Strategic Insights: The Prisoner's Dilemma
by Shannon Appelcline
Five short years ago, as 2003 dawned, I kicked off a mini-series on the design of tabletop board games. Ever since, I've continued the series on-and-off, with some of the more recent articles linked at the bottom of this one.
Nowadays most of my board game insight instead appears over at my tabletop gaming column, Gone Gaming, which as of last week is now a part of Boardgame News. However I've decided to return to my old stomping grounds here on TT&T for two reasons: first, I'll be looking at the deeper theory, and second, I'll be relating these theories not just to board games, but also to some to the reality TV game shows that I've talked about on occasion here.
This week I'm going to kick off this new four-part series by talking about the Prisoner's Dilemma. Over the next two columns I'll move on to the Tragedy of the Commons and the Free-Rider Paradox. Finally I'll finish the series off by looking at how all these theories relate to each other.
Defining The Prisoner's Dilemma
The Prisoner's Dilemma was originally described by Merrill Flood and Melvin Dresher in 1950. They said:
Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?
The two possibilities of the Prisoner's Dilemma are traditionally called "cooperation" and "defection". The dilemma of the titles arrives from the balance of the punishments. Clearly the optimal choice for the community as a whole is cooperation, because then the total sentence is only 1 year, the least of all possibilities. However, for an individual it's best if he defects and his partner cooperates, resulting in all the penalty being given to his partner. Unfortunately this often results in the double-defection scenario, where each player ends up suffering much more than if they'd both cooperated.
Based on the definition, there are three core requirements for the Prisoner's Dilemma:
Defection might be the optimal play in one-off Prisoner's Dilemma play. However there's a variant called the Iterated Prisoner's Dilemma, where a succession of Prisoner's Dilemmas is carried out, each time with the participants knowing all of the past decision.
A tournament for the Iterative Prisoner's Dilemma was held around 1984. The winning solution of the tournament was a very simple "Tit for Tat" algorithm. Here the Tit for Tat player started out cooperating, but thereafter did whatever his opponent had done on the previous iteration. Over time, cooperation resulted as the optimal result.
More recent studies, as discussed by Christopher Allen in Dunbar, Altruistic Punishment, and Meta-Moderation, suggest that some variations on the punishment ("Tit for Tat") can produce even higher levels of cooperation.
Applying the Prisoner's Dilemma to Board Games
The Prisoner's Dilemma has a core problem when addressed to strategic games: in a 2-player game--as the Dilemma is standardly modeled--only a defector can get ahead of his competition. This is relevant due to real differences between the Prisoner's Dilemma as a theory and the Prisoner's Dilemma as a gaming reality.
In theory, both players want to avoid jail time, and it's ultimately a non-competitive element: neither player cares if the other player gets more, less, or the same amount of jail time as him. He only cares about his own result.
Conversely in a strategic game, almost everything is competitive. If both players receive the same punishment--be it due to joint cooperation or joint defection--neither has "gotten ahead." Instead, the only way to get ahead via the Dilemma is to defect when your opponent cooperates. Thus, there's no reasonable response, except to defect, and the Dilemma falls apart.
As a result, if you want to use the Prisoner's Dilemma as a mechanic in a game, you have to go about it in a somewhat different manner.
One answer is to try and duplicate the original Dilemma exactly, by introducing some non-competitive element. For example, if players received a cash payout depending on their response, it wouldn't matter how they did in relation to each other. However, I suspect that this type of non-competitive element can only be introduced by bridging the interface between the game and reality, and thus is ultimately limiting.
The better method for using the Prisoner's Dilemma in a game is to allow two (or more) players to share a Dilemma, and then to compare their results with other players in the game who were not involved. This is largely what's been done to date.
Existing Prisoner's Dilemma Mechanics
There are few if any games that explicitly include the Prisoner's Dilemma, but there are many games that implicitly do. Pretty much any game that allows for possibilities of cooperation or betrayal is touching upon it.
Diplomacy is perhaps the most classic example. This non-random game of world conquest requires players to work together in order to gain traction against their foes, but at the same time requires players to eventually break away in order to win. Per my list of requirements, there's simultaneous play, because orders are all written at the same time. However the exact costs of cooperation and defection are less clear. I suppose if you defect first you probably have an advantage against your non-prepared opponent. However, permanent cooperation isn't a viable strategy, while simultaneous betrayal may not be as greatly penalized as in the classic Dilemma.
Any strategic wargame is likely to implicitly feature the same Prisoner's Dilemma elements, since cooperation is both a possibility and an advantage in the gaming style. However few if any of them really consider that aforementioned costs.
Michael Schacht's Intrigue is one of the few board games I've played which I think might have been explicitly based on the Prisoner's Dilemma. In this game you send scholars to other players' courts, where they'll earn you money. However, each court is under a constant barrage of new scholars and is thus constantly being bribed and pressured to throw your scholar out and accept someone new.
The game isn't simultaneous. However the costs are clearer. There's benefit from cooperation (you keep each others' scholars in your courts), but at the same time defection is very actively encouraged. The last is, I think, the most notable element of the game, and the one that most games miss: you have to encourage defection a lot, because it's human nature to be somewhat nice to the people you know.
Another Prisoner's Dilemma game is Bruno Faidutti's Incan Gold. As you move into Incan ruins, you discover treasures, which are divided among players, and artifacts, which are left on the ground. Each turn everyone has a simultaneous option to leave the ruins ("defect"). If one player does, he picks up any recently discovered artifacts, but if multiple people do, they don't.
(To a certain extent, any simultaneous action game offers the opportunity for Prisoner's Dilemmas, just like any war game does.)
A Prisoner's Dilemma Mechanic
In each of these articles I'm going to offer up a short idea for using the theory in a relatively pure manner in a strategic game. Here's my thoughts on a pure Prisoner's Dilemma design:
The Mine. Imagine a mine (or other sort of resource production) which can be shared by multiple people, and which increases its production the more people are there. Each turn, each player secretly decides whether to cooperate or betray at the mine.
If all players cooperate, each player gets "1" element of the resource.
If one player defects, he gets "N" elements of the resource, equal to the number of players there, and wipes out all other player control markers.
If more than one player defects, they all lose all their player control markers.
I'm not sure if the balance of rewards is right, but it's certainly a start at a pure Prisoner's Dilemma element in a game.
Applying the Prisoner's Dilemma to Reality TV Shows
One of the things that got me thinking about the Prisoner's Dilemma was my recent discussions of Reality TV shows. Games like Survivor, Big Brother, and Pirate Master all offer the opportunity to exploit the Prisoner's Dilemma because of the fact that they're voting games largely depending on the tyranny of the majority: you have to betray people as the game goes on.
However, Survivor kicked off the genre by offering a huge disincentive to defect: the jury vote at the end, where the people you beat in the game get to decide whether you win or not. Of the games only Pirate Master largely overcame this initial design. It did have a jury vote, but it was held when there were still three contestants, to determine which of two losers went home. A strong competitor could win that competition and never have to face the anger of his peers.
Generally, I think that reality TV shows of this sort show the need for a much larger incentive for defecting. Just staying in the game has proven insufficient incentive to get people to defect to a team which could offer them a better positioning. This is primarily because hope springs eternal. The natural belief that things will turn out OK, combined with the strong disincentive caused by the final jury vote, has made defections pretty rare. So, something more is required.
How could you fix this?
Unlike my board game thoughts, I don't plan to offer up full game systems for reality TV shows, but these thoughts should be enough to get you thinking more.
That's it on the Prisoner's Dilemma. In two weeks, I'll look the first of two very similar theories, each taken from a different sphere of knowledge, beginning with the sociological Tragedy of the Commons.