Categories:
Game Theory
Here’s a question from my final exam for Ph.D. Micro. Care to give it a try in the comments?
Suppose that
greeting other people is a special kind of Coordination game. We are in the equilibrium where everyone
shakes hands; but there is an equally polite equilibrium where no one shakes hands. The only bad result is when some people offer
to shake hands, and others refuse. How
you would modify this simple model to account for the rise of swine flu – a
disease that might be spread by hand-shaking?
Is it possible for this disease to change the number of equilibria in
the game? Explain using both words and a
normal form.
Personally, I think now’s a great time to switch to bowing. Can economists lead the way?
READER COMMENTS
Jared
May 14 2009 at 1:22pm
So I used bowing in my answer to your question, but I must point out that, at the high end, we estimate about 3,300 cases of swine flu *all across the U.S.* It appears to be no more lethal than the regular flu. And last, but certainly not least, the infection (and many like it) is likely airborne.
Thus, what I really wanted to answer on your exam is this: if people were *at all* rational, they would recognize that the additional risk handshakes in a world of swine flu are negligible, and continue shaking hands. Hand washing would rise slightly. The end. 🙂
chipotle
May 14 2009 at 1:29pm
Bryan, I think utility would be maximized with a move in the other direction.
Zac Gochenour
May 14 2009 at 2:49pm
Jared’s point about the likely innocence of this particular flu outbreak is valid, so maybe it is helpful to replace “swine flu” in the question with “an epidemic of a highly fatal, easily communicable disease.”
So the introduction of swine flu changes our payoff matrix, and it now resembles a game of chicken. If no one shakes hands, consider that 0 payoff – no one appears especially polite or impolite, swine flu does not spread. If everyone shakes hands, it is a large negative payoff for all because of the spread of deadly infectious disease. If some people offer to shake hands and others refuse, the people who offered to shake hands benefit (appear polite, not scared of some so-called disease) and those who refuse to shake hands appear impolite, incurring a small negative payoff.
So now what was once a coordination game is now an anti-coordination game. The two pure-strategy equilibria are the situations where some people offer handshakes and some do not.
handshake, handshake | handshake, no
no, handshake | no, no
originally (before disease):
0,0 | 0,-1
-1, 0 | 0,0
after disease:
-10,-10 | +1,-1
-1,+1 | 0,0
There is also the mixed equilibrium where some people will probabilistically choose between the two pure strategies.
This is simplistic but an interesting point- people would likely keep offering handshakes with confidence that no one will accept. Like when people offer to have you over for dinner even when everyone knows it will be a disaster, because they are confident you’ll refuse the invitation.
Tom
May 14 2009 at 3:48pm
Zac,
Then it be a race to be the first to offer a handshake before some else offers, knowing that if you offer first you will look good but also know that no one will accept.
Handshake offers begin at one pace away from coming face to face. Then the “arms” race begins. Person A then offer a handshake at two paces away from B knowing it will be refused. On the next encounter or “game”, B offers a handshake at three paces away before coming face to face with A. The “arms” race escalates: 4, 5, 10 paces.
Then it becomes a game of chicken. A offers his hand at 10 paces, B at 9 paces. As A and B approach one another, A drops his hand at one pace away and B is the winner. On the next game, A offers at 10 paces, B at 9 paces; and at one half pace away A’s hand is still extended and B drops his hand.
The permutations are endless.
Tom
May 14 2009 at 3:53pm
Zac,
I meant, “Then it becomes a race…”
“I ain’t be got no weapon.”
twv
May 14 2009 at 4:33pm
In an age when the hug is replacing the handshake, this discussion is very, very useful. But only as a starting point.
When it comes to handshakes, chicken games can easily be “one-upped.” A offers hand to B. B thrusts his arm out and grabs A’s forearm, in what I think of as the Roman soldier’s shake. No hand contact. B has asserted a manly response to A without loss of face, and while minimizing skin contact (except in summer when short shirts are de rigeur — I’m in the Pacific Northwest where this is not much of a problem).
Hugs are worse. A approaches B with a wide smile, a twinkle in his eye, and wide-open arms. A hug is . . . inevitable? It depends on B’s speed. B opens his arms, then quickly brings them to his chest, and bows. If A is a predatory hugger, moving too fast, there’s a possibility of head bumps. Otherwise, B has given A an option to save face in a similar bow.
What we have to practice, then, is one-upmanship in the face of unwanted contact. The soldier’s armgrasp becomes a response to an unwanted handshake, and the bow becomes the response to the hug.
And as for a stranger coming at you with puckered lips, quickly turn around and offer your posterior.
Michael
May 14 2009 at 4:56pm
Maybe there would only be a polite mix of shaking and not shaking if the infected couldn’t keep from signalling that they are infected.
Bob Murphy
May 14 2009 at 5:40pm
I would only refuse to shake the hands of people eating quiche.
Econ geek jokes aside, I really think handshaking is a bad custom. It’s so tough when you go to a business meal and everyone shakes 4 other hands, then what? Do we all pull out our bottle of Purell? (Yeah I’ve got one.) Do we all run to the bathroom?
And of course, it’s not the similarly germaphobic people who concern me. It’s the guy who doesn’t even think about shaking 4 hands then chowing down, who worries me.
blink
May 14 2009 at 8:06pm
The way Bryan has phrased the question, it sounds like an offer-refuse result is bad for both participants. Since Bryan goes out of his way to say that the no handshake equilibrium is “equally polite,” this game is analogous to deciding whether to drive on the right or left hand side of the street, at least until the flu is factored in.
With a lethal disease spreading, the payoffs for both participants in the offer-offer case fall considerably. If they fall enough (perhaps the likelihood of infection rises sharply), offer-offer will be a worse outcome than offer-refuse. In this case, we quickly switch to the refuse-refuse equilibrium without any effort. If the payoffs do not fall far enough to overcome the embarrassment of offer-refuse, then we will remain in the sub-optimal equilibrium. On this interpretation, the mixed strategy Zac suggests – the person who offers expecting to be refused – make no sense.
Dr. T
May 14 2009 at 8:09pm
Culture is strange. We started with open hand greetings to prove we were unarmed. That morphed into clasping each other’s open hand which sometimes turned into contests of strength or pain tolerance.
Bowing is a display of subservience: you bow to rulers or superiors, thereby exposing the back of your neck to attack. If the ruler likes you, you get to keep your head.
I propose dropping all the physical forms of greeting and just using words: “It’s nice to see you again,” “It’s nice meeting you,” “Hello, John, this should be a productive meeting,” etc. I never understood the need for bowing and scraping or touching and holding when meeting acquaintances.
As for the original scenario: handshaking rarely spreads flu viruses (bacteria, however, are often transferred by handshakes). But, if people thought swine flu could be transmitted by handshakes, then game theory shows that handshaking would rapidly disappear (assuming everyone knows about the risk).
hacs
May 14 2009 at 10:15pm
Considering its dynamic version, to get swine flu could be a probabilistic punishment to deviations from the equilibrium “no one shakes hand”. Using the folk theorem….
Snark
May 15 2009 at 12:48am
A stable equilibria would result in no contact, no disrespect, and no contagions. Solutions as follows (in decreasing order of formality).
– In Thailand, the “Wai” is used to greet one another. It’s a gesture that conveys mutual respect and is performed by joining one’s hands at the palms and raising them to a position somewhere between the chest and forehead. It means hello and goodbye.
– Tebetans greet one another by sticking out their tongues. The tradition started following the death of a black-tongued 9th century king known for his cruelty. Because they believed in reincarnation, they would display their tongues to show that it wasn’t black or that they weren’t evil.
– Maori warriors greet strangers by charging at them with a spear while pulling on their faces.
However, I would rather enjoy seeing a convention of economists chest-bumping each other during cocktail hour.
redbud
May 15 2009 at 5:15am
WE ALL shake hands, while we know another equilibrium doesn’t. We hear the flu might be spread by shaking hands. We don’t want swine flu. So we clean our hands after shaking, or change the shake to avoid germs, or stop shaking altogether.
In my view, WE ALL touch to establish trust. Then we clean hands before meals, in restrooms, and before we touch our faces, so shaking seems quite supportable for folks embracing cleanliness. Sanitizer and wipes sell clean!
To avoid germs and cleaning … fist-bumps work.
Or we can stop touching hands altogether. At that point, I vote for the Indian raised hand greeting. HOW ya doin?
Normal form? No idea 😉
Larry Peoples, Sr.
May 15 2009 at 10:16am
Traditional handshaking is already disappearing as the culture becomes less formal and more germ phobic.
1. Bumping fists? You only touch the back of the fingers and not the palm. (Of course the back of the fingers is what you wipe/scratch your nose with).
2. Slapping hands. (No – Palms again).
3. Both people turn around back to back and rub the soles of their shoes together (Nope – not enough personal space).
4. Head Butts (Ouch!)
5. Spell your gang name with your fingers (Like WSJ or IBD)
6. Calling Cards handed to each other. The fingers would only touch the corners (Nah – Peepel cant spel).
7. Fake celebrity hugs/kisses (Too trendy).
8. Pageant Queen Wave (Hmmm – Maybe)
9. Palm held straight & upright (Too Nazi)
Enough. I’m stumped!!
mobile
May 15 2009 at 11:21am
Let p = payoff for appearing polite (by offering to shake hands)
Let –s = marginal cost of transmitting a disease by hand-to-hand contact
Then payoff matrix for two-player game is
Shake Bow Shake (p-s,p-s) (p,0) Bow (0,p) (0,0)If p > 0 and p–s >= 0, then Shake is a dominant strategy. When s > p and p > 0, there is a Nash equilibrium where the strategy is to Shake with some some probability q and Bow with probability (1-q). As s increases, q decreases and the Bow,Bow outcome becomes more likely.
The more players fear swine flu, the more s increases and steers the game toward a Bow,Bow outcome.
Eric Hancock
May 15 2009 at 1:48pm
Just walk into the room coughing and clearing your throat. Gives everyone an out.
Zac Gochenuor
May 15 2009 at 1:57pm
Bryan, any chance we can get a peek at the answer key? I wonder what you had in mind.
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