deal or no deal decision making under risk in a large-payoff game show

7/30/2019 Deal or No Deal Decision Making Under Risk in a Large-Payoff Game Show

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38

American Economic Review 2008, 98:1, 3871

ttp://www.aeaweb.org/article.pp?doi=10.1257/aer.98.1.38

A w g k b p, g

xp J N Ok Mg (1944) p

pp D K A Tk (1979). Ag k -

b , p g p

b .

M b M A (1953), D Ebg (1961), wk b K Tk w b g xp w

p q. W g pp xp , k

xp w k b pp, b b b-

g xp k. S xp

pb b g pg , b

g ; , xp, H P. Bwg (1980, 1981) S J.

K M S (1992). S, k xp p

g p b k g-

g pp g w.

Nxp p p pg b w p-

pb. R b k p - pb,b pbb b kw b b b

Deal or No Deal?

Decision Making under Risk in a Large-Payoff Game Show

By Thierry Post, Martijn J. van den Assem,Guido Baltussen, and Richard H. Thaler*

We examine te riky coice o contetant in te popular TV game owDeal or No Deal and related claroom experiment. Contrary to te tradi-tional view o expected utility teory, te coice can be explained in large partby previou outcome experienced during te game. Rik averion decreaeater earlier expectation ave been attered by unavorable outcome or ur-paed by avorable outcome. Our reult point to reerence-dependent coiceteorie uc a propect teory, and ugget tat pat-dependence i relevant,even wen te coice problem are imple and well defned, and wen largereal monetary amount are at take. (JEL D81)

* P: E S E, E U R, P.O. Bx 1738, 3000 DR, R, N (-: gp@w..); V A: E S E, E U R (-: @w..); B: Tbg I E S E,E U R (-: b@w..); T: G S B, U Cg, 5807 S. Ww A., Cg IL 60637 (-: @ggb.). W k Nk Bb,Ig D, G H, P M, P Wkk, pp BDRM X S M,FUR XII 2006 R, EFA XXXIII 2006 Z, EEA XXI 2006 V, EWGFM XL 2007 R, - pp E U R, U Z, U Gg, U A, U Lg, , gg.W k Mq Kg, E, TROS, S.1, pg w / g D N D, M S g g w xp, Nk H J-H P k . F pp b Tbg I, E R I Mg, E C F R g kwg. A g w.


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VOL. 98 NO. 1 39POsT ET AL.: DEAL OR NO DEAL?

kw . F xp, k

p, kw w b gg -

b . W k q

q p 7 p p , w p b xp b -

b w b p ? A p b pb bw k : -

w p pbb.

I pb, z b -

TV g w, xp C Sk (Rb H. G 1993), Jp!

(Aw Mk 1995), I I R (Pp L. H G S. MDg

1997), Lg (R M. W. J. B P C. S 2001), H M

(C R. Fkp, R A. T, Rb H. B 2003) W W b

M? (Rg H, G L, I Wk 2006). T g g

w k g xp pb

p b .

T g w w , D N D, b pp b g b xp TV w. H

g. A w 26 b w

, gg 0.01 5,000,000 ( D ). T pk

b w kw . Nx, 6 25 b

p. E p b 26 pz not w b. T

p bk pp wk w w

k p q: D N D? I N D,

p b, w b w bk . T g

p bk ,

w b. T bk p p b; , xp, p g- b, bk .

T g w w zg k . T k g

w-gg: g p p-. Uk

g w, D N D p p-g (D N

D) q k, kwg, g, pbb b

p kw w - ( bk g pb, ).

F, g w p g , q p

g zg p-p, . T E J.

J (1990) k b p -

, k p pg g. Ag

D N D p w pk, g pp p g- b (g xp wg

), f bq . (Tg w w

p-, b w

g xp.)

W x g 151 N, G, U

S 20022007. T g g N w b

w. Ag D N D g ,

w . F xp, I, F,

Sp, bk kw b k , -

g g bw bk . I A, p g p kw C Sp

g-w p D. T p


3/36

MARCh 200840 ThE AMERICAN ECONOMIC REVIEW

w p , b pbb b kw,

g p k g. F , w

g p N, G, U S.

T g , p b

k. W g pz b w D g400,000, g G US g 25,000 100,000,

p. A g, k p pg

k p . (W , k g

w p .) Hw, - , w,

p k . T

k k , w xp w

g pp. I xp, w pz w ,

w , xp, 100 b w bw

b xp.

O g w xp . T

pp b g p b p xp g g. Rk xp b b pg g-

b, w bk- . S, k

xp b p b pg w- b, w

- .

T x p xp w w ,

b b p g pb, p

p b g pb. O p -

p , pp , p-p ,

w g, k. W pp pp

w p-p p xp .O , w b w g xp bg

k pp . Ag p xp b

xp w, b b w

x g ( pp b, xp, M F

L J. Sg 1948, H Mkwz 1952), p p . T,

p . R, g p

-p p-p, p p p-

xp , b pp . A pb xp

b g w p. A w

p xp w k b g

g g k TV w xp.

T pp gz w. I S I, w b g w

g . S II . S III p

k D N D b xg bk -

p (D) (N D) . S IV z

g xp w g, fxb- xp-pw . S

V z g pp w p p w p

b p p g. T p-

pp xp p w xp x-

p. S VI p xp w p D N D. T xp p p gg

k p p


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. S VII g k gg . F,

pg g p D N D b b

w b Ob 2005.

I. Description o the Game Show

T TV g w D N D w p b D p p

E w N Db 2002. T g w b

pp w xp z , g G U

S. T wg p pp D p D N D. Exp

, g G US

.

E p w p: g b qz q

, g w p D N

D. A b b b x p: p

pg w pp k bq b pp. O g b . Exp

g , g f

g. T w pz b g g.

T g w x kw 26 gg 0.01

5,000,000, w b 26 b b.

O b b b b p

g.

T g p x . I ,

25 b b p, g pz . Nx, bk

b b b kg . C w bw D N D,

w b.1 T g pz bk p

b b z b . I p

(D), wk w w g ;

(N D), g x .

I , x b b p, bk

b g 20 pz. T b b b p x

g bq 5, 4, 3, 2, 1, 1, 1, 1. Ag, b pz

g 15, 11, 8, 6, 5, 4, 3, 2. I

pz w b. Fg 1 b g.

T p g, Fg 2 w p xp w g p TV . A -p w

g pz g . E pz w

k g pz bg . T bk p p

.

A b b, pz g p p kw.

Dg g, p kw g

b p. I , , b p , b

50/50 gb w w g b.

1 I US G , / g b . I D G , p p .


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A.Bank Beavior

Ag kw x bk , bk b

g p. F p b z p:

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

CSJFGDBTFT

PQFODPOUFTUBOUTCSJFGDBTF

PQFODBTFT

PQFODBTFT

PQFODBTFT

PQFODBTFT

PQFODBTFT

PQFODBTF

PQFODBTF

PQFODBTF

PQFODBTF

PQFODBTF

CBOLPGGFS

CBOLPGGFS

CBOLPGGFS

CBOLPGGFS

CBOLPGGFS

CBOLPGGFS

CBOLPGGFS

CBOLPGGFS

CBOLPGGFS

Figure 1. Flow Chart of the Main Game

Note: I , b b b p, gg w b kw pz w b. A pz b , bk p . I p (D), wk w w g ; (N D), p x . I - N D , pz w b. T fw pp D US G . T G w g w 20 b.


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R 1. Bk p p b: w w (g)

pz , g g pz () bkk b (w) .

R 2. T p w pg ( 10 p) -

g g pz g 100 p

. T g b g pg

g g x.

R 3. T , , b w

g pz b. O p kw

b pz b. I, bw

pg bk pz w b.

R 4. T bk g b g g pg -

g g pz. T p w p-p k . I

g-w p k g ,

g kp g

g w. Ug g, w xp p

g g; , w, , pp b w g k, g

g.

S III g p bk p S IV p p p b b. T k g bk

g pb.

@ 13,000

; 0.01

; 0.20

; 0.50

; 1

; 5

; 10

; 20

; 50

; 100

; 500

; 1,000

; 2,500

; 5,000

; 7,500

; 10,000

; 25,000

; 50,000

; 75,000

; 100,000

; 200,000

; 300,000

; 400,000

; 500,000

; 1,000,000

; 2,500,000

; 5,000,000

close-up of the

contestant is

shown here

Figure 2. Example of the Main Game as Displayed on the TV Screen

Note: A -p w . T pb pz g . Pz w k g pz bg . T p b b w bk . T xp w pp pg x b : p bk 13,000 pw g 20 b, w w. T xp f pz Dp.


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II. Data

W x D N D 151 ppg p

N (51), G (47), U S (53).

T D D N D Miljoenenjact ( Cg M).T D p w Db 22, 2002, p

J 1, 2007. I p, g w w 51 , g

wk p p Nw Y D, w

p p. A gg D g k: -

g pz q g 400,000 (391,411 p 147 419,696 p 4851).

C g w 5,000,000. T D p b

pbb xp w D g pz. T g pz

b p w p w

xpg b. P 51 w w p b

p g w w b D bg p TROs.

I G, Deal or No DealDie sow der Glckspirale J23, 2005, bg J 28, 2006.2 Ap b pz, w

. T 20 pz 26 p x

8 g 9. B 8 x q 29

g b g pz b b-

b p, w z b kpp.

B x pz (250,000) g pz

p q (26,347 25,003, p). I pp w

w w G b bp. T w b

wk 10 p, w w pg g q. T

w w wk 27 p, w - p p, bgg b G p 47. Cp

w b TV sat.1 E p -

p E D. T w b .

I U S, g w b Db 19, 2005, g

TV Fb 27, 2006. T 34 p

J 2006. T 39 p b g 53 , w -

g p g g x. T g US

x pz $1,000,000 (g 800,000) g $131,478 (105,182).

I g x , w, p pz g w g k

. A US w w b . US

b g g x 0.80 p $ ( xg ww 5 p b 2005 2006 p).

F , w g pz, bk ,

D N D g , g p w -

( g ) - ( ).

W g, g, . Ag

k g g. T

b, w 1 g w

b g g (g ) q wk xp. Ag

xp ,

2 A Der MillionenDeal M 1, 2004. T g pz w 237,565 g pz w 2,000,000. T w 6 p .


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p. W g g b p pp

k, xp, g .

Hw, g, g, g xp pw . I

p w, f k pg . F xp, g g,

p w , b, p, - g k b p gp, gg

g, g . F k b, w w p

. M, p

, pbb w

b p-p, w k .

Tb 1 w p. Cp G US -

, D g p w pg bk (76.3 p

91.8 91.4 p) p g w g (5.2 8.2 7.7

). T f b k

w, , p. I , g k (IRRA) p xp . A D g k

G US , k

Table 1Summary Statistics

M S. . M. M Mx.

A. Neterland 1N5512Ag () 45.31 11.51 21.00 43.00 70.00

G ( 5 1) 0.27 0.45 0.00 0.00 1.00E (g 5 1) 0.55 0.50 0.00 1.00 1.00Sp R 5.22 1.75 3.00 5.00 10.00B O R (p) 55.89 32.73 10.17 55.32 119.88O Ap (p) 76.27 30.99 20.77 79.29 165.50A W () 227,264.90 270,443.20 10.00 148,000.00 1,495,000.00

B. Germany 1N5472Ag () 36.47 8.17 20.00 35.00 55.00G ( 5 1) 0.34 0.48 0.00 0.00 1.00

E (g 5 1) 0.47 0.50 0.00 0.00 1.00Sp R 8.21 1.53 5.00 8.00 10.00B O R (p) 89.07 33.90 37.31 88.22 190.40O Ap (p) 91.79 19.15 52.78 95.99 149.97A W () 20,602.56 25,946.69 0.01 14,700.00 150,000.00

C. United state 1N5532Ag () 34.98 10.03 22.00 33.00 76.00G ( 5 1) 0.57 0.50 0.00 1.00 1.00

E (g 5 1) 0.49 0.50 0.00 0.00 1.00Sp R 7.70 1.29 5.00 8.00 10.00B O R (p) 80.98 17.57 44.04 83.52 112.00O Ap (p) 91.43 15.31 49.16 97.83 112.50A W ($) 122,544.58 119,446.18 5.00 94,000.00 464,000.00

Note: T b w p p 151 N (51; p A),G (47; p B) U S (53; p C). T , g , k bw . Ag .G b w g . E b k

w b g g (g ) q wk xp. Sp R b w bk p. T b G p b 11 w b b g ; w p g , p q 10. B O R g pg bk - (N D). O Ap pg bk p b (D), 100 p w . A W q p bk , pz w b w .


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zb p pg. F, b b p f b b bk. T pg bk

w p g q

k g b g p. T,

bw D G US -

w IRRA.

A. Cro-Country Analyi

Ap k, g w -

. S, w p p. I D G p p

p g w w qz q, w w g

Table 2Bank Offers and Contestants Decisions

U D N D

R % BO Sk N. % BO Sk N. % BO Sk N.

A. Neterland

1N5 51

21 6 387,867 51 0 6 387,867 512 14 376,664 51 0 14 376,664 513 34 369,070 51 36 409,802 10 33 359,135 414 61 348,820 41 69 394,860 11 58 331,939 305 77 317,618 30 82 557,680 7 76 244,555 236 88 234,877 23 90 237,416 12 87 232,107 117 98 243,868 11 104 414,106 6 91 39,582 58 96 50,376 5 100 78,401 3 90 8,338 29 106 11,253 2 91 17,500 1 120 5,005 1

B. Germany1N5 4721 8 24,277 27 0 8 24,277 272 15 24,915 47 0 15 24,915 473 34 23,642 47 0 34 23,642 474 46 21,218 47 0 46 21,218 475 59 22,304 47 59 29,976 2 59 21,963 456 72 20,557 45 67 48,038 7 73 15,494 387 88 15,231 38 85 21,216 5 88 14,324 338 98 15,545 33 91 28,813 10 101 9,776 239 103 14,017 23 109 13,925 11 99 14,101 12

C. United state1N5 5321 11 152,551 53 0 11 152,551 532 21 151,885 53 0 21 151,885 533 36 147,103 53 0 36 147,103 534 50 148,299 53 0 50 148,299 535 62 148,832 53 79 118,517 1 61 150,434 526 73 150,549 52 74 139,421 9 73 152,879 437 88 154,875 43 91 204,263 15 86 128,416 288 92 114,281 28 96 183,917 14 88 44,644 149 98 39,922 14 99 53,825 8 97 21,384 6

Note: T b w pg bk p 151 N (51; p A), G (47; p B) U S (53; p C).T g bk pg g g pz (% BO), g g pz (k), b (N.) p g (r5 1, , 9). T w p pg bk (D) g bk (ND). T b G p b 11 w b b g .


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VOL. 98 NO. 1 47 POsT ET AL.: DEAL OR NO DEAL?

p g w . O p D x

b- g: b , q, w

g g g p- b pg kw

pz b w 20,000 (ppx 5 p g

pz g) p b pz w p . I k- p- k x g g, D

g b xp b k g. I U S,

b g b p -

, p pp b b p pp p-

. (T Wb w pp

pp pg . T w -

p g .) C ( ) b .

A k-kg pp b wg p

pg g g-k -k . T

pb, S VI p TV w w xp

g pp.

III. Preliminary Analysis

T g gp k p D N D, w z

b bk, p g

.

S b g b Tb 2. F, bk b

g b g g pg g pg (R 2). T p

g pz pp 100 p . T

g bw pg D (p A), G (p B), US (p C) gg bk b w

.3 T b g w

D p p w bk G

US . Ag, f b g k D -

, , , b k w, -

, p. T, g xb w g b

k . I US G p, kp pg

bk xp pz p b.

I 3 N, 20 p (10 51) p

g 36 p xp p b, b k

x 400,000. M w 70 p x-g 100,000. F, b w p, w , k

. I D w, b pg

, w . I , k

k, q kw pz.

I pp b w p p p k

k. T g xp b k p,

p Fk, w pp D p J 1, 2005 ( Tb 3). I 7,

k pk, Fk p b w g g pz

(500,000) w xp pz b 102,006 2,508. T bk

3 A pk E, p p, g bk p.


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2,400, 96 p g g pz. Fk p

. I bq , Fk b gb,

p w b w 10. Sp, 8, 105 p-

g g pz; 9, 6,000

50/50 gb 10 10,000. W k-kg

b, b g, p, gb w k. A, w wg Fk w w p gb

g, b xp b b

xp g.

I , xg S, x w

pp G p Ag 23, 2006 ( Tb 4). A k

pk, pz 1,000 8. I 9, 50/50

gb 100,000 150,000, w g pz G . W

w g , bk

125,000, xp gb; p k-kg b

p , p wg 150,000.T b k Fk k S xb w k ,

k-kg, w w k .

Table 3Example Frank

G (r)

Pz () 1 2 3 4 5 6 7 8 9

0.01 x x

0.20 x x0.50 x x x x x x x1 x x x x x5

10 x x x x x x x x x20 x x x x x x x x50

100500

1,000 x2,500 x x x5,000 x x7,500

10,000 x x x x x x x x x

25,000 x x50,000 x x x x75,000 x x x

100,000 x x x200,000 x x x x300,000 x400,000 x500,000 x x x x x x

1,000,000 x2,500,0005,000,000 x

Ag () 383,427 64,502 85,230 95,004 85,005 102,006 2,508 3,343 5,005O () 17,000 8,000 23,000 44,000 52,000 75,000 2,400 3,500 6,000O () 4 12 27 46 61 74 96 105 120

D N N N N N N N N N

Note: T b w gb p D Fk D N D b g 19. T p p w b J 1, 2005. F g , b w g pz, g g pz, bk , pg bk , D N D . Fk p w pz 10.


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Fk b w bk- , wg gb g

bk p p. S b w -

, wg gb w k pg w

.

T z p x xp

b Fk Sz, w p g g w w z

g p.

O k w k p p g -

bk . A g g pz pg

b w, b- g w g pz w

. Ug r g, g g pz b- :

(1) BCr5nrxr 2 x

minr

nr 2 1,

w nr b g b g r5 1, ,9 min

r g pz. S, w b g g pz

w- g g g pz, maxr :

Table 4Example Susanne

G (r)

Pz () 1 2 3 4 5 6 7 8 9

0.01 x x x x

0.20 x x x0.50 x x x x x x x15

1020 x x50 x x

100 x x x x200300 x x x400 x500

1,000 x x x x x x x x2,500 x x x x x x

5,000 x7,500

10,000 x x12,500 x x x15,000 x20,000 x x25,000 x x x x x50,000 x

100,000 x x x x x x x x x150,000 x x x x x x x x x250,000 x

Ag () 32,094 21,431 26,491 34,825 46,417 50,700 62,750 83,667 125,000O () 3,400 4,350 10,000 15,600 25,000 31,400 46,000 75,300 125,000O () 11 20 38 45 54 62 73 90 100

D N N N N N N N N N

Note: T b w gb p G S D N D b g 19. T p p w b Ag 23, 2006. F g, b w g pz, g g pz, bk , pg bk , D N D . S p w pz 150,000.


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(2) WCr5nrxr 2 x

maxr

nr 2 1.

M p, w g g BCr bg

w - g w WCr bg

b -.4 G w ( b

) .

4 T pz w ( S II), BCr BWr b g pz.

Table 5Deal or No Deal Decisions after Bad and Good Fortune

L N W

R % BO N. % D % BO N. % D % BO N. % D

A. Neterland (N5 51)

1 6 17 0 6 17 0 6 17 02 15 17 0 12 17 0 15 17 03 40 17 12 29 17 41 31 17 64 69 14 14 58 13 46 54 14 215 82 10 10 71 10 20 78 10 406 94 8 50 85 7 43 86 8 637 99 4 25 97 3 67 99 4 758 105 1 0 91 3 67 100 1 1009 120 1 0 0 91 1 100

29 72 14 70 31 72 25

B. Germany (N5 47)

1 7 9 0 7 9 0 8 9 0

2 16 16 0 13 15 0 14 16 03 35 16 0 33 15 0 33 16 04 46 16 0 44 15 0 47 16 05 65 16 0 54 15 13 57 16 06 83 15 0 67 15 20 66 15 277 107 13 0 80 12 25 76 13 158 117 11 0 89 11 55 86 11 369 107 8 38 106 7 57 98 8 50

29 111 3 105 17 111 13

C. United state (N5 53)

1 9 18 0 10 17 0 13 18 02 19 18 0 19 17 0 25 18 03 41 18 0 29 17 0 39 18 0

4 57 18 0 42 17 0 51 18 05 69 18 0 55 17 6 62 18 06 78 18 11 68 16 31 73 18 117 92 15 27 87 13 23 84 15 538 94 9 22 95 10 70 87 9 569 92 4 50 101 6 67 99 4 50

29 118 8 113 18 118 14

Note: T b z D N D p 151 N(51; p A), G (47; p B) U S (53; p C). T p p b xp b g g. A g g pz g w g pz g w - g ; w g g g g pz g b -. F g g , b p pg bk (% BO), b (N.) p-

g g D (% D). T b G p b 11 w b b g .


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O , w p w g-

. T w w b , p -

w w k g p: -

k p g wk x p g.

F xp, pg g ( r) g bw w p g, k w

k g p.

Tb 5 p b. W

, p w g, b w

g p. W 31 p D N D

gp D D p, D pg 14 p

p g p (R 4). T w D pg

gg k w b k g

w b p. I , g p g xb k-kg

b b g bk x g g pz.

T w D pg b xp p b k b w k k, g k (IRRA). Hw,

g k gb

g p w k p (g

g w xp ). A, k xp w k

, w w xp g k w. Hw, k

w k w- b. T

D pg w 25 p, bw 31 p gp.

Ig, p . T D pg

G US w D , w IRRA

b k. W , w, w w D pg.

T gg p p k . T

w p xp w p-

g pb p p b g

pb. B , p-p b p q pp .

T w k bk- , k-

bg wg k k p p p . S,

w D pg w w - ,

w k g.

Ob, p D pg . I p

xp k p (bk g pz) . F, p

g g g . T x w

x-k g z D N

D g .

IV. Expected Utility Theory

T z b D N D w xp -

w . T ppp p, b

p . W w pw xp , b

k (CRRA) b k (CARA)


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. T w pb b g k (IRRA)

g b k (DARA), w p fxb xp-pw

A S (1993) w b M Ab, C B,

P P. Wkk (2007) b C A. H S K. L (2002):

(3) u 1x 2 51 2 exp 1 2 a 1W1 x 212b

2a .I , p kw: k a b,

w p W. T CRRA pw g w

a S 0 CARA xp p w b5 0. T,

w b w, g p

. Hw, w bb pb

g xg w w p g. T, w w

p .

W w kw p g x k p k b D N D b p ,

bk , , xp

kw wg w g . I g r, B 1xr 2 bk g pzxr. T p p:

(4) sv 1xr 2 5u 1B 1xr 2 2 .Azg p. W b ,

bk , p bw.

A. Continuation Value

T g p bk

p . I , w p-

z pb b bkw , g R E. B pp p-

. Sg w , w p D N D

pg g , g pb p

bq . T pp , w, k

pb bq g . S bkw

p g- bgg xp gg b g

w p g g g p bkw p

(, xp, J . 2002; K B . 2002). T p g p p g.

O gg g k .

T g-w w w pp bk x

p b b w

p (g g p

). W p p . Ug , p

bk w kw x , g p -

p .

G pz (xr), b pz x

( r11) kw:

(5) Pr 3xr115y 0xr 5a nrnr11b21

5pr


16/36


g by nr11 xr. I w, pbb p

b b pb b nr11 nr. T, gX1xr2 b, p g b

(6) cv 1xr 2 5 ay[X1xr2u 1B 1y 2 2pr.G g b -g , ppp

g. Hw, b k, w p

g bkw p

p g . I g , w bkw -

pp , p . S,

p g p N D, b xp bk

b g , p g

g p . I g , bkw p,

b w g b p b xpbk w w. F w , Fk S,

pb g p w .

T w pp w g D q

pzzg p bkw .

B.Bank Oer

T pp p , w q b bk. S I -

bk q . F w gpzxr pg bk br g r5 1, , 9, w q b

g wg p :

(7) B 1xr11 2 5br11xr11,(8) br115br 1 11 2 br 2r192r2,w r, 0#r# 1, p w pg g 100 p. S

p k , p

x . T bk b p, b w

b w D N D b . B 1x10 2 5 10 b1051 pz w b.T xp p . Hw, b ,

b b , p pg

b . A b k, p

pg xp x g .

F , w r b g p pg

g g q g .

T g : 0.832 D , 0.815

G , 0.735 G , 0.777 US w. T

g kb g . Fg 3 g-- b pg p- bk g . T g pb -

, g w p . F p,


17/36


xp w 70 p

pg

. T xp pw g

, w R-q

g 95 p p. Agb,

k

pg , b b -

w g wg

xp . O , -

z k b wg

g pz, w

. I

g g b

pg . I -

, r p , p

ppx ,

g g.

S pp b bk

b g w w,

bk (7)(8) -

kw . Ug

bk w

x , g w

. F , bk p, kg

z w

p.

C.Maximum Likeliood Etimation

I p G M. Bk, M H.

DG Jb Mk (1963) J

D. H C O (1994), w

D N D g i5 1, ,N g g

r5 1, , 9 b bw

p ,

cv 1xi,r 2 2 sv 1xi,r 2 , p . T p, b-

b w z

si,r . Agb, b g

p . A

p :

(9) d 1xi,r 25ay[X1xi,r2 1u 1B 1y 2 2 2 cv 1x i,r2 22pr .

"1FSDFOUBHFCBOLPGGFST

"DUVBM

1SFEJDUFE

3

Figure 3.Predicted Bank Offers versus Actual Bank Offers

Note: T g p g bk

b pg p bk bk g p p 151 N,G, U S. P A w pg bk p B w bk ( ). A 45-g (p ) p.

#.POFUBSZCBOLPGGFST

"DUVBM;

1SFEJDUFE;

3


18/36


W pp , , i,r5

d 1xi,r 2s, ws p. A p, p g wg . W g

w wgg. T (p) w p

. I , w wgg, p - g g, w D g b g

G US . T f g

D G US ;

D p : () g k b g pz; (b)

g pz b x g g. T

(9) pk p w . T g

p , p g wgg .

G p, w p k D N D

F

cv

1xi,r

22 sv

1xi,r

2d 1xi,r 2s b N D,(10) l 1xi,r 2 5 Fasv 1xi,r 2 2 cv 1xi,r 2d 1xi,r 2s b D,

w F[ b .5

Agggg k , g-k D

N D g b

(11) ln 1L 2 5aN

i51a

Ri

r52 1l 1x

i,r

2 2 ,wRi g p b i.

T w pb , w p-

(, xp, J M. Wg 2003).

N g 1r5 22 . T G pw g g g , g

p w p, w x 1r5 12 w g . D bk , w

( p D); g

, b w k G p k p.

T kw p (a, b, W, s) xz

g-k. T wk g b k

, w p k .

5 T w - (FSD). T pbb D p b g z , w bk (N D D) g g (D N D). A p b , FSD. I , w, bk w b g b g , FSD .


19/36


D.Reult

Tb 6 z . Ap p-,

w p p q xp ,

(CC), 50/50 gb 0 10z

, z5 1, , 6. T p p b g p . Nb,

CC b p bk ( xp 50/50

gb) w k bw D N D. I CC 5 1,

k . W CC . 1, k kg, CC pp

z, b x k . T p p g ,

w pg, pg p D N D

.

I D p, k p a b b g

z, ggg IRRA DARA CRRA pw

CARA xp xp g w. T

w 75,203 g x z. S, g D g 25,000 p , w b

w w, g p. T

pp g w w p

w g p pp . A w w

w Mw Rb (2000) b pb k

p pb g k g

g w w. I, p k

k, w CC 0.994 50/50 gb 0 1,000, g w

w p k g gb.

Rb p b pg g k w bxp b H L (2002) g w k p b. H

L b p g k k, w, Rb ,

Table 6Expected Utility Theory Results

N G U S

a 0.424 (0.000) 1.58-5 (0.049) 4.18-5 (0.000)

b 0.791 (0.000) 0.000 (1.000) 0.171 (0.000)W 75,203 (0.034) 544 (0.481) 101,898 (0.782)

s 0.428 (0.000) 0.467 (0.000) 0.277 (0.000)

MLL 20.365 20.340 20.260LR 24.29 (0.000) 3.95 (0.267) 15.10 (0.002)H 76 p 85 p 89 pN. 214 327 349

CC (0/101) 1.000 1.000 1.000CC (0/102) 0.999 1.000 1.000CC (0/103) 0.994 0.996 0.998CC (0/104) 0.946 0.960 0.984CC (0/105) 0.637 0.640 0.859CC (0/106) 0.141 0.088 0.302

Note: T b p xp p 151

N (51), G (47), U S (53). Sw x k a bp w (W, ) (3), p s. T b w g-k (MLL), k (LR) k , p-g p D N D (H), b D N D p (N.). F, p (CC; q xp) w 50/50 gb 0 10z, z 5 1, , 6.p- w p.


20/36


p x k g kb p.

I, w H L p w g-

p D g , b w b. W

, gg w Rb, xp w xpg

b b g k.T fxb g xp w

. T xb g IRRA, g p-

b w CC 0.141 50/50 gb 0 1,000,000. I, b p-

g w w p . I k w k,

w p g pp p bk , pp w

w b; w xp D pg Tb 5. Hw, g IRRA

xp b , w g bk

p w k. S, p k kg

k; w CC 0.946 50/50 gb 0 10,000g Fk

k 9. T, b pg w p

.Ig, G q

D . T p CARA xp (b5 0)

w b g z. S,

b pz, w xb p b

g IRRA g k w. Ag, b pg -

w w p . T b

xp g b

k p D w bk

x g g pz.

C D G , US ppx- g CRRA pw (a 0). T CC g g

k. F g k, b w p

w , fg w pp D US w

g k. T g p w

101,898, w k k. S, w

g z, b p b b w w

b p CARA xp .

T p , Tb 7 w p

w ( S III). Cg w D pg ,

w k g CC gp. T

b b b k kg, w pg g p bk x g g pz. T

p , p zb pz.

F xp, D g g k US

G gp. S, k kg (CC . 1) gp. O,

gg xp p g p

.

V. Prospect Theory

I , w pp z b D N D .C w g w

gg w p p pp . F, w w


21/36


Table 7Path Dependence

L N W

A. Neterland

a 2244.904 (0.022) 0.044 (0.204) 0.125 (0.831)

b 0.993 (0.000) 0.687 (0.000) 0.736 (0.011)

W 0 (1.000) 304 (0.671) 3,061 (0.824)

s 0.627 (0.000) 0.323 (0.000) 0.309 (0.000)

MLL 20.300 20.383 20.325

H 89 p 81 p 83 p

N. 72 70 72

CC (0/101) 1.330 0.994 0.999CC (0/102) 1.338 0.945 0.992

CC (0/103) 1.347 0.723 0.928

CC (0/104) 1.355 0.392 0.630

CC (0/105) 1.363 0.150 0.216

CC (0/106) 1.371 0.032 0.035

B. Germany

a 27.914 (0.117) 0.364 (0.000) 0.087 (0.000)

b 0.814 (0.000) 0.759 (0.000) 0.651 (0.000)

W 930 (0.825) 50,926 (0.481) 113,582 (0.180)

s 0.659 (0.000) 0.241 (0.000) 0.454 (0.000)

MLL 20.276 20.257 20.278

H 90 p 87 p 88 p

N. 111 105 111

CC (0/10

1

) 1.012 1.000 1.000CC (0/102) 1.113 0.999 0.999

CC (0/103) 1.584 0.990 0.995

CC (0/104) 1.823 0.911 0.949

CC (0/105) 1.891 0.485 0.614

CC (0/106) 1.929 0.072 0.101

C. United state

a 2203.512 (0.006) 1.96-5 (0.000) 0.938 (0.000)

b 0.995 (0.000) 0.086 (0.000) 0.998 (0.000)

W 54 (0.691) 934,904 (0.331) 29,468 (0.107)

s 0.193 (0.000) 0.308 (0.000) 0.326 (0.000)

MLL 20.194 20.275 20.253H 92 p 86 p 91 p

N. 118 113 118

CC (0/101) 1.004 1.000 1.000CC (0/102) 1.023 1.000 0.999

CC (0/103) 1.054 0.999 0.992

CC (0/104) 1.071 0.986 0.927

CC (0/105) 1.081 0.863 0.646

CC (0/106) 1.089 0.252 0.289

Note: T b w x k xp p 151 N (51; p A), G (47; p B), U S (53; p C). T -p p b xp g g. A (w) g g pz g w (g) g pz g w (b) - g . T p -p Tb 6.


22/36


g p p bk w kw

x . Ag p pp ,

g p xp . A

S IV, p ppp xp . F pp ,

w, b . Pp w k-kg b w , k k g k p g

w pb wg g g pz. I, w

g bk xp pg g g pz (

g b bk x ). P p

pp g p b w w k

p g . T p , w, b k kg p

g. A g, w g

p g g ppx. T, w p w p

b w p g xp .

T p pp w

xp , w xp-pw (3) p b pp , w g

p:

2l(RP2x)a x#RP(12) v 1x 0RP 2 5 u ,

(x2RP)a x.RP

w l. 0 - p,RP p p

g, a. 0 . T g p-

p w p (x#RP)

g (x.RP). T b p, w q b .6

A.Reerence Point specifcation

K Tk (1979) g pp q

p w q. S D N D p

w pk, p w q z w xp-

. T gz, w, w g

xp p q

(286). T p p w p w k p

gb w b pb w (287). T p b b T J (1990), g w p g

. O g b B Kzg Rb (2006, 2007).

T p b p ( g xp)

w g g , w

g w w g. Sw k

p bk- - , w k

g. I p w ,

g p , w k kg pp. S,

6 Ep g . Tk K (1992), xp, 0.88 b . F, b b b w ; V Kbbg Wkk (2005).


23/36


p k , b g, g

pz p g, g .

Fg 4 w g 50/50 gb 25,000 75,000. C

D N D p gb 9. T g w -

g p Tk K (1992), a5 0.88 l5 2.25,

p p. I w p, p q xp (RPN5 50,000). I ,

gb g 25,000 (50,00025,000) wg 25,000

(75,00050,000). T q gb CEN5 44,169, g

bk bw w b g w b p. T k p-

5,831 b , w g g wg g.

Nw L, w g k 50,000

g b g 50/50 gb 9. Spp L w

p p g g pz (RPL5 75,000). I

, L gb g 25,000 wg 25,000, b g

50,000 (75,00025,000) bkg (75,00075,000). B pz p w k kg pp. I, L w bk bw -

q gb, CEL5 52,255, w p g k p 2,255.

v(x)

vL x:75,000

vWx:25,000

vNx:50,000

75,00025,000 x

Figure 4. Break-Even and House-Money Effects in Prospect Theory

Note: T g p pp (12) p (RP) q (CE) 50/50 gb 25,000 75,000. V vN(xZ50,000) w RPN5 50,000 CEN5 44,169, vW(xZ25,000) w w RPW5 25,000 CEW5 47,745, vL(xZ75,000) wRPL5 75,000 CEL5 52,255. A b p Tk K (1992), a5 0.88 l5 2.25. T q 50/50 gb.


24/36


F, W, w k 50,000

g g b g 50/50 gb. D w , W p

p q g pz (RPW5 25,000) p b -

g pz g. I , W gb bkg

(25,00025,000) gg 50,000 (75,00025,000). S pp g, k W w W

w bk bw CEW5 47,745, pg k p 2,255,

5,831 .

I b xp b pp p p

. I , w w , pp

p-p . U, p

bb pp p g g

p. W g

b p. T k g p

p , w p p b p-

p.I w w pb g bw bk

k bk x , w k p

bk . T bk p pp

k . F, bk k g g pz

xp gg . A p p w b

RPr5u1B(xr). Iu15 0, p q q (RPr5 0) p-

b g; u1. 0, p p -

xp (pp) , g p w

pk. A p bw bk , u1, 1, (p)

w pb bk x pb g. B , p

p, u1. 1, pb w pb g.

T g bk g , g

p p. D w , w, p b

b g . W j,

0 #j,r, b g g pz, d jr 5 1x]r2 x]j 2/x]r. Fj5 0,d1j2r g g, x

]0 .

I, w g ( pb

). Hw, g bw gg

b b, w b p. W -

w : d1r222r d102r . T d1r222r g x g b b ( ) g;d102r , g b g, p g g . Ag

w gg , p

(13) RPr5 1u1 1 u2d r22r 1 u3d 0r 2B 1xr 2 .I , u2, 0 u3, 0 p p k

g u1B(xr) g g pz

w .

I w g w b, p- w b , b w

g p b x , .., w


25/36


pb bk g g pb bk . W

p x bk , .., y[X(xr)B(y)#RPr

# xy[X(xr)B(y). T p p b

p p .

O p pp p: l, - a, p p u1, u2, u3. W

p p s w x k p

xp . W pp bk .

O g b pbb pbb

wg. T pp p w w pbb -

. I k p pb ,

w wg pbb pb , gg k kg

x . F xp, ppg

Tk K (1992) wgg p gb w

w q k , wg 55 p 50

p. S, w p p w gpbb wgg k p. T p k b ,

p p , w pbb

g wg w b pbb (

b 50/50 gb).

B.Reult

Tb 8 z . F D , p-

g . T

xp w bk x g g pz; xp w g p bk bw g pz. B

p k pb w p xp .

I, g p q Tk K (1992) p

g .

T p u1 g g z, pg xp

(pp) , w p b xp

xp p . T p g ,

g p g k bw bk

.

T p u2 u3 g z, g

p k g w g. I g, u2 g u3, ggg

g xp. Hw, g

g g pz g w g g

g g g, g p . I ,

g g, p g b . I

, p q g pb bk ( b),

g p .

T w p w pp w

D. N pg, pp b

w g-k g g xp . W xp p 76 p D N D

, pg pp 85 p.


26/36


T G US p w

D p, b p w . T

g k g pp D D -

. I G US p, p b g

D p. T g p p xp w G

US p g pg bk D -

. R p , w k kg pp.

I , g xp D. I,

b g D p. Ag, k gg. Hw, p p w

k p . T G US

g pg g D . I , b

b p, b w b b p w .

T w g p G US g

D . T g

w g b xp w p.

T w g w w

pp D ( Tb 5). C, pp w b k

p pb xp p-p p. S, w

pp xp pb xp, q w. F xp, w g p

b pbb . T p p w

w w g p pbb wgg. F p

wg g,

wg p g , k-p -

. W .

VI. Experiments

T p g p p-p- k . A, k b p, w g pp-

g k . P k , w, g

Table 8Prospect Theory Results

N G U S

l 2.375 (0.013) 4.501 (0.008) 4.528 (0.001)

a 0.516 (0.000) 0.486 (0.000) 0.836 (0.000)

u1 0.474 (0.000) 1.096 (0.000) 1.163 (0.000)

u2 20.285 (0.000) 20.026 (0.000) 0.031 (0.329)u3 20.028 (0.000) 20.052 (0.000) 20.093 (0.023)

s 0.345 (0.000) 0.533 (0.000) 0.193 (0.000)

MLL 20.309 20.303 20.228LR 48.41 (0.000) 27.44 (0.000) 37.28 (0.000)H 85 p 89 p 91 p

N. 214 327 349

Note: T b w pp p 151 N(51), G (47), U S (53). Sw x k (l) (a) , p p u1, u2, u3, p s. T b w g-k (MLL), k (LR) k , pg p D N D (H), b

D N D p (N.). p- w p.


27/36


w g w: b (pg g- b)

w k b (pg w- b) k. T

g k, xp wk pp D , b

xp w D pg w. T z

k, w xp w E U p D N D. W w xp-

b , b w

pp.

B xp p pb (, xp,

H L 2002). I p xp w g-

TV w p b p bw w xp,

xp g D .7 A xp,

40 p w b. T g w w b

1,000 10,000, w p . Dp g

g, g k g xp . Ag -

w p, b w g w p g p b. R, b w

g g b p ( g

p). T k w gz g p , b

b g p w b x

. I, xp D N D

w g pz w b.

W p g g w pb , g g

w ( pp E U) ( b

). V w p , g .

T g (p b, g pz, bk ) w p p g ( ) p g

( ). T p w p

xp TV . O pp ,

b w x g xp, ppg

g , w p .

A b w , b 20 g. A 160 b

w g pp E U

w pp pp xp g 20052006. Ag

xp q 40 b, 80 w g g

b b w b b

w p. T, ppx w p g. T pb g , w g b g

g p.

A bgg b xp w b, -

g g TV w p xpg

xp. Nx, g . E g b 5 10 ,

xp (40 g) g 5 , q w

b g, g w .

7 Og pz b w b p D TV p. Tg pz (b xp), bk g p b g p.


28/36


A. small-stake Experiment

I xp, g pz bk D w

b 10,000, g g pz g 40 x pz 500.

T k xp w g TV w.C g p ( 6.9 5.2 TV w) g

pg bk . S, g g k 10,000

TV w. I TV w, g b k

k kg w k. I xp-

, k , b g k . T gg

k k g wk. B ,

p g; w xp (b) D pg (

29 b) 3, 21, 19 , , w, p.

T Tb 9 w x k . T

xb p x IRRA g w, b w

. S, xp, CC 0.072 50/50 gb 0 1,000. Iw Rb (2000) b pb k q w

w -k gb g-k gb. I, w

b 11 xp, g 10,000 w g

TV p. A g p, b pg w

w p . Pp w k p

b b xp , b g-k

pg.

B.Large-stake Experiment

T g xp g-k TV w

gg k g. O , xp

pb w TV , b, xp, xp b-

TV p (). O xp

g k b pg xp w g k.

T xp g b, w bg g-

b 1,000 b 10,000, g g pz

g 400 x pz 5,000 x g xp-

. F xp, 80 w b w w pp, xg

xp.

B g IRRA xp, xp w p g k xp. Hw, g p x q

g -k xp ( 6.9), b pg

bk ( g bk g 82.5 p 82.4 p

-k xp). T, k wk g-

g b IRRA xp.

T Tb 9 p x k . W

k b , xp

z . I , pp

k, 50/50 gb 0 1,000 w ppx CC

50/50 gb 0 100 -k xp. B , pp , p g -k b b-

p xp .


29/36


I b xp, k g b p , w g

k witin xp, b k k

acro xp. S k b

, pb xp p

k k g.

C. Pooled sample

T Tb 9 w p p w xp. A

b, b w p , p g

k. T p k p wk

w p w . Sk pp -

b . Cbg b p w pb xp

, g p b k. Ug

g p p g w

p. T pp pb b b w D pp w p w

p pp k p. I w,

Table 9Experimental Results

S k Lg k P

A. Expected utility teory

a 0.019 (0.000) 0.002 (0.001) 0.002 (0.001)

b 0.000 (1.000) 0.000 (1.000) 0.000 (1.000)W 11 (0.920) 50 (0.930) 0 (1.000)

s 0.306 (0.000) 0.294 (0.000) 0.354 (0.000)

MLL 20.342 20.337 20.351LR 10.17 (0.017) 10.14 (0.017) 9.37 (0.025)H 81 p 83 p 80 p

N. 231 234 465

CC (0/101) 0.953 0.995 0.995CC (0/102) 0.583 0.953 0.953CC (0/103) 0.072 0.588 0.586CC (0/104) 0.007 0.074 0.074CC (0/105) 0.001 0.007 0.007

CC (0/106) 0.000 0.001 0.001

B. Propect teory

l 2.307 (0.000) 2.678 (0.000) 2.518 (0.000)

a 0.732 (0.000) 0.695 (0.000) 0.693 (0.000)

u1 1.045 (0.000) 1.024 (0.000) 1.023 (0.000)

u2 20.119 (0.000) 0.019 (0.000) 0.013 (0.250)

u3 20.086 (0.000) 20.046 (0.000) 20.049 (0.000)

s 0.267 (0.000) 0.196 (0.000) 0.218 (0.000)

MLL 20.275 20.265 20.272LR 40.94 (0.000) 44.04 (0.000) 83.29 (0.000)H 87 p 88 p 87 p

N. 231 234 465

Note: T b w x k xp. T (k) p xp w g D TV D N D b 10,000; (g k) p xp w pz w b 1,000; (p) p w p b. P Aw xp . P B w pp . T p Tb 6 Tb 8, p.


30/36


g k b k. W

g p x. A 100 k b p

g -k xp (w g pz g 40), b

pbb p g-k xp (w

g pz g 400).

VII. Conclusions

T b g w w b gz w

p w kg k . W k

w w, - -

g g g. S, w b

p g w w , b pb

p w-, k g. F, p w,

b k b w g ,

g w g g w - w . I , b b

g pp g. I, pb g

g w

, g gg g g.

W ? F, w b, g, w g b

k . E w k,

g x 75 p xp . I xp w

wk, k g k w

k -k xpb , b

xp. S, g k g, pp p g g ; g k b ppg

g pg bk , w xb

k-kg b b g b g g pz b

g gb. W b

k , b p b xp b

xp b p g. M b, k

g p xp b b g g- b-

xp b p b pg w- b. T

p-p p g, p zb

k . L w g wk pp

D p.T w k w xp w xp -

p -p pp

. I, g w bk- ( bg

wg k k p p p ), - (

w k w p p p g). A p

pp w k p xp D N D b-

b xp . T g gg -p

p-p p, w pb p w-,

w g k.

O , w b w g xp bg p-p . W fxb xp-pw , w b pp

p xp , b p


31/36


xp w g w. Hw, ()

k-kg g p p

b . S x p b b bw w , w -

p w.

O g p -p p-p, p- g p xp . P

pb k g g pb. A k

b g x g w b p xp, b

pbb g w bw p xp.

F w xp w , 10,000 pbb

; k pp g w

w xp.

T k, w w xp

g pp TV w pb .

W k . M,

xp kb g TV w, p xp k g k. C w

TV , bk- - g xp.

T xp g g b p-

. T b () g k b b

w g (b) wk k g

pp x pb .

T p N, G, U S,

b p g . F , w b -

g b g z

p g x , , bkg . I w b g x

xp. W k , xp w

, , ,

b. O xp w g TV p-

, b xp k p b b p

- .

VII. Epilogue

Fwg D N D N, g w w

z ww. O gp g p . T p , b

g (p ) , -

. Rg g p w b b x,

b b p . W w p p -

b , w p bw pb , g k.

Ug UK , S A . (2006b)

, g k g w-kg b-

. T xp gg CRRA w g q g

UK ; k-p xp pbb-

wgg g w ; pp pbb wgg g, g pb p

p. A . (2006) UK w b


32/36


33/36


k g b . T k

p g g, b w. Lk

D R S, g C Sp , b

k bw p g.

C, D N D b pp w g , , ppg

. S k b xg g

. F, z k w g bg

g g, z b g. O ,

x w p g p bk g

pp, b . S, g

k p , z p g w

xp w k. W

xp, k p p , w -

b p. T, w g p , p z

b . F xp, w - p g pz

x bk , q

pb, p k pz.

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