Vincent
Crawford, "Modeling Behavior in
Novel Strategic Situations via Level-k
Thinking," to be
presented in the Marketing Seminar, Haas School of Business, University
of California, Berkeley, 3 April 2008; the Applied Micro Theory
Workshop, University of Pennsylvania, 28 April 2008; and at GAMES 2008,
Third World Congress of the Game Theory Society, 14 July 2008
(This
paper is an extensive revision of Gneezy and
Rottenstreich, “The Power of
Focal Points is Limited: Even Minute Payoff Asymmetry
yields
Massive Coordination
Failures,” 2005.)
Framing the game in our "Chicago Skyscrapers" treatment: the Sears
Tower, with the AT&T Building in the background on its left
Vincent
P. Crawford, "Level-k
Thinking" Lecture
slides (there is no paper
yet), presented at the
2007 North American Meeting of the Economic Science Association,
Tucson, October 18-21
Previous
version, July 2006; Previous version, November 2005 (this
version extends our
October 2005 specification of truthful level-k types to allow L0 to condition on its own
information in a more sensible way, which changes the model's
predictions for Avery and Kagel's (1997) design; and corrects an error
in our derivation of the implications of random level-k types in
Goeree, Holt, and Palfrey's (2002) design); First
version, October 2005
Reference
(without screen credit, and with no real appreciation
of the importance of level-k
thinking...) on 2005 episode of the CBS series Numb3rs, "Assassin," first aired
10/21/2005 (courtesy of William
Nguyen Phan; YouTube Clip; Text; Moriarti
Comment)
Charlie: Hide and seek. Don: What are you talking about, like the kids’ version? Charlie: A mathematical approach to it, yes. See, the assassin
must hide in order to accomplish his goal, we must seek and find the
assassin before he achieves that goal. Megan: Ah, behavioral game theory, yeah, we studied this at
Quantico. Charlie: I doubt you studied it the way that Rubinstein,
Tversky and Heller studied two person constant sum hide and seek with
unique mixed strategy equilibria. Megan: No, not quite that way. Don: Just bear with him.
Thoughts on Hide and Seek games
played on naturally occuring
"landscapes" from Edgar Allan Poe's The
Purloined Letter (complete
story)
General principles:
"…But he perpetually errs by being too
deep or too shallow, for the matter in hand; and many a schoolboy is a
better reasoner than he. I knew one about eight years of age, whose
success at guessing in the game of 'even and odd' attracted universal
admiration. This game is simple, and is played with marbles. One player
holds in his hand a number of these toys, and demands of another
whether that number is even or odd. If the guess is right, the guesser
wins one; if wrong, he loses one. The boy to whom I allude won all the
marbles of the school. Of course he had some principle of guessing; and
this lay in mere observation and admeasurement of the astuteness of his
opponents. For example, an arrant simpleton is his opponent, and,
holding up his closed hand, asks, 'are they even or odd?' Our schoolboy
replies, 'odd,' and loses; but upon the second trial he wins, for he
then says to himself, the simpleton had them even upon the first trial,
and his amount of cunning is just sufficient to make him have them odd
upon the second; I will therefore guess odd'; --he guesses odd, and
wins. Now, with a simpleton a degree above the first, he would have
reasoned thus: 'This fellow finds that in the first instance I guessed
odd, and, in the second, he will propose to himself upon the first
impulse, a simple variation from even to odd, as did the first
simpleton; but then a second thought will suggest that this is too
simple a variation, and finally he will decide upon putting it even as
before. I will therefore guess even' guesses even, and wins. Now this
mode of reasoning in the schoolboy, whom his fellows termed 'lucky,'
--what, in its last analysis, is it?"
"It is merely," I said, "an identification of the reasoner's intellect
with that of his opponent."
(glossary: "arrant simpleton" = L1 (conditional on shared history,
which makes one choice focal in a way that would attract L0);
"simpleton a degree above the first" = L2; boy with all the marbles =
L2 or L3, depending on his assessment of
how simple his opponent is)
Specific
application:
"At length my eyes, in going the
circuit of the room, fell upon
a trumpery filigree card-rack of pasteboard, that hung dangling by a
dirty blue ribbon, from a little brass knob just beneath the middle of
the mantelpiece. In this rack, which had three or four compartments,
were five or six visiting cards and a solitary letter. This last was
much soiled and crumpled. It was torn nearly in two, across the middle
--as if a design, in the first instance, to tear it entirely up as
worthless, had been altered, or stayed, in the second. It had a
large black seal, bearing the D-- cipher very conspicuously, and was
addressed, in a diminutive female hand, to D--, the minister, himself.
It was thrust carelessly, and even, as it seemed, contemptuously, into
one of the upper divisions of the rack.
"No sooner had I glanced at this
letter,
than I concluded it to be
that of which I was in search. To be sure, it was, to all
appearance, radically different from the one of which the Prefect
had read us so minute a description. Here the seal was large and
black, with the D-- cipher; there it was small and red, with the
ducal arms of the S-- family. Here, the address, to the Minister, was
diminutive and feminine; there the superscription, to a certain
royal personage, was markedly bold and decided; the size alone
formed a point of correspondence. But, then, the radicalness of
these differences, which was excessive; the dirt; the soiled and
torn condition of the paper, so inconsistent with the true
methodical habits of D--, and so suggestive of a design to delude
the beholder into an idea of the worthlessness of the document;
these things, together with the hyperobtrusive situation of this
document, full in the view of every visitor, and thus exactly in
accordance with the conclusions to which I had previously arrived;
these things, I say, were strongly corroborative of suspicion, in
one who came with the intention to suspect."
Vincent
P. Crawford, "Look-ups
as the Windows of the Strategic Soul:
Studying Cognition via Information Search in Game Experiments"
(based
on joint work with Miguel
A. Costa-Gomes and
Bruno Broseta), to appear in Andrew Caplin and Andrew
Schotter, editors, Perspectives on
the Future of Economics: Positive and Normative Foundations,
Volume 1 in the series Handbooks of
Economic Methodologies, Oxford University Press, 2008; Lecture Slides presented atMethodologies of Modern Economics
Conference,
Center for Experimental Social Science, New York University, 28-29 July
2006; Lecture Slides to be
presented at the Conference on the Foundations of Positive and
Normative Economics, New York University, 25-26 April 2008.
Miguel
A. Costa-Gomes and
Vincent P. Crawford, "Studying
Cognition via Information Search in Two-Person Guessing Game
Experiments," paper still in progress
Lecture Slides,
Berkeley
Psychology and Economics Seminar, 6 March 2007, and the Barcelona JOCS
Seminar, 26 March 2007;
focusing on cognitive and experimental issues
Lecture Slides, Workshop
on Econometrics and Experimental
Economics, Northwestern University, 28 April 2006; focusing on
econometric issues
Earlier version of Lecture Slides,
Chicago,
2007, AEA Meetings; focusing on cognitive and experimental issues
"The truth deserves a bodyguard of lies." -- Winston
Churchill,
Teheran, 1943
"The threat reporting that we received in the Spring and Summer
of 2001
was not specific as to time, nor place, nor manner of attack. Almost
all of the reports focused on al-Qaida activities outside the United
States, especially in the MiddleEast and North Africa. In fact, the
information that was specific enough to be actionable referred to
terrorist operations overseas. More often, it was frustratingly vague.
Let me read you some of the actual
chatter that we picked up that
Spring and Summer:
· 'Unbelievable news in coming
weeks'
· 'Big event ... there will be a
very, very, very, very big
uproar'
· 'There will be attacks in the
near future'
Troubling, yes. But they don’t tell us
when; they don’t tell us where;
they don’t tell us who; and they don’t tell us how." -- Condoleeza
Rice, Opening Remarks to the National Commission on Terrorist Attacks
Upon the United States, 8 April 2004.
Question for Rice, Bush, Cheney, and Rumsfeld: If
Al-Quaeda
had sent
you a message saying "We're going to hijack airplanes and crash them
into the World Trade Center--the one in New York City--on September
11--this September 11", would you have believed them?
Readers (and potential Routledge
authors) should note that
Routledge eliminated crucial parts of Figure 6.2(b), making it
meaningless. There should be a closed dot at (2,0) and an open dot at
(0,0), as in the UCSD Discussion Paper 97-19 version.
Vincent
Crawford, "Theory
and Experiment in the Analysis of Strategic Interaction," in David
Kreps
and Ken Wallis, editors, Advances
in Economics and Econometrics: Theory and Applications, Seventh World
Congress,
Vol. I, Econometric Society Monographs No. 27, Cambridge, U.K., and New
York:
Cambridge University Press, 1997, 206-242; reprinted
with minor changes
and
additions in Colin Camerer, George Loewenstein, and Matthew Rabin,
editors, Advances in Behavioral Economics, Princeton,
NJ: Princeton University Press, 2003,344-373.
"The
Protestant Ethic
and the Spirit of Stuffiness" or "Who is Gerard Wanrooy and why did he (and his boss at Elsevier, JoopDirkmaat),
overriding JEBO editor Barkley Rosser's decision,
refuse to publish one of these photographs in the article or to post
them as accompanying materials linked on JEBO's website; and why did they try even
to refuse us the right to publish a link in JEBO to the photographs posted on
this website?"
Vincent Crawford, "John Nash
and the Analysis of Strategic
Behavior," Economics
Letters 75 (May 2002),
377-382; UCSD
Discussion Paper 2000-03;
reprinted in Greek translation, with minor changes,
as "O John Nash και η ανάλυση της στρατηγικής συμπεριφοράς," in Θεωρια
Παιγνιων: Αφιερωμα στον John Nash (Game Theory: A Festschrift in Honor
of John Nash), Constantina Kottaridi and Gregorios Siourounis, editors,
Athens: Eurasia Publications, 2002
Sara
Robinson's August 24, 2004 New York Times article, "Tweaking
the Math to Make Happier Medical Marriages"
(html)
and the graphic published with the article (jpg),
discussing:
Interview of
Distinguished Professor at the University of California, San Diego,
Professor Vincent P. Crawford: "In the
Laboratory We Learn
How Decisions are Made," in the special inset "MBA
Open" of the Greek newspaper "The News," 15 March
2005 by Constantina Kottaridi (Lecturer
in Economics, University of Peloponnese) (html
in Greek; archive link in Greek; doc
in English)
Patricia Morén's March 29, 2007 Diario Medico
(free online registration
required) article about the
proposal, "La flexibilidad salarial del residente mejora su
asignación a distintos centros" (pdf)
"This was the Dyer house originally. It was built in the 1930s. It
became part of the Park history. It is—was our headquarters. And now
you see, because of the fire, what remains.
The Park is over 26,000 acres. Most of it is burned over. The majority
is burned, because of the fire.
Being one of the rangers here, I was raised in this area. And looking
at the headquarters and all around us to see the devastation, it takes
your heart and your soul. It's—it's really devastating. It's
a beautiful place, but you can see now what's happened.
But with fires and with destruction, out of the ashes, we'll rise
again. We'll come back. We'll be back. The public can come back at a
future date to enjoy the park. It's a magnificent area. It's one of the
most beautiful areas in San Diego County. And I just want to say that
we’ll be back."
Previous version
(UCSD
Discussion Paper 2001-16)
