J. Bradford DeLong's Blog, page 293

Prisoner's Dilemma, or Prisoners' Dilemma?: Hoisted from the Archives

Hoisted from the Archives: Prisoner's Dilemma: An extended passage from William Poundstone's (1992) marvelous book Prisoner's Dilemma (New York: Doubleday: 038541580X) https://books.google.com/books?isbn=0307763781. Economists will find it hilarious and thought-provoking. Others will probably find it bizarre and weird. It comes from pp.106-118.

Flood and Dresher devised a simple game where [the Nash equilibrium wasn't such a good outcome for the players].... The researchers wondered if real people playing the game--especially, people who had never heard of Nash or equilibrium points--would be drawn mysteriously to the equilibrium strategy. Flood and Dresher doubted it.

The two researchers ran an experiment that very afternoon. They recruited two friends as guinea pigs, Armen Alchian of UCLA ("AA" below), and RAND's John D. Williams ("JW"). The game was presented purely as a payoff table. The payoffs were:

(AA's payoff, JW's payoff)
JW's Strategy 1 [Defect]
JW's Strategy 2 [Cooperate]


AA's Strategy 1 [Cooperate]
(-1, 2)
(1/2, 1)


AA's Strategy 2 [Defect]
(0, 1/2)
(1, -1)

[The Nash equilibrium is defect-defect, of course]... Alchian is always better off choosing his strategy 2, and Williams is
better off choosing his strategy 1. But when both players choose
their "better" strategy, both do relatively poorly.
They actually do better choosing their "worse" strategies--provided
both do it.

The Nash theory suggests the lower left cell as the rational
outcome. Neither player can do any better by switching unilaterally:
a player is always better off defecting, no matter what the other
does....

In the RAND experiment, Alchian and Williams played the game
100 times in succession.... Flood's 1952 paper reports not only
the strategies the two players chose but a log of running comments....
The comments were written after each player had decided on a
strategy in that particular game, but before the other player's
choice was known. Some comments thus refer to the other player's
choice on the previous game. For clarity, strategy numbers have
been replaced with [C] for "cooperate" and [D] for
"defect."

Round
AA
JW
AA's Comments
JW's Comments


1
D
C
JW will play D--sure win. Hence if
I play C--I lose
Hope he's bright.


2
D
C
What is he doing?!!
He isn't, but maybe he'll wise up.


3
D
D
Trying mixed?
OK, dope.


4
D
D
Has he settled on D?
OK, dope.


5
C
D
Perverse!
It isn't the best of all possible
worlds.


6
D
C
I'm sticking to D since he will mix
for at least 4 more times.
Oh ho! Guess I'll have to give him
another chance.


7
D
C
 
Cagey, isn't he? Well...


8
D
D
 
In time he could learn, but not in
ten moves or so.


9
D
D
If I mix occasionally, he will switch--but
why will he ever switch from D?
 


10
D
D
Prediction. He will stick with D
until I change from D. I feel like DuPont.

I can guarantee myself a gain of 5, and guarantee that player
AA breaks even. On the other hand, with nominal assistance from
AA, I can transfer the guarantee of 5 to player AA and make 10
for myself, too. This means I have control of the game to a large
extent, so player AA had better appreciate this and get on the
bandwagon.

With small amounts of money at stake, I would (as above) try
(by using C) to coax AA into mutually profitable actions. With
large amounts of money at stake I would play D until AA displayed
some initiative and a willingness to invest in his own future.
One play of C by AA would change me from D to C, where I would
remain until bitten.

n the last play, it would be conservative for me to switch
to D, but I wouldn't do so if the evidence suggested that AA
was a nice stable personality and not in critical need of just
a little extra cash



11
D
C
 
Probably learned by now.


12
C
C
 
I'll be damned. But I'll try again.


13
C
C
 
That's better.


14
C
C
 
Ha!


15
C
C
 
(bliss)


16
D
C
 
 


17
C
D
 
The stinker.


18
C
D
 
He's crazy. I'll teach him the hard
way.


19
D
D
I'm completely confused. Is he trying
to convey information to me?
Let him suffer.


20
D
D
 
 


21
D
C
 
Maybe he'll be a good boy now.


22
C
C
 
Always takes time to learn.


23
C
C
 
Tim3.


24
C
C
 
 


25
C
C
 
 


26
D
C
 
 


27
C
D
 
Same old story.


28
D
D
He wants more C's by me than I'm
giving.
To hell with him.


29
D
D
 
 


30
D
D
 
 


31
D
C
Some start.
Once again.


32
C
C
JW is bent on sticking to D. He will
not sahre at all as a price of getting me to stick to C.
---, he learns slow.


33
C
C
 
On the beam again.


34
C
C
 
 


35
C
C
 
 


36
C
C
 
 


37
C
C
 
 


38
D
C
 
 


39
C
D
 
The ---.


40
D
D
 
 


41
D
C
 
Always try to be virtuous.


42
C
C
 
Old stuff.


43
C
C
 
 


44
C
C
 
 


45
C
C
 
 


46
C
C
 
 


47
C
C
 
 


48
C
C
 
 


49
D
C
He will not share.
 


50
C
D
 
He's a shady character and doesn't
realize we are playing a 3rd party, not each other.


51
D
C
 
 


52
C
C
 
He requires great virtue, but he
doesn't have it himself.


53
C
C
 
 


54
C
C
 
 


55
C
C
 
 


56
C
C
 
 


57
C
C
 
 


58
C
C
He will not share.
 


59
C
C
He does not want to trick me. He
is satisfied. I must teach him to share.
 


60
D
C
 
A shiftless individual--opportunist,
naive


61
C
C
 
 


62
C
C
 
Goodness me! Friendly!


63
C
C
 
 


64
C
C
 
 


65
C
C
 
 


66
C
C
 
 


67
D
C
He won't share.
 


68
C
D
He'll punish me for trying!
He can't stand success.


69
D
D
 
 


70
D
D
I'll try once more to share--by taking.
 


71
D
C
 
This is like toilet training a child--you
have to be very patient.


72
C
C
 
 


73
C
C
 
 


74
C
C
 
 


75
C
C
 
 


76
C
C
 
 


77
C
C
 
 


78
C
C
 



79
C
C
 
 


80
C
C
 
 


81
D
C
 
 


82
C
D
 
He needs to be taught about that.


83
C
C
 
 


84
C
C
 
 


85
C
C
 
 


86
C
C
 
 


87
C
C
 
 


88
C
C
 
 


89
C
C
 
 


90
C
C
 
 


91
C
C
When will he switch as a last minute
grab of D? Can I beat him to it as late as possible?
 


92
C
C
 
Good.


93
C
C
 
 


94
C
C
 
 


95
C
C
 



96
C
C
 
 


97
C
C
 
 


98
C
C
 



99
D
C
 
 


100
D
C
 
 

For all the confusion, mutual cooperation was the most common outcome (sixty of the 100 games). Had Flood and Dresher used a "fair" [i.e., symmetric] payoff table, the cooperation rate might have been higher yet.

Flood and Dresher wondered what John Nash would make of this. Mutual defection, the Nash equilibrium, occurred only fourteen times. When they shoowed their results to Nash, he objected that:

the flaw in the experiment as a test of equilibrium point theory is that the experiment really amounts to having players play one large multi-move game. One cannot just as well think of the thing as a sequence of independent games.... There is too much interaction, which is obvious in the results of the experiment.

This is true enough. However, if you work it out, you find that the Nash equilibrium strategy for the multi-move "supergame" is for both players to defect in each of the 100 trials. They didn't do that....

What Poundstone means is that, since both players know that the supergame is going to last for 100 periods, there is no reason for people to cooperate in round 100 to induce subsequent cooperation. Hence���whatever else people do���the Nash equilibrium strategy must be to defect in period 100.

But once you know that the other player will defect in period 100 no matter what you do, the same argument applies to period 99: whatever else people do, the Nash equilibrium strategy must be to defect in period 99. Thus the situation "unravels." As long as there is a known, certain last period the only Nash equilibrium is to defect, always, from the first period.

And real people don't do that���at least not unless they are John von Neumann or John Nash.

Alchian wound up with +40

Williams wound up with +63

The full 100-round C,C outcome is +50, +100; the full 100-round D,D outcome is 0, +50.

So even though we identify with Williams���as the smart one, the one trying to induce cooperation, the one understanding that it was the two of them playing the umpire���nevertheless, Alchian "won" in that he got much closer to the total possible value of the game for his payoff matrix...

#hoistedfromthearchives
#gametheory
#behavioral
#prisonersdilemmaorprisonersdilemma

http://www.bradford-delong.com/2018/10/prisoners-dilemma-or-prisoners-dilemma-hoisted-from-the-archives.html

Note to Self: This one goes to 11!#notetoself#acr...

Note to Self: This one goes to 11!

#notetoself
#acrossthewidemissouri
#caffeine

http://www.bradford-delong.com/2018/10/note-to-self-this-one-goes-to-11.html

A Baker's Dozen of Fairly Recent Links

Wolfenoot : "Eat roast meat (because wolves eat meat) and cake decorated like a full moon. A holiday to the spirit of wolves that celebrates people who are kind to dogs? I can 100% get behind this. So we will be celebrating Wolfenoot. It���s on the 23rd November.... If you���re posting publicly about it, use #wolfenoot...
Emma Christensen: Recipe: Chili-Rubbed Ribeye Steak with Maple-Bourbon Butter | Kitchn : "For the steaks: 1 tablespoon cacao nibs 1 tablespoon chili powder 2 teaspoons brown sugar 1 teaspoon salt 1/2 teaspoon smoked paprika (optional) Black pepper 2 (1-pound) boneless ribeye steaks. For the maple-bourbon butter: 1 tablespoon bourbon 1 teaspoon maple syrup 1/2 stick (4 tablespoons) butter, very soft...
John Bell: +Against Measurement_
Daniel Swain: Substantial early-season rainfall in California to dampen explosive wildfire conditions : "Significant rainfall now appears likely from about the SF Bay Area south to Los Angeles County, with at least some precipitation pretty much statewide...
John Williams: 'Normal' Monetary Policy in Words and Deeds : "We could return to a system... in which the supply of reserves... was kept relatively scarce, and the interest rate was set by... open market operations.�� Alternatively, we could continue with the system that we���ve been using since the crisis, in which bank reserves are abundant and the federal funds rate target is achieved through adjustments to administered rates...
Doug Jones: Logarithmic History : "The history of the universe���from the Big Bang to the end of the year���day by day...
Great China Restaurant
Zach Weinersmith: Saturday Morning Breakfast Cereal : "The Program...
Wikipedia: Hexapodia Is the Key Insight!
Noah Smith: Why Millennials Are Sour on the Economy : "Lack of mobility, stagnant incomes and thwarted expectations��is a painful��mix...
Noah Smith: How to Fill the Gaps in the U.S. Economy : "Many of these advances have come through a single agency���the Defense Advanced Research Projects Agency, or DARPA (also known as ARPA at some points in its history)...
Jason Snell: Why Are Apple Watch Faces Such a Mess? : "a lot of Apple Watch users have been surprised that they can���t add older complications to those faces. Apps need to be updated to explicitly support the new complication style, which was only introduced to developers on the day the Apple Watch Series 4 was announced...
Moses Abramovitz (1986): Catching Up, Forging Ahead, and Falling Behind



#shouldread

Note to Self: A new one from United Airlines: ���No drink...

Note to Self: A new one from United Airlines: ���No drinking personal alcohol on this flight���...

#notesoself
#acrossthewidemissouri

http://www.bradford-delong.com/2018/10/nore-to-self-a-new-one-from-united-airlines-no-drinking-personal-alcohol-on-this-flight.html

Nore to Self: A new one from United Airlines: ���No drink...

Nore to Self: A new one from United Airlines: ���No drinking personal alcohol on this flight���...

The Appalachian and Other Trails

https://www.icloud.com/keynote/0HORQ6Ql3Ejvf5PSeGJkEXOyQ

Let's consider the United States in the time of major westward expansion and "Amerindian removal": the century 1760 to 1860 before the Civil War. We have U.S. output-per-worker growth then at about 1.0% per year, in contrast to British output-per-worker growth at about 0.5% per year. We have the U.S. population and labor force growing at 2.5% per year, from 2.5 to 30 million. Our conclusion:

An America penned behind the Appalachians would probably have seen its living standards and productivity levels not growing at 1% per year from 1760 to 1860 but shrinking. For the $ \gamma = 3.0 $ benchmark case, living standards and productivity levels would have shrunk at a pace of -0.325% per year had population growth been the historical 3% per year.

Why? Let's, first, recall our basic Solow Growth Model. When natural resource scarcity is important, it consists of our log-form production function of:

$ \ln(y) = \ln\left(\frac{Y}{L}\right) = $
$ \left(\frac{\alpha}{1-\alpha}\right)\ln\left(\frac{K}{Y}\right) + \ln(E) $

plus the dependence of the efficiency-of-labor E on���non-rival���useful economic ideas H and on���rival and potentially scarce���natural resources R per worker L, with a parameter $ \gamma $ summarizing the relative importance of ideas vis-a-vis resources in driving gorwth in the efficiency-of-labor:

$ \ln(E) = $
$ \left(\frac{\gamma}{1+\gamma}\right)\ln(H) + $
$ \left(\frac{1}{1+\gamma}\right)(\ln(R) - ln(L)) $

Let's, second, suppose the capital-output ratio is constant (variations in it are not important here).

Let's, third, take derivatives to see growth rates. And let's remember that the growth rates of ideas H and the labor force L are h and n, respectively. And let's set the rate of growth of natural resources to be $ \rho $ (we reserve r for interest rates):

$ \frac{d\ln(y)}{dt} = \left(\frac{\gamma}{1+\gamma}\right)h + $
$ \left(\frac{1}{1+\gamma}\right)(\rho - n) $

Let's last, fit this to history in the century before the 1860 election of President Abraham Lincoln and the ensuing American Civil War:

output-per-worker growth $ \frac{d\ln(y)}{dt}=1.0% $ per year
labor-force growth $ n = 2.5% $ per year
natural-resource growth from westward expansion $ \rho = 4.5% $ per year

We have two parameters left: $ \gamma $ and h, the weight of ideas in efficiency-of-labor growth and the rate of growth of the stock of useful ideas for the economy in American heads, respectively. Plugging in the parameters we know gets us:

$ 0.010 = \left(\frac{\gamma}{1+\gamma}\right)h + $
$ \left(\frac{1}{1+\gamma}\right)(0.045-0.025) $

Solving for h:

$ \left(1+\gamma\right)0.010 = {\gamma}h + 0.020 $

$ \left(1+\gamma\right)0.010 - 0.020 = {\gamma}h $

$ -0.010 + 0.010\gamma = {\gamma}h $

$ h = 0.010 - \frac{0.010}{\gamma} $

This tracks: if natural resources were unimportant in determining the efficiency of labor���if $ {\gamma} ��� ��� $���then in order to produce 1% per year growth in output-per-worker at a constant capital-output ratio, you need a 1% per year rate of growth h of the useful economic ideas stock.

Thus if $ {\gamma} ��� ��� $ then $ h = 0.010 $.

Conversely, if ideas were unimportant in determining the efficiency of labor���if $ {\gamma} = 0 $���then in order to produce 1% per year growth in output-per-worker at a constant capital-output ratio, you need a value $ \gamma = 1.5 $ to generate 1% per year of increase in the efficiency-of-labor from increased natural resource abundance alone.

Thus if $ {\gamma} = 1.0 $ then $ h = 0.00 $.

And:

If $ {\gamma} = 3.0 $ then $ h = 0.00667 $.

Looking across the Atlantic Ocean to Great Britain, we see that over there it is indeed the case that $ h = 0.005 $ from 1760 to 1860. Faster growth of h in America due to some catchup with the world's first and leading industrial nation seems likely. So $ \gamma = 3.0 $ has some claim to be the most likely value.

There is a colonial-era British Imperial Proclamation that suggests an obvious counterfactual. In 1763, when all of settled North America east of the Mississippi River was part of the British Empire, King George III Hanover:

declare[d] it to be our Royal Will and Pleasure. that no... Governor or Commander in Chief in... our... Colonies or Plantations in America do presume... grant Warrants of Survey, or pass Patents for any Lands beyond the Heads or Sources of any of the Rivers which fall into the Atlantic Ocean from the West and North West, or upon any Lands whatever, which, not having been ceded to or purchased by Us as aforesaid, are reserved to the said Indians, or any of them...

British settlement was to be limited by the peaks of the Appalachian mountain range. The British government did not want to wage war on the Amerindians. And the British government did want to exercise a modicum of control over where settlers settled.

Suppose that Royal Proclamation of 1763 had stuck. The rate of growth of the natural resources open to the American settlers would then have been $ \rho=0 $. Thus the equation:

$ h = 0.010 - \frac{0.010}{\gamma} $

implies:

If $ \gamma ��� ��� $ and $ h = 0.010 $ then $ g = 0.01 $

If $ \gamma = 3.0 $ and $ h = 0.00667 $ then $ g = -0.00125 $

If $ \gamma = 1.5 $ and $ h = 0.000 $ then $ g = -0.01 $

An America penned behind the Appalachians would probably have seen its living standards and productivity levels not growing at 1% per year from 1760 to 1860 but shrinking. For the $ \gamma = 3.0 $ benchmark case, living standards and productivity levels would have shrunk at a pace of -0.125% per year had population growth been the historical 2.5% per year. Productivity in 1860 would have been not 2.7 times what it had been in 1760, but rather only 0.88 of its 1760 level. Wages in America then would have been closer too but still in advance of Britain's.

Of course, a poorer America would probably have seen fewer immigrants. But it might not have seen that many fewer immigrants. It would no longer have been quite as attractive to move from Britain to America over 1760 to 1860. But it still would have been very attractive to move from France, Germany, Scotland���or most of all from Potato Blight-ridden Ireland...

In what other ways might this counterfactual alternate-history "little America" would likely have been different in 1860 than America actually was?

A large chunk of America's pre-1860 visible growing prosperity was based not just on African-American slavery, but also on "Amerindian removal". Cf.: Trail of Tears:

 

http://www.bradford-delong.com/2018/10/the-apallachian-and-other-trails.html

http://www.typepad.com/site/blogs/6a00e551f08003883400e551f080068834/post/6a00e551f080038834022ad3701f2e200c/edit?saved=e

http://nbviewer.jupyter.org/github/braddelong/LSF18E101B/blob/master/The_Appalachian_and_Other_Trails%20%282018-10-03%29.ipynb

https://www.icloud.com/keynote/0HORQ6Ql3Ejvf5PSeGJkEXOyQ

The search for "robust determinants" has always seemed to...

The search for "robust determinants" has always seemed to me to be wrong-headed. We should be searching for effective policies. And which determinants are "robust" will depend on what other determinants are in the mix. And an effective policy is likely to shift the values of more than one "determinant": Dani Rodrik: "Is 'export sophistication' (as in Hausmann, Hwang, and Rodrik 2007) the only robust determinant of economic growth? Robust, that is, to correcting for endogenity and OVB as best as possible? This new paper from the IMF says yes https://t.co/C3DkRzqr8d...

#shuoldread

Dan Drezner: The world is laughing at President Trump: "T...

Dan Drezner: The world is laughing at President Trump: "That is bad news for America.... Trump claimed that he intended to inspire the laughter, but that dog won���t hunt...

...Matthew Choi noted, ���It���s unusual for a U.S. president to draw unintentional laughs at a gathering of world leaders, and Trump has long complained that foreign governments are laughing at the U.S. for what he views as weak policies on trade and other issues.��� The New York Times' Mark Landler tweeted, ���The laughter at Trump���s UN speech underscores a hard reality for him: After 20 months of bombast, he���s now viewed by many foreign officials as a source of humor rather than fear.��� The spontaneous laughter clearly rattled Trump. What should really rattle him, however, is that in the 24 hours surrounding his U.N. General Assembly speech, the rest of the world was finding ways to move while Donald Trump was standing still.

Consider that the other signatories to the Iran nuclear deal agreed to create a structure to work around reimposed U.S. financial sanctions.... This is about the European Union, Russia and China devising a payments and settlement system that bypasses the United States. The more adept that these countries become at circumventing U.S. capital markets, the more it erodes the power of U.S. financial statecraft. China is not only trying to blunt U.S. financial power, however. In the wake of U.S. withdrawal from activities at the United Nations, China is filling the vacuum.... In part China is filling a space created by the withdrawal of the US from bodies such as the Geneva-based UN Human Rights Council and the UN���s cultural arm, Unesco.... Whatever objections the Trump administration might have with UNESCO and other U.N. agencies, its strategy of withdrawal has accomplished little other than ceding influence over these organizations to China. Meanwhile, U.S. allies continue to resist the Trump administration���s pressure to make trade concession...

#shouldread

Comment of the Day: Ronald Brakels: Strong AI: "Just so y...

Comment of the Day: Ronald Brakels: Strong AI: "Just so you know, once we get something that can accurately transcribe podcasts that will be strong AI. It'll be some mightily powerful strong I. I'm not saying podcast transcribers are going to take over the world, but I am saying that we fix this one little annoying thing and we change the world beyond recognition...

#commentoftheday

How important was the financial panic as a cause of the Great Recession? - EconSpark

Over on EconSpark, I think this is wrong: Ben Bernanke: How Important Was The Financial Panic As A Cause Of The Great Recession?: "The collapse of the housing bubble was certainly a primary cause of the Great Recession. ��The unwinding of the bubble (1) depressed aggregate demand through its adverse effects on consumer wealth and residential construction, and (2) triggered a financial panic...

The unwinding of the bubble set the table for the financial panic, but it did not trigger it. The bubble had already been unwound before the panic. The triggers of the panic lay elsewhere: in the events in financial markets that produced a sudden, discontinuous boost in the demand for safe assets. One picture I have always found very illuminating is this one:

Real exports, real private nonresidential fixed investment, real residential fixed investment, real government purchases, all as deviations from their 2007:IV shares of real potential GDP.

From 2005 through the end of 2007 the housing bubble breaks���and real housing investment relative to potential real GDP falls by 3.3%-points of real potential GDP. Yet there is no recession. Expenditure is smoothly switched from residential investment to exports and non-residential investment. Consumption is not noticeably weak in spite of the impact of diminished housing wealth on households.\

Thus my belief that if the financial crisis had been managed���if the Bagehot Rule had been followed, and if there had been authorities to lend freely at a penalty rate on collateral that was good in normal times���and if 2008 had passed without a crash, then our proves would have been over. It was not the case that the economy in November 2008 "needed a recession" as John Cochrane liked to claim, "because people pounding nails in Nevada needed to find something else to do". The expenditure-switching had already happened. All that needed to be done was to keep demand for safe assets from exploding���and that is what lending freely at a penalty rate on collateral good in normal times is supposed to do.

And then, of course, in late 2008 things go to in a handbasket. And fiscal support is inadequate by orders of magnitude. And then after 2008 nothing is done to restart financial intermediation in the housing sector at its normal pace. And after 2010 we see fiscal shock after fiscal shock after fiscal shock...

And so here we are, 10% poorer than we thought a decade ago we would be now. And with lots of scarring ��on lots of lives and organizations......

#shouldread
#monetarypolicy
#Bagehotrule
#financialcrisis
#finance