Game theory by Nuran Kisi

As you know, in international relations we always want to know about "Why a state (because we accept the state as the main actor in IR) should act in a specific way?", "Should it go on war or not?" "...cooperate with another state or not?" or "how should decide on its strategy?" Most international relations studies are focusing on such topics.

What is game theory?

Game theory is the study of strategically interdependent behavior. (Strategically interdependence: what I do affects your outcomes and what you do affect my outcomes.) Generally it is not just about winning and losing. However sometimes it can be like this: I can do something to beat you or you can do the same. I can prefer losing for your victory or the opposite...

Why do we study game theory?

Firstly, today the logic of strategically interdependent situations get extremely complicated extremely fast. So, game theory gives us the "accounting tools". Secondly, game theory allows us to quickly draw parallels from one situation to another. So, this will allow us to think on our feet much better than we can today.

When do we need?

The theory is mainly used economics, political science, psychology, logic, computer science, biology. It is today an umbrella term for the logical side of decision science including both humans and non-humans such as computers and animals.

It can be asked whether it is popular or not. Yes it is popular:

·         Based on the book by Sylvia Nasar, the life story of the game theorist and mathematician John Nash was turned into the biopic called "A Beautiful Mind", starring Russel Crowe.

·         Game theory also mentioned in the military science-fiction novel "Starship Troopers" by Robert Heinlein. In 1997, the book was filmed with the same name.

·         The video game: "Zero Escape: Virtue's Last Reward" is also based on game theory. Some of the characters even reference the prisoner's dilemma.

In the theory, there are same example situations to study. We will focus on two of them today:

1. Prisoner's Dilemma

Here is the situation:

Two suspects are arrested. The police think that they were trying to rob a store. But the police can only prove that the suspects were trespassing. So, the police need one of the criminals rat out the other.

Here is the potential deal:

·         If no one confesses to robbery, the police can only charge the prisoners for trespassing. Punishment: 1 month in jail.

·         If one confesses and the other doesn’t, the police will be lenient on the rat and severely punish the quiet one. Punishment: 20 months in jail for the quiet one, 0 months for the rat.

·         If both confess, the police punish both of them equally. Punishment: 5 months in jail.

The question is: "Should they confess or not?"

The answer is "Yes, they should." Maybe they agreed to keep quiet before the interrogation, but as soon as they enter the room, they can change their minds under pressure. But, why they will confess? It will take us to the term "strict dominance".

Strict dominance: A strategy dominates strategy for a player if that strategy generates a greater payoff than the other strategy regardless of what the others do.

2. The Stag Hunt

Let me explain the situation:

There are two hunters and they go out to catch meat. There are two hares and one stag in their range. The hunters can bring the equipment necessary to catch only one type of animal. The stag has more meat than hares combined, but both hunters must chase the stag to catch it. (Stag = 6 units of meat & each hare = 1 unit of meat) The hare hunters can catch all of their prey themselves.

The question is: "Which animal they should choose to chase?"

It looks like the first issue, the prisoner's dilemma, but it is not. Let's see why.

If the one wants to catch the stag the other one also should choose to stag, because 3 units of meat better than 2 units. In the second possibility, the first one wants to hunt hare, the second hunter also want to hunt hare because 1 unit of meat is better than to get nothing at all. So, it means that the first one's optimal strategy is depend on the second one's choice. The second one's situation is the same. They can hunt hare or stag together. There is no strict domination here because two ways are positive. How we solve this issue? "Nash equilibrium" will help us here.

Nash equilibrium: A Nash equilibrium i a set of strategies one for each player such that no player hac incentive to change his or her strategy. There are some point about it.

-In such situations we only care about individual deviations, not group deviations. The strategy can be changed by the group, but if individuals changes the strategies and it affects the outcome, the first example is mostly used: strict dominance. However, by looking at the situation the group can change the strategy as a whole.

-Nash equilibria are inherently stable. It means that what you are doing is optimal given what I'm doing and its opposite. So , I'm happy with what I'm doing and you're happy with what you're doing, there is no regrets.

If we want to find whether there is a Nash equilibrium or not, we should focus on the changes in the strategies: whether one could change his/her strategy to maximize his/her profit?

We find two optimal outcomes: stag-stag and hare-hare options. Any hunter doesn't want to change his/her strategy because, 3 units of meat better than 2 units of meat and in the other possibility, to get 1 unit is better than getting nothing at all. (Mostly, there are more than one optimal strategies if we are talking about Nash equilibrium. Otherwise, it will become strict dominance.) So, all hunter happy with this outcome. And these two strategies are Nash equilibrium.

*Think that the day that they go out to catch meat is "the Hare Hunting Day", so they can change their mind even if they know that the hares meat is less than the stag's. It depends on their expectations.

"A Nash equilibrium is a law that no one would want to break even in the absence of an effective police force."