Thursday, March 29, 2007

Game Theory and "Commitment"

Jack Hirshleifer, "Game-Theoretic Interpretations of Commitment"

Where to begin? We can start by looking at the examples of game situations that Hirshleifer uses to illustrate his points.

1. Chicken. Two people drive cars directly at each other. If one of them bails out, the other wins; if neither bail out, they both get killed.

2. Land or Sea. The British choose to attack by land or by sea. The Americans choose to defend either the land or the sea. The Americans win if they defend where the British attack, otherwise the British win.

3. Prisoner's Dilemma. Two prisoners have to choose whether or not to rat out their co-conspirator. If both prisoners keep quiet, they each face a small punishment. But if one of them sells out, he gets off free while the other gets screwed.

4. Battle of the Sexes. A boy and a girl try to arrange a date. The boy prefers to attend a sporting match while the girl prefers to attend the opera. However, each prefers going on a date to not going on a date.

The games all involve two self-interested parties that must each be concerned with the other's actions. In Battle of the Sexes, interests are largely aligned; in Land or Sea, interests are entirely opposed. In Prisoner's Dilemma, the optimal outcome involves cooperation but each party has a selfish interest in defecting. Chicken has a similar structure to Prisoner's Dilemma...

The alignment of interests in Battle of the Sexes means that it is advantageous to have the first move (in this case, decide where you want to go for the evening). The opposite is true in Land or Sea (it is better to be able to react to your opponent). Flexibility is a crucial advantage in Land or Sea but is somewhat of a hindrance in Battle of the Sexes. We can view "commitment" as the opposite of the flexibility -- it's the ability to lock in your move, to tie your hands. Often tying your hands can be an advantage. A child who throws an uncontrollable temper-tantrum gains an advantage over a responsive parent.

If the Prisoner's Dilemma is not an anonymous one-off, parties may reach an optimal outcome through the use of promises and threats. For example, consider the announcement that "like will be met by like." This is essentially a promise that cooperation will be matched by cooperation (because pure cold calculation implies that defection will be matched by defection). If the promise is sufficiently credible, then it will be in the other player's interest to cooperate. (It is not necessary for the promise to be 100% credible.)

Similarly, in Chicken, the second player might announce that "I will defect." This is a threat to crash the car if the other player stays on the road. If the threat is sufficiently credible, then it will be in the other player's interest to bail out. One way to make the threat credible would be to remove the steering wheel and conspicuously throw it out of the window.

It is also possible to combine a threat with a promise. For example, in Chicken a player might announce that "like will be met by like." The advantage in combining a threat with a promise is that the credibility of the promise can make up for a deficiency in the credibility of the threat.

It seems likely that this sort of analysis can provide insights into human passions such as anger and gratitude.

2 comments:

Unknown said...

A few clarifying points at the beginning would make this post easier to understand (although it is quite clear -- I know I'm being nit-picky about this).
1. What discipline does this paper fall under? Economics? Psychology?
2. Is "commitment" a widely accepted term or is Hirshleifer coining it here?
3. I gather the thesis of the article is something along the lines of: whereas flexibility usually seems like a positive trait, looking at some situations in game theory we can see that the opposite of flexibility (commitment) can be advantageous (as long as the other player is aware of it!). Is this correct, roughly? I would like to see the thesis clearly stated close to the beginning, so that I know what argument I'm following later.

And of course, what are those implications for anger and gratitude? Let me know!

Thanks!

SNOOZY said...

1. Discipline would be economics primarily (since that's where game theory is), although as I suggest at the end there might be implications for psychology.

2. Commitment is a widely accepted term. Hirshleifer is exploring how commitent is interpreted in game theory.

3. Flexibility is a negative trait is not really the thesis -- it's more the "insight" of game theory, where something that you might not have realized beforehand is made clear. I know I'm breaking the rule of explaining clearly "What is the article about?" But Hirshleifer is basically saying, "OK, commitment is a big concept in game theory, let's discuss it and go through some examples and see if we can walk away with a clearer picture of what it is."

The thesis is: There are two kinds of commitment, pre-emptive and reactive. Pre-emptive means taking the first move -- this is not always desirable (contrast Land or Sea with Battle of the Sexes). Reactive commitment means making threats and promises. The problem with making threats and promises is that they are not always believed (sometimes combining a threat with a promise is a good way to overcome this hurdle -- I think I could definitely be more clear on this point). Hirshleifer also talks about mechanisms for commitment.

4. Well, we can think of anger and gratitude as being devices through which people are able to make game-theoretic threats and promises. It may not be rational to often get into a fight, since you end up dirty and injured and there isn't much to gain. But this rational approach can allow people to push you around; anger serves a useful function by allowing you to credibily threaten to respond to violence with violence (as opposed to responding to violence by backing down and running away).