Introducing Game Theory

Game theory was worked on quite a bit by RAND Corporation back during the cold war. The question: We want to be able to project power without escalating the situation with the Soviets to the point of a nuclear war. Or, bluntly, how do we predict what others will do in certain situations.

There are a lot of different games that have different attributes, but one of the more popular ones is the prisoners dilemma. It goes something like this:

Jack and Jill get arrested under suspicion for a bank robbery. The cops don’t have enough evidence to hold them for long. They take Jack and Jill into separate rooms so they can’t coordinate. They tell each, if you rat out your buddy (defect with each other), you’ll go free and your buddy gets 20 years. However, if you both rat each other out, you’ll both get 7 years. That being said, if you both keep your mouths shut (cooperate with each other), we can still hold you each for a year.

We can display the options in the matrix form below.

Matrix showing punishments for Jack and Jill deciding to rat each other out (defect) or keep their mouths shut (cooperate).

The least amount of time serves happens if both keep their mouths shut (one year each). However, this is problematic because it turns out it’s always better for the individual to defect. For instance, look at Jack’s options. He doesn’t know if Jill will cooperate or defect. Suppose she’ll cooperate with him. Well, then if he cooperates he’ll serve one year. However, if he rats her out, he’ll serve zero years, which is less time than one year. Likewise, suppose he thinks Jill would defect. If she rats him out and he cooperates, then he serves 20 years. If he defects, then he only serves seven years. In either case, it’s better for him that he defects than cooperates, leading to a rational decision of both serving seven years. Except that’s worse than both only serving one year by both cooperating.

The situation in the South China Sea is a classic prisoner’s dilemma. With as much as 50% of the world’s maritime trade passing through the region and massive natural resource reserves, it’s a strategic area to both China and American allies. In a perfect world, everyone would cooperate over the area. For China, if America and our allies defect and are able to defend the area militarily, China stands to be denied access. Likewise, if China is able to defend the area militarily, then China stands to be cut off. As a result, everyone is defecting and China has been aggressively building military bases and America has been attempting a Pivot to Asia.

So that’s the one-off case for a prisoner’s dilemmas. However, once we start doing this multiple times (I suppose Jack and Jill might want a career change because they get caught a lot), things change. Suppose they get caught 10 times. A multitude of strategies have been developed to deal with these iterated games. For instance, Tit-for-Tat, developed by Robert Axelrod in the 1980s, means that you cooperate only if your partner cooperates. So, the first time Jack and Jill are arrested, Jack would cooperate and keep his mouth shut. If Jill defects and rats him out, once he gets out of jail and they get arrested again, Jack’ll defect until Jill cooperates and then he’ll go back to cooperating. Other strategies include always defecting, always cooperating, randomly choosing, and so forth.

The Cold War itself was an iterated prisoner’s dilemma where both sides managed to cooperate the entire time on the issue of not-nuking one another. If either side defected and the other went for tit-for-tat, that would have resulted in everyone nuking each other. Tit-for-tat was our actual strategy, although whether or not we would have actually followed through is another question.

Outside of prisoner’s dilemma, game theory was also used for a variety of games that eventually were used by early AI to solve problems like Chess. These strategies used elements like Minimax, where the player would attempt to minimize the value of the opponent’s maximum possible score on their subsequent moves. Then there are strategies like Maximax, which tries to maximize your own maximum possible score (of course, that can run into problems if your maximum possible score would give your opponent even more points). In contrast, there’s Maximin, which tries to maximize your maximum minimal outcome.

There’s also a distinction between games which are zero-sum and others which are not. Zero sum just means that whatever benefits one player gets, the other cannot. For instance, in a game of poker, however much one party wins another party loses. There are non-zero sum interactions as well, for instance, when a factory hires someone to build a product, the value of the product is greater than the amount that the factory pays for parts and labor (if that is not the case, then the owner needs to rethink her business model).

When dealing with foreign policy, whether or not a situation is zero-sum matters for game-theorying out a strategy. For Russia, American influence in their periphery is a zero-sum game; whatever influence the US has, that means Russia doesn’t have that influence. In that situation, they can choose between strategies like trying to maximize their greatest potential influence (maximax) or minimize America’s greatest potential influence (minimax). In the former, they make a high-risk bet that the US will choose a strategy that leaves the US with little influence, whereas in the latter their bet is lower-risk because regardless of what the US does, there is a ceiling for the greatest US influence.

The problem is, we don’t know what strategy Russia chose for every region. We can guess, but to do this right requires a database of their activity in each area and how they’re trying to manage perceptions along with all the other relevant parties.