unless you managed to capitalize on the extra resource card by building a settlement or city, I would argue that you are now at a net loss. You have lost the one resource advantage and now you will suffer the production capacity loss of the robber.

Furthermore, the robber retaliation is not the end of the negative consequences of the early robber aggression. Some would now say that you're even with the other player; you placed the robber on him and he retaliated. However, I believe the relationship will still have some hostility. All things being equal, he will be less inclined to help you. For example, say he wants to make a trade and both you and a non-aggressive player are willing. The robbery victim is going to trade with the non-aggressive player. And if he rolls another seven, all things being equal, he's more likely to put the robber on you than on a player who has never demonstrated any hostility. This is basic human nature.

Surprisingly, I've found that even innocent bystanders will react negatively to this display of early aggression. All things being equal, I've observed other players reluctant to trade with an early aggressor. Since at the beginning of the game there is no reason to single out any player for robbery, every player is thinking, "That could have been me.">

Early aggression in multi-player games is not unlike an Iterated Prisoner's Dilemma (IPD).

[Quick intro to prisoner's dilemma: Two partners-in-crime are held in separate interrogation rooms. If only one confesses, he is released and the other serves the maximum time of 5 years. If neither confesses, they each serve one year for a lesser crime. If both confess, they each serve 3 years.]

For a single, isolated example of the prisoner's dilemma, the best strategy is to defect (i.e., confess). [That's because the sum of its possible outcomes is better.]

Most games are more like an Iterated Prisoner's Dilemma. In an IPD, the same two players (or prisoners) play a series of games. The outcome of each game is known before playing the next. Axelrod and Hamilton have shown that unlike an isolated Prisoner's Dilemma, in an iterated Prisoner's Dilemma defecting every time is a poor strategy. The best strategy they found was called Tit-for-tat (TFT) and was submitted by Anatol Rapoport. This simple program would always cooperate unless the other player defected on the previous iteration. That is, if the other player defected, it would tit-for-tat defect the next game.

The key here is that unlike a classic prisoner's dilemma, in an IPD we have additional information upon which to act. This knowledge allows us to discriminate between the possible choices of the other player and play accordingly.

Similarly, in Settlers of Catan, a roll of a seven is not like a classic isolated Prisoner's Dilemma between strangers with no history, but an IPD. Like an IPD, a common and successful response to a defection is a retaliatory, tit-for-tat defection. If you put the robber on me, I'm going to put it back on you.

Not only does a given game of Settlers of Catan resemble an IPD, but I've seen this sort of retaliation carry over into subsequent games. After being robbed blind by one player in one game some players will get revenge in the next. This is sort of like an iterated Settlers of Catan game.

The situation does not improve if you place the robber on a hex shared by multiple opponents. You simply have increased the number of opponents that will have a grudge against you. Some may argue that it's poor sportsmanship to hold a grudge. My response is that it is natural and that it is good tactics. The Spielfrieks posters suggested picking a victim at random.

Do you suppose they used the digits of pi to ensure that their choice was truly random? No, I'm sure they just arbitrarily pick someone and call it random. If that is your gaming group's custom, it is easy to get revenge and call it random. But why go through that charade? By robbing the aggressor you get your resource back and by explicitly linking the two actions you have demonstrated a deterrent to future thefts.

Although I'm against early aggression, I am not a complete pacifist. I frequently use the robber in the middle and end game. The simplest case is when one player is one victory point from winning. Obviously it then makes sense to not only put the robber on him but to use your roads and ships to block him, set up trade embargos, etc.

Somewhere in between the beginning and near victory it also makes sense to use the robber. I usually wait until someone is 2 victory points ahead but this varies. It is good to emphasize your rationale for the theft. For example, I might announce, "I'm putting the robber on you because you have a city and everyone else is in huts." This helps the victim realize that it's nothing personal and illustrates a condition for the hostility to cease. In this example, friendly relations will resume when others have cities. Leader-bashing also largely avoids the "That could have been me" syndrome because the leader is resented and bashing the leader improves everyone else's chances.

To relate this back to the Iterated Prisoner's Dilemma, you can think of a player being in the lead as a defection. Cooperation in this sense means that the leader has the same number of victory points as you. The tit-for-tat strategy then mandates that you defect until the leader starts cooperating (i.e., has the same number of points). No doubt Axelrod would make a prisoner of me if he read such a gross stretch of his theory but I think this illustrates the point.

I used Settlers of Catan as an example because it was the game that inspired this discussion on Spielfrieks and is familiar to most Games Journal readers. However, this strategy is equally valid in most multi-player games with moderate player interaction such as Evo, Illuminati, Elfenland, Diplomacy and Samurai Swords to name a few. A battle of attrition between a subset of players only weakens the subset.

Statistically, most thieves steal from other poor people. Robin Hood stole only from the rich and was a hero.

- Jeffrey P. Ganong

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