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-mean lab-students

0.00

0.05

0.10

0.15

0.20

67

chosen numbers

rela

tive

fre

qu

enci

es

22 50 10033

mean: 36.732/3-mean: 23.49

14

2/3-mean, gametheorists and experimenters

0.00

0.05

0.10

0.15

0.20

chosen numbers

rela

tive

freq

uenc

es

22 50 10033

mean: 18.982/3-mean: 12.65

0 14

Beauty contest results (Expansion, Financial Times, Spektrum)

0.00

0.05

0.10

0.15

0.20

numbers

rela

tive

fre

qu

en

cie

s

22 50 10033

average 23.07

0

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)

:no eliges un numero encima 44.44 (2/3*66.66) nivel 2: (dado nivel 1)

:no eliges un numero encima 29.63 (2/3*44.44) nivel 3: (dado nivel 2)

66.6644.4429.63 0

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

mejora respuesta iterativa ... ... E(3) E(2) E(0)

E(1)

0 14.89 22.22 33.33 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?     Clara distinción entre razonamiento limitado y la solución de la teoría de los juegos         Juego tiene una única solución      se pueden ignorar los factores estratégicos y motivaciones sociales (cooperación, justicia, altruismo)   

   juego puramente estrategica   comportamiento se puede interpretar por razonamiento limitado puro 

    “detección” de distintos etapas (uno a infinito) de razonamiento via

       mejor respuesta iterativa        eliminación iterativa de estrategias dominadas

  

Mean behavior over time

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

time

mea

n

4/3-mean

0.7-mean, 3 players

2/3-mean, 15-18players

1/2-median

some variations

Median-choice of all pairs

0

10

20

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40

1 3 5 7 9 11 13

time

me

dia

n

no info

info

2-person all

Dos personas en el juego

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 DA-markets) 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)

0

50

100

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200

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400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price

Period

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.

• Coordination problem. No one wants to be the first to leave a good party. Investors face a “synchronization risk”, they must attack the bubble simultaneously for it to burst. Some make money “riding the bubble”(Peter Temin and Joachim Voth on South Sea bubble)