In the original Star Wars movie (Episode IV), Luke Skywalker pleads with Han Solo to help the Rebel Alliance battle the Empire, but Han refuses and a disgusted Luke storms off. Chewbacca, being a student of game theory, lays out the payoff bimatrix to Han in their “conversation”:
Han understands that the Rebels have a dominant strategy of fighting. Knowing that, although he has no dominant strategy, and being the self-centered person he has already shown himself to be, Han realizes he is better off choosing to aid the Rebels and fight. (Fight, Fight) is a Nash equilibrium and also a Pareto optimum. I wonder how many other Star Wars games there are.
(Hat tip: J.S.)
and 
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MAN’S VOICE: (over loudspeaker) All flight trooper, man your stations.
All flight troops, man your stations.
Han is deliberately ignoring the activity of the fighter
pilots’ preparation. Luke is quite saddened at the sight of
his friend’s departure.
LUKE: So…you got your reward and you’re just leaving then?
HAN: That’s right, yeah! I got some old debts I’ve got to pay off with
this stuff. Even if I didn’t, you don’t think I’d be fool enough to
stick around here, do you? Why don’t you come with us? You’re pretty
good in a fight. I could use you.
LUKE: (getting angry) Come on! Why don’t you take a look around? You
know what’s about to happen, what they’re up against. They could use a
good pilot like you. You’re turning your back on them.
HAN: What good’s a reward if you ain’t around to use it? Besides,
attacking that battle station ain’t my idea of courage. It’s more like
suicide.
LUKE: All right. Well, take care of yourself, Han. I guess that’s
what you’re best at, isn’t it?
Luke goes off and Han hesitates, then calls to him.
HAN: Hey, Luke…may the Force be with you!
Luke turns and sees Han wink at him. Luke lifts his hand in
a small wave and then goes off.
Han turns to Chewie who growls at his captain,
HAN: What’re you lookin’ at? I know what I’m doing.
What are we talking about here? Shouldn’t we be revising the health care system? Get the Rich to pay for the Poor. We also need a Food care plan and Shelter plan for everyone — everyone has a right to Free food and Free shelter. Oh, don’t forget about clothing too. We can have poor people running around naked all the time.
Hmmm, why do we think Han Solo was so dumb?
I think it’s a lot more likely that, in terms of expected value, the choice (Fight, Fight) yields the best result for the Rebel Alliance, but not for Han Solo.
So Han, being smart and self-interested, chose not to Fight, until Chewbacca laid out an altruistic argument. After all, I remember Chewbacca having sort of a sad face when he spoke to Han.
From the table:
If both Han Solo and the R.A. choose to fight, they both come out ahead, presumably Han helps the Rebel Alliance and gets Princess Leia. (Win, Win)
If Han Solo fights and R.A. does NOT, Solo will be hammered by the empire.
If neither fights, both get hammered by the empire.
If R.A. fights and Han does not, presumably the R.A. ekes out a win and Han oh, sells the R.A. the Millenium Falcon and turns a nice profit but looses Princess Leia.
There is a win, win if both Han and the R. A. fight.
This is actually a bad example of Nash equilibrium. In a Nash equilibrium, neither side knows what the other is chosing to do. In the above scenario, Chewy and Hans Solo know the rebel alliance are going to fight, regardless of their desicion. So it was a simple choice fight (+8) or don’t fight (+5). Had their been some risk of the rebels not fighting, then I doubt Hans and Chewy would have stayed. In addition, the fact that the rebels score a (-5) if the don’t fight regardless of Hans and Chewy’s choice, and score a positive if they fight regardless of Hans and Chewy’s choice, also makes it a poor example.
Man, this is the nerdiest blog post in the history of the internet.
I dig it.
Andrew, because Han, as a free-market opportunist (read: smuggler) knows that his livelyhood and his days are numbered if the empire wins; ergo, his long-term goals and the republic’s are aligned. Short-term, of course, Han is far better served if the republic wins and he does nothing. Faced with the prospect of a suicide mission without his help however, Han has to help, so he does.
it’s galactic basic.
You want complicated, you should see the game theory for Admiral Piett…
Han had no idea that his help would be the deciding factor in whether the Alliance would succeed or fail, nor could the Alliance for that matter. While the Alliance would be strictly better off with Han’s help, Han would probably only see himself being better off fighting if he saw the probability of victory– and subsequently getting a piece of Leia, his payout– as being sufficiently high to justify the additional risk of death.