reglas del concurso sobre bellezas (beauty contest)
 Participantes tienen que elegir un numero del intervalo 0 a 100.
 El ganador será aquella persona que escoja el número que más se acerque a los 2/3 del promedio
de todos los números elegidos
 El ganador recibe un precio fijo ($10 –dos billetes a NY). En caso de un empate el premio se dividirá
entre los ganadores.
 Tiempo para pensar: 5 minutos – 3 semanas
 Se puede repetir el mismo juego por varias rondas.
 Se puede variar la información después una ronda
Se piden comentarios sobre las decisiones.
2/3-m e a n , g a m e th e o rists a n d
2/3-m e a n la b -stu d e n ts
e x p e rim e n te rs
0.20
0.20
m ean: 18.98
2/3-m ean: 12.65
re la t iv e f re q u e n c e s
0.15
m ean: 36.73
2/3-m ean: 23.49
0.10
0.10
0.05
0.05
0.00
14
22
33
50
100
67
0.00
0
ch o s e n n u m b e r s
14
22
33
50
100
ch o s e n n u m b e r s
Beauty contest results (Expansion,
Financial Times, Spektrum)
relative
frequencies
re la t iv e f re q u e n c ie s
0.15
average 23.07
0.20
0.15
0.10
0.05
0.00
num bers
0
22
33
50
100
Teoría
• Equilibrio en el juego básico: todos eligen 0; eliminación iterativa de
estrategias dominadas
nivel 1: no eliges un numero encima 66.66 (2/3 de 100)
nivel 2: (dado : no eliges un numero encima 44.44 (2/3*66.66)
nivel 1)
nivel 3: (dado : no eliges un numero encima 29.63 (2/3*44.44)
nivel 2)
0
29.63
44.44
66.66
Comportamiento
•
•
•
•
•
nivel 0: al azar
nivel 1: mejor respuesta al azar: promedio 50
nivel 2: mejor respuesta al level 1
Etc
Hasta: nivel infinito: ….=>0
m ejora respuesta iterativa
... ...
0
E (3) E (2)
14.89 22.22
E (1)
33.33
E (0)
50
100
Quizá también: hay jugadores que piensan en distribución sobre distintos
niveles y dan mejor respuesta a esto? Si => Camerer; Ho, Chong (2004)
Porque un estudio de comportamiento es interesante con este juego?
n Clara distinción entre razonamiento limitado y la solución de la teoría de los juegos
 Juego tiene una única solución
n se pueden ignorar los factores estratégicos y motivaciones sociales (cooperación, justicia,
altruismo)
 juego puramente estrategica
 comportamiento se puede interpretar por razonamiento limitado puro
n “detección” de distintos etapas (uno a infinito) de razonamiento
via
 mejor respuesta iterativa
 eliminación iterativa de estrategias dominadas
M ean b eh avio r o ver tim e
som e variations
100
mean
80
4/3-m ean
60
0.7-m ean, 3 players
40
2/3-m ean, 15-18
players
20
0
1/2-m edian
1
2
3
4
5
6
tim e
7
8
9
10
Dos personas en el juego
Median-choice of all pairs
median
2-person
all
40
30
no info
info
20
10
0
1
3
5
7
time
9
11
13
Asset market
• Assets are different from ordinary goods in
that they derive their value:
• 1. from a stream of dividents
• 2. from capital gains
• These are UNCERTAIN and depend on
the state of nature and trader’s
expectations
• In the lab we may control for exogenous
uncertainty and study endogeneous
uncertainty (expectations)
• In an efficient market, all relevant public
information is reflected in the price of an
asset. Prices cannot be too high or too
low.
• Bubbles are a theoretical impossibility: if a
stock’s price exceeded its fundamental
value, rational investors would sell the
shares they own as well as sell stock
short, putting pressure on the price.
• Before the 2000 crash, in 1997, Ivo Welch
surveyed 110 financial economists. Fewer
than 1 in 10 disagreed with the statement:
“By and large, public securities market
prices are efficient”
Double Auction Asset Markets
(Smith, Suchanek and Williams 1988)
• Subjects are endowed with assets and cash which can
be transferred to future periods.
• Total cash holdings at the end of the final period T are
paid to the subjects.
• At the end of each period t assets yield a dividend of 0,
8, 28 or 60 cents with equal probability.
• Expected value of dividend payment is 24 cents.
• At the end of the final period, after the realization of the
dividend return, assets are worthless.
• Assets can be traded in a double auction.
Predictions
• If the rationality and risk neutrality of all traders is
common knowledge there should be no trade.
• Trade only takes place in case of heterogeneous risk
preferences.
• Suppose that for risk loving agents the certainty
equivalent of the asset is .24 +  (>0 but small) per
period while for risk averse agents it is .24 - . Then,
under rational expectations, the price in period t must
be within (T – t)(.24 ± ).
Results
• Inexperienced and professional traders who participate
for the first time in the asset market (not in other DAmarkets) trade a lot at prices far above the fundamental
value.
• Traders who participate for a second time trade less at
lower prices but still above the fundamental value.
• Twice experienced traders trade, if at all, at the
fundamental value.
• Interpretation: If rationality is not common knowledge
even rational traders may have an incentive to speculate
(analogy to the guessing game).
Price Bubbles and Experience
Volume of Trades
Price Bubbles in Asset Markets
(Becker, Fischbacher and Hens
2002)
400
350
300
250
Price
200
150
100
50
0
1
2
3
4
5
6
7
8
Period
9
10
11
12
13
14
15
Extensions
• Short selling (selling unowned assets) and
buying with credit exacerbate speculative
bubble. Reason: Crazy types can have a
bigger impact on the bubble because their
financing constraints are softened.
• Derivatives do not remove the bubble
(Porter/Smith 1995).
• Increase in liquidity blows up the bubble.
The Nation too, too late will find
Computing all their Cost and Trouble
Directors Promises but Wind
South Sea at best a mighty Bubble
Jonathan Swift, December 1720
Why bubbles persist?
• Investors may not recognize that a stock is
overvalued (they may believe that somebody
has privileged information) Joerg Oechssler
(University of Heidelberg) "Asset Bubbles without
Dividends - An Experiment" (joint with C. Schmidt and
W. Schnedler)
• Investors who recognize that a stock is
overvalued pour money into it not to forgo
profitable opportunities if they pull out too
soon.
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