236 Ex p erimental Business Research Vol. I I T able 3. Advice Takin g in the Action-Plus Advice Experimen t S uccessor C hoose A C hoose B P redecessor Cutoff ( − ) Cutoff ( + ) Cutof f = 0 A ction A/Advice B 13 ( 15.66% ) 33 ( 39.76% ) 6 ( 7.23% ) A ction B/Advice A 17 ( 20.48% ) 7 ( 8.43% ) 7 ( 8.43% ) T he Action-Plus-Advice experiment provides us with an extremel y g ood oppor- t unity to try separating the impact of advice and action on behavior. The reason is th at i n a num b er o f s i tuat i ons su bj ects were f ace d w i t h a d v i ce t h at was diff erent from the action taken b y the sub j ect in the previous round. For example, in the A ction-Plus-Advice experiment 83 out of the 5 2 5 decisions excluding the first deci- s ion turn (15.8 percent) were made under circumstances where the advice offered was different from the action observed in the p revious p eriod. If when these situa- t ions occurred, subjects chose to follow the advice of their predecessors rather than c opy i ng t h e i r act i on, we wou ld i nterpret t hi s as i n di cat i ng t h at a d v i ce was more i nfluential than action . T o pursue this line of inquiry, consider the choice of a negative cutoff as indicat- i ng a pre f erence f or t h e A c h o i ce an d t h e c h o i ce o f a pos i t i ve cuto ff as a pre f erenc e for the B choice. If the advice and action of a predecessor sub j ect differ, then two c ases can be observed. The p redecessor chooses A and advises B or the p redecessor ch ooses B an d a d v i ses A. Base d on e i t h er o f t h ese occurr i ng, t h e successor su bj ect c ould choose to set either a ne g ative cutoff (a hi g her probabilit y of takin g action A) or a positive one (a higher probability of taking action B). This defines four contin- genc i es as d ep i cte d i n Ta bl e 3. T able 3 shows that when the advice and action of one’s p redecessor differ , s uccessors are far more likely to choose an action consistent with the received advice than the observed action. For example, in 6 0.2 percent of the cases where the advice offered differs from the action, sub j ects chose to follow the advice the y r eceived rather than imitate their predecessor’s action, while only 24.1 percent of the t ime they imitated the action taken, and 15.7 percent of the time they were neutral and choose a cutoff zero . T able 3 looks at behavior when the advice offered by a subject’s predecessor diff ers f rom t h e act i on s h e too k . But we m i g h t a l so as k w h et h er gett i ng a d v i ce t h at i s consistent with the action taken b y one’s predecessor makes a sub j ect more likel y t o follow it and if so more likely to set a more extreme cutoff indicating stronger agreement. A pr i or i we wou ld expect t hi s to b e t h e case s i nce w h en a d v i ce agrees with a predecessors’ action we should expect a sub j ect to view it as more compel- ling. Consider Table 4 . T a bl e 4 supports our con j ecture. Su bj ects are, i n d ee d , more lik e l y to f o ll ow advice (as indicated b y the si g n of their cutoff) when it is backed up b y action. Note D ECISION M N AKING MM W ITH W W N H AÏVE N N A E DV I CE 23 7 T able 4. Decision Con f ormity with Advice and Action Action Ta k e n Concurring Neutra l Contrar y A ction-Only 44.2% 1 6 . 6 % 39.2% Advice-Only 74.1% 9.1% 1 6 .8% A ct i o n − +− A d v i ce 84.2% 7.0% 8.8% t h at if a su bj ect i s to ld to f o ll ow an act i on b y a pre d ecessor w h o too k t h at act i on h imself, such a recommendation is followed 84.2 p ercent of the time, while such a dvice is followed only 74.1 percent of the time in the Advice-Only experiment. W h en j ust t h e act i on i s o b serve d , i t i s i m i tate d on l y 44.2 percent o f t h e t i me. So i t should be clear that a predecessor who does as she sa y s is seen as bein g more believable than one whose advice cannot be backed up by action. Ironically, when a su bj ect f o ll ows a p i ece o f a d v i ce t h at i s b ac k e d up b y t h e act i ons o f one’s pre- d ecessor, the cutoff he sets is not si g nificantl y different than the one set b y a sub j ect i n the Advice-Only experiment who also followed advice. Hence, it appears that w hil e see i ng act i ons support a d v i ce i ncreases t h e pro b a bili ty o f f o ll ow i ng t h e a d v i ce o ffered, the stren g th of conviction in the advice is not different from that in the Advice-Only Experiment. 3.1. Does A d vice Increase Efficiency? P ro b a bl y t h e most i mportant quest i on t h at we can as k a b out t h e i mpact o f a d v i ce on social learnin g is whether the presence of advice increases the welfare of sub j ects o ver and above what it would be without it. In answering this question, we will have to exam i ne t h e i mpact t h at a d v i ce h as on h er di ng an d casca d e b e h av i or o f su bj ects since one wa y that advice affects behavior is throu g h its propensit y to cause sub j ects to herd with greater frequency than they would in its absence. To begin, consider Table 5, which presents a summary our four experiments. It is c lear that the mean pa y offs of our sub j ects were hi g hest in those experiments where a dvice was p resent . As we see, w hil e earn i ngs f or ta ki ng t h e correct act i on i n t h e Act i on-On l y ex- periment avera g ed $18.8 the y avera g e $23.3 and $21.8 for the Action-Plus-Advice a nd Advice-Only experiments. These increases represent increases of 24.3 percent a nd 1 6 .4 percent, respectively. In the Perfect-Information experiments of Celen and K ariv (2003) where sub j ects could see the entire histor y of actions before settin g their cutoff values (but did not receive advice), earnings averaged $ 22.0 indicat- i ng t h at a d v i ce w i t h i mper f ect i n f ormat i on i s approx i mate l y as e ffi c i ent as per f ect i nformation without advice. A set of binar y Wilcoxon tests indicates that there is a 238 Ex p erimental Business Research Vol. I I T able 5. Efficienc y and Herdin g in Social Learnin g Experiment s Action-Only Advice-Only Action-Advice Perfect Advice-Only Action-Advice I n f ormation Earnings $18.8 $21.8 $23 $22 $18.8 $21.8 $23 Herds* 8 25 36 27 825 36 % o f Her ds + 10.7 33.3 48 36 33.3 48 Cascades 18 24 21 26 18 24 21 % o f casca d es + 24 32 28 34.7 32 28 * Herds of at least five sub j ect s + Out of all 525 decision points excludin g the first decision turn . s ignificant difference between the sample of subject payoffs in the Action-Onl y e xperiment and all other experiments at the 5 percent level of significance. It also i ndicates that no difference exists between the pa y offs of sub j ects in the Perfect- Information experiment and any of those with advice, substantiating our conclusions th at t h e presence o f a d v i ce seems to b e a su b st i tute f or t h e extra i n f ormat i on c ontained in the p erfect information ex p eriment. 4. HERD BEHAVI O R AND INF O RMATI O NAL C A SC ADE S O ne o f t h e ma i n reasons w h y a d v i ce i ncreases t h e payo ff s an d h ence t h e we lf are of our sub j ects is that it has a dramatic impact on our sub j ects’ inclination to herd. W e identify a subject who engages in cascade behavior as one who reports a cutoff o f − $ 10 or $ 10, and thus takes either action A or B no matter what private signal s he receives. In contrast, a sub j ect who j oins a herd but does en g a g e in cascade behavior is one whose cutoff is in the o p en interval ( − 10, 10), indicating that there are some s i gna l s t h at can l ea d h er to c h oose act i on A, some to c h oose B, b ut w h en her private si g nal is realized she will act as her predecessors did. Finall y , we sa y that a c ascade occurs when beginning with some subject all others thereafter follow c asca d e b e h av i or , an d h er d b e h a v io r occurs when, beginning with some subject, r all take the same action . 4.1. Herd beha v io r W hile in our Action-Only experiments we observed herding of at least five sub- jects in only 8 of the 75 rounds (10.7 percent), in the Advice-Only and Action- P lus-Advice sessions herdin g occurred in 25 (33.3 percent) and 36 (48.0 percent) r ounds respectively. Moreover, in the Action-Plus-Advice experiment herd behavior D ECISION M N AKING MM W ITH W W N H AÏVE N N A E DV I CE 239 d eve l ope d even more f requent l y t h an i n t h e Per f ect In f ormat i on exper i ments o f C e l en an d Kar i v (2003) w h ere su bj ects can see a ll t h e d ec i s i ons ma d e b y a ll o f t h e i r predecessors before makin g their choice, we found that herdin g was the outcome in 27 of the 75 rounds (36.0 percent). Finally, the frequency in which herd behavior o ccurs i n t h e Act i on-P l us-A d v i ce exper i ment compares f avora bl y to t h e 47 percent predicted b y the theor y . O b v i ous l y, two con di t i ons must b e met if a d v i ce i s go i ng to b e we lf are i ncreas- i ng. F i rst, t h e a d v i ce must b e correct an d secon d i t must b e f o ll owe d . M i racu l ous l y, i n these experiments, both conditions seemed to have been met. In the Advice-Onl y e xper i ments, w h enever h er d b e h av i or ar i ses a ll o f t h e a d v i ce g i ven was cons i stent w i t h t h e act i on h er d e d upon. In t h e Act i on-P l us-A d v i ce exper i ments, t hi s was not the case in onl y 5 of the 36 herds. In other words, when herds occurred those who h er d e d ten d e d to f o ll ow t h e a d v i ce g i ven. More remar k a bl y, i n a ll exper i ments a ll h er d s turne d out to b e on t h e correct d ec i s i on. T hi s resu l t i s o f a part i cu l ar i nterest since one of the ori g inal concerns of the social learnin g literature was that herds a n d casca d es m i g h t support or re i n f orce i ne ffi c i ent c h o i ces. Fo ll ow i ng An d erson a n d Ho l t (1997), t h ese f ears were supporte d b y t h e resu l ts o f many l a b oratory e x p eriments . To sum up, our resu l ts on h er d b e h av i or i n di cate t h at a d v i ce i s a strong f orce i n t h e creat i on o f un if orm soc i a l b e h av i or an d i s we lf are i ncreas i ng . 4 .2. In f ormational cascades While all cascades must be herds, the opposite is certainl y not true. Our experiment i s un i que l y d es i gne d to di st i ngu i s h b etween t h e occurrence o f casca d es an d h er d s s i nce we are a bl e to o b serve su bj ects’ cuto ff s t h at are typ i ca ll y uno b serva bl e. Sur- prisin g l y , advice did not have a si g nificant impact on the rate of occurrence of i n f ormat i on casca d es. In t h e Act i on-On l y exper i ments, casca d es, i n t h e sense t h at f rom some su bj ect on a ll acte d i rrespect i ve o f t h e content o f t h e i r pr i vate s i gna l s b y settin g either − 1 0 or 10 as their cutoffs, were observed in 18 rounds (24.0 p ercent) , w h ereas i n t h e A d v i ce-On l y an d Act i on-P l us-A d v i ce exper i ments casca d es f orme d i n 24 (32.0 percent) an d 21 (28.0 percent) roun d s, respect i ve l y. I n summar y , it appears that in this informational settin g words speak louder t h an act i ons i n t h e sense t h at su bj ects are more lik e l y to f o ll ow t h e a d v i ce o f t h e ir pre d ecessors to ta k e spec ifi c act i ons t h an t h ey are to copy t h e i r b e h av i or. 5 . WHY FOLLOW ADVICE? (IYENGAR AND SCHOTTER (2002) ) O ur results above lead us to question wh y advice should be so beneficial. Wh y s h ou ld peop l e g i ve b etter a d v i ce to t h e i r successors t h an t h ey gave to t h emse l ves? An exper i ment con d ucte d b y Iyengar an d Sc h otter (2002) attempts to answer t hi s q uestion. I n t hi s exper i ment, su bj ects h a d to c h oose a num b er, e , b etween 0 an d 100 ca ll e d t h e i r d ec i s i on num b er. T h ey were to ld t h at t h ey were p l ay i ng aga i nst a computer i ze d 240 Ex p erimental Business Research Vol. I I p artner w h o wou ld a l ways c h oose t h e num b er 37. A f ter t hi s num b er i s c h osen a r an d om num b er i s i n d epen d ent l y generate d f rom a un if orm di str ib ut i on over t h e i nterval [ − a , + a ] for both the sub j ect and his computerized opponent. These num- b ers (t h e d ec i s i on num b er an d t h e ran d om num b er) are t h en a dd e d toget h er an d a “ tota l num b er” i s d e fi ne d f or eac h o f t h e rea l an d computer i ze d p l ayers. Payo ff s are determined b y comparin g the total numbers of the real and computerized sub j ects, an d awar di ng t h e rea l p l ayer a fi xe d payo ff o f M if her total is larger than that of the M c omputer i ze d opponent. I f h er tota l num b er i s sma ll er, t h en s h e rece i ves a payo ff o f m , m < M . The cost of the decision number chosen is g iven b y a convex function c ( e ) = e 2 / r , w h ere r is a constant. This amount is then subtracted from these fixed r p ayments to d eterm i ne a su bj ect’s fi na l payo ff . Hence, t h ere i s a tra d e-o ff i n t h ese e xperiments in the choice of decision numbers: hi g her numbers g enerate a hi g her p ro b a bili ty o f w i nn i ng t h e bi g pr i ze b ut at t h e same t i me a l so i mp l y a hi g h er d ec i - si on cost. By l ett i ng r = 500 , a = 40, M = 2 9 an d m = 17.2, an d h o ldi ng t he c omputerized pla y er’s choice fixed at 37, our sub j ects face a rather simple decision p ro bl em w i t h a qua d rat i c payo ff f unct i on w h ose pea k i s at 37 . Thi s tas k was use d b y Mer l o an d Sc h otter (1999, 2003) to test t h e i mpact o f i nformation on learnin g . The y used what the y called a “surprise quiz” method to t est h ow we ll su bj ects l earne d t h e tas k put i n f ront o f t h em. In t h ese exper i ments, s ubjects performed the exact task as described above 75 times and received payoffs e ach period. When the 7 5 rounds were over the y were surprised and told that the y would play the game once more but this time the stakes were multiplied by 75 so th at t h ey cou ld earn f or t hi s one tr i a l an amount equa l to t h e sum o f w h at t h ey earne d i n all of the previous 7 5 rounds. Their choice in this hi g h-stakes round should be a s ufficient statistic for all that they have earned in the previous 75 rounds since the on l y way t h ey can max i m i ze t h e i r earn i ngs i n t hi s roun d i s b y c h oos i ng t h at d ec i s i on n umber which the y feel is best. It is b y comparin g behavior in surprise quizzes that we can i nvest i gate t h e i mpact o f var i ous treatments on l earn i ng . Mer l o an d Sc h otter (1999, 2003) per f orme d t hi s exper i ment un d er a num b er o f different conditions. In one the y simpl y had one sub j ect perform the experiment e xactly as described above and make a surprise quiz choice after the 75 rounds were d one. In anot h er exper i ment, t h e su bj ect (w hi c h we ca ll t h e d oer) per f orme d t h e e xperiment with another sub j ect (the observer) silentl y watchin g what he did over his shoulder. After the 75 rounds were over we took the observer out of the room , he was to ld t h at h e wou ld d o anot h er exper i ment t h at was re l ate d to w h at t h e d oer was doin g but the specifics were not mentioned, and performed a surprise quiz on the d oer. We t h en pa id t h e d oers an d l et t h em go an d returne d t h e o b servers to t h e l a b where we announced that the y were now to do a one-shot surprise quiz for 75 times t he stakes of the doers the y j ust watched. I yengar an d Sc h otter (2002) repeate d t hi s exper i ment b ut i n a s li g h t l y diff erent m anner. Instea d o f h av i n g one su bj ect d o t h e exper i ment a l one, t h e y sat anot h er “ advisor” sub j ects next to him or her at the computer. This advisor (t y pe-P sub j ect) m a k es wr i tten suggest i ons to t h e su bj ect d o i ng t h e exper i ment as to w h at h e or s h e thi n k s i s t h e b est c h o i ce f or t h at roun d . T h e c h ooser (t y pe-A su bj ect) i s f ree to D ECISION M N AKING MM W ITH W W N H AÏVE N N A E DV I CE 241 T able 6. Experimental Desi gn T reatment Merlo and Schotter 1999 Decision maker alone Merlo and Schotter 2003 Decision maker + over l oo ki ng su bj ec t Iyengar and Schotter (2002) Decision maker + A d v i sor T able 7. Mean Sur p rise-Quiz Choice s Mean (Median) Sur p ise-Quiz Choice M erlo-Schotter–1999 51.33 ( 50 ) M erlo-Schotter–2003 Doer: 5 1.06 ( 5 0) Observer: 40.6 5 (37) I y en g ar-Schotter–2002 Doer: (No Cost) 31.20 (39.5) Advisor: 43.35 ( 43 ) Doer (Costl y Advice): 36.1 (37) Advisor: 33.52 ( 38 ) f o ll ow t hi s a d v i ce or not b ut i n one treatment i s pena li ze d f or not d o i ng so w i t h a quadratic penalt y function based on the difference between the action chosen and the action advised. In another treatment no penalty is assessed for not following advice (i t i s s i mp l y c h eap ta lk ). T h e a d v i sor’s payo ff i s equa l to 3/4’s o f t h at o f hi s a d v i see. After the initial 7 5 round ex p eriment run in this manner, both he adviser and advisee are separated in given surprise quizzes. These experiments are summarized in Table 6 belo w: I t appears as if the process of g ivin g advice and receivin g g reatl y enhances t he decision-making abilities of the Iyenga and Schotter subjects. Table 7 presents th e mean c h o i ces o f our su bj ects i n t h e surpr i se qu i z roun d s i n eac h o f our f our t rea t men t s . I n the MS (1999) experiment subjects performed our task alone without either an a d v i sor or a spectator l oo ki ng over t h e i r s h ou ld er. In t h at exper i ment, as was true i n t he Merlo-Schotter (2003) experiment where sub j ects did the experiment with a 242 Ex p erimental Business Research Vol. I I s pectator l oo ki ng over t h e i r s h ou ld er, su bj ects appeare d to f a il to l earn w h ere t h e p ea k o f t h e payo ff f unct i on was. In t h ose exper i ments t h e mean an d me di an surpr i se q uiz choices of sub j ects who did the experiment for 7 5 rounds was 5 1 and 5 0, r espect i ve l y . Th e i nterest i ng resu l t f oun d i n t h e MS (2003) paper was t h at w hil e t h ose w h o did t he experiment failed to learn, those who watched them did quite well havin g a mean an d me di an surpr i se-qu i z c h o i ce o f 40 an d 37 respect i ve l y. In ot h er wor d s, watc hi n g was a b etter l earn i ng exper i ence t h an d o i ng; h ence t h e t i t l e “Lean i ng b y Not Do i ng”. A median test re j ects the h y pothesis that 37 is the median of either the MS (2003) or MS (1999) d oer c h o i ces b ut f a il s to re j ect t h e h ypot h es i s t h at 37 was t h e me di an ch o i ce o f o b servers i n MS (2003). T h e message o f t h ese papers i s t h at peop l e f a il to learn appropriatel y when the y repeat experiments in which the y receive pa y offs after e ac h per i o d an d t h e tas k i s repeate d o f ten. I yengar an d Sc h otter (2002), h owever, reporte d a remar k a bl e resu l t, name l y, t h at t he process of g ivin g advice enhances the learnin g abilit y of both t y pe-A and t y pe- P su bj ects. For examp l e, i n t h e Cost l y-A d v i ce exper i ment t h e mean an d me di an c hoices of the type-A and type-P subjects were 3 6 .1 and 37 for the type-A subjects, and 33. 5 and 38 for the t y pe-P sub j ects, respectivel y . Neither of these medians i s s i gn ifi cant l y diff erent f rom 37 us i ng a me di an test at any mean i ng f u l l eve l o f si gn ifi cance ( ( p ≤ 1) f or t h e type-A agents an d ( p ≤ . 6 48) for the type-P subjects). For the No-Cost Advice experiment, the situation is sli g htl y different. Here the mean and median choices of the type-A and type-P subjects were 31.28 and 39.5 for the type-A and 43.35 and 43 for the type-P subjects. Only the type-A subjects had a m edian that was not si g nificantl y different from 37. For the t y pe-P sub j ects we ha d to re j ect t h at h ypot h es i s at t h e 2% l eve l . H owever, w hil e t hi s m i g h t i n di cate t h at a d v i sors w h ose a d v i ce was i gnore d did n ot learn as well as those who received this advice (which the y were at libert y to i gnore), t h e type-P a d v i sors st ill l earne d b etter t h an t h ose i n t h e MS (1999) an d (2003) exper i ment w h o actua ll y did t h e exper i ments. For examp l e, a W il coxon test i ndicates that we can re j ect the h y pothesis that the sample of t y pe-P surprise quiz r oun d s came f rom t h e same popu l at i on as e i t h er t h ose o f t h e su bj ects i n MS (1999) ( p ≈ 0) or t h e d oers i n MS (2003) exper i ment ( p ≈ 0). Another feature of the learnin g experience sub j ects have when advice is g iven is t h at a d v i ce seems to di m i n i s h t h e num b er o f su bj ects w h o c h oose d om i nate d strate- g i es. For examp l e, i n t h e surpr i se qu i z roun d s o f a ll f our exper i ments (w h ere t h ere are no disa g reement costs) an y choice of 6 5 or more is dominated b y choosin g 0. Whil e i n MS (1999) 10 out o f 24 su bj ects c h ose a d om i nate d strategy i n t h e i r s urpr i se-qu i z roun d an d i n MS (2003) 9 out o f 31 d oers did so, i n our No-Cost A dvice experiment onl y 1 t y pe-P sub j ect and 1 t y pe-A sub j ect made dominated ch o i ces. In ot h er wor d s, t h ere were on l y 2 out o f 28 suc h c h o i ces. For t h e Cost l y Ad v i ce exper i ment, t h e resu l ts are t h e same. On l y 1 type-P su bj ect an d no type-A s ub j ects made surprise-quiz choices strictl y g reater than 6 5 . This is a ver y stron g diff erence i n di cat i ng t h at t h ese su bj ects c l ear l y l earne d some m i n i mum l esson t h at s eeme d not to b e l earne d b y ot h ers i n t h e No-A d v i ce treatments. D ECISION M N AKING MM W ITH W W N H AÏVE N N A E DV I CE 243 T h e punc h li ne t h en i s t h at l earn i ng i s f ostere d w h en a d v i ce i s g i ven even if t h ere i s no cost f or i gnor i ng i t. T h ose w h o l earn we ll are b ot h t h e peop l e w h o g i ve t h e a dvice and those who receive it. I t i s re l evant to po i nt out h ere t h at i t appears t h at su bj ects h ave a h ar d t i me l earn- i ng i n env i ronments w h ere d ec i s i ons are repeate d an d su bj ects rewar d e d f or eac h c hoice at the end of ever y round. However, it is precisel y these t y pe of environments t h at ex i st w h en peop l e f unct i on i n mar k ets an d ma k e c h o i ces repeate dl y w hi c h are re i n f orce d b y an i mme di ate payo ff . Hence, we f ee l t h at our resu l ts h ave di rect relevance to learnin g in market environments and the beneficial aspect of social l earn i ng or a d v i ce g i v i ng i n t h em. (Stoc k b ro k ers may not b e t h at b a d a f ter a ll .) T h e reason w h y we f ee l t h at a d v i ce g i v i ng an d rece i v i ng f ac ili tates l earn i ng i s that the process of g ivin g advice seems to focus the attention of advisers on the pro bl em at h an d i n a manner t h at l ea d s to greater l earn i ng on t h e i r part. Su bj ects seem to l earn b etter w h en t h ey g i ve a d v i ce an d w h en t h ey rece i ve i t. We t hi n k t hi s i s true because g ivin g and acceptin g advice causes decision makers to not onl y think t h roug h t h e pro bl em anot h er t i me b ut to d o so i n a manner diff erent f rom t h e way t h ey d o w h en t h ey are ma ki ng d ec i s i ons a l one. This result offers a possible explanation of wh y it is advanta g eous to follow ad v i ce w h en i t i s o ff ere d an d w h y a d v i ce i s b etter t h an act i ons. T h e reason i s t h at we c an expect su bj ects to l earn b etter w h en t h ey g i ve a d v i ce an d t h at a d v i ce i s t h ere f ore worth listenin g to. The process of advice g ivin g makes us think about the problems f ac i ng us diff erent l y t h an we ten d to d o w h en we are actua ll y engage d i n t h em. 6 . WEAK-LINK GAMES WITH ALMOST COMMON KNOWLEDGE A ll o f t h e a b ove exper i ments are ones w h ere su bj ects rece i ve pr i vate a d v i ce f rom one and only one predecessor. However, in many situations we get advice from severa l or many peop l e an d t hi s a d v i ce i s many t i mes pu bli c. To i nvest i gate t h e ro l e o f a d v i ce i n t h ese s i tuat i ons, C h au dh ur i , Sc h otter, an d Sop h er (2002) stu dy w h at V an Huyck, Battalio, and Beil (VBB) (1990) have called “the Minimum Game” w h ose payo ff structure i s presente d i n Ta bl e 8. T hi s g ame i s g enerate d by a s i tuat i on i n w hi c h a set o f a g ents c h oose an i nte g er fr o m t h e set e i ʦ { 0, 7 } , i = 1, 2, . . . , n . The pa y off to each a g ent, i , is e q ual to π i = a + b { m i n ( e 1 , , e n ) } − c ( e i ) , w h ere a , b , c > 0 are constants. I f a = $ 0.60 , b = $ 0.20 and c = $ 0.10, we get the matrix defined above. I n this g ame all outcomes in which all a g ents make the same choice are equilibri a b ut t h e b est equ ilib r i um outcome f or soc i ety i s w h ere a ll c h oose 7 w hil e t h e worst i s wh ere a ll c h oose 1. When Van Hu y ck et al. ran this g ame with g roups of 14 or 16 the y all quickl y c onverge d to t h e worst a ll -1 outcome an d t hi s resu l t i s remar k a bl y ro b ust. Groups ten d to c h oose t h e w orst outcome f or t h emse lv es. Now think of this g ame bein g pla y ed as an inter- g enerational g ame with advice. Here, one m i g h t expect t h at if agents i n generat i ons cou ld ta lk to eac h ot h er t h ey m i g h t , e ven w h en t h e i r generat i on h as f a il e d to ma k e t h e correct d ec i s i on, g i ve a d v i ce to 244 Ex p erimental Business Research Vol. I I Table 8. Payo ff Table in VBB’s Minimum Gam e Minimum Choice o f Other s 7654 3 2 1 7 1.30 1.10 0. 9 0 0.70 0.50 0.30 0.1 0 6 – 1.2 0 1. 00 0 . 80 0 . 60 0 .4 00 .2 0 5 – – 1.10 0.90 0.70 0. 5 0 0.3 0 Y our C h o i c e 4 – – – 1.00 0.80 0. 6 0 0.4 0 3 –––– 0. 9 0 0.70 0.5 0 2 ––––– 0 . 80 0 . 60 1 –––––– 0 .7 0 the next generation that instructs them to learn from their mistakes and choose higher . Th at i s, we expecte d t h at su bj ects wou ld te ll t h e i r l a b oratory o ff spr i ng, “Do as we sa y but not as we did”. This inter g enerational talk, we expected mi g ht be able to a llow subjects to “talk themselves to efficiency” and achieve optimal outcomes. 6.1. Did Advice Improve Welfare? Ch a dh ur i , Sc h otter, an d Sop h er (2002) fi n d t h at i t was muc h h ar d er f or soc i et i es to “talk themselves to efficienc y ” than the y expected. More precisel y , the y find that e fficient (all choose 7) outcomes emerge only in circumstances where advice is n ot on l y pu bli c ( i n t h e sense t h at a ll a d v i ce f rom a prev i ous generat i on i s o ff ere d to e ach successor in the next g eneration) but its publicness is common knowled g e (in the sense that it is read aloud for all members of a generation to hear). Private ad v i ce b etween a pre d ecessor an d hi s or h er successor or even pu bli c a d v i ce t h at i s shared (i.e., all pla y ers in g eneration t are given a sheet specifying each piece of t a dvice offered by the members of generation t − 1 and all subjects know that all o t h ers h ave b een g i ven t h e same s h eet) b ut not rea d a l ou d d oes a poor j o b o f ra i s i ng the minimum . F igure 6 exhibits the period-by-period minimum choices of subjects for five experi- menta l runs, t h ree o f w hi c h are i nter-generat i ona l games run w i t h e i t h er a d v i ce o nl y , advice plus last period’s histor y (i.e., the abilit y to see what happened in each o f the 10 rounds of the previous generations experience) and public advice. (There a re 8 su bj ects i n eac h group). T h e ot h er two are t h e VBB (1990) resu l ts an d t h e results of an ex p eriment run to re p licate them in our lab for com p arison p ur p oses. D ECISION M N AKING MM W ITH W W N H AÏVE N N A E DV I CE 2 4 5 T hese are called the replicator experiments and have neither advice nor histor y a vailable. As can be seen in Figure 6 , the behavior of group minima in the VBB, our No- Advice, and all p rivate advice ex p eriments is dramatic. In all of them, the minimum c onverges to 1 by at least the fourth round. Our remarkable finding is that efficient all -7 outcomes b ecome poss ibl e on l y w h en peop l e h ave access to pu bli c a d v i ce that is also common knowled g e. The discontinuit y of behavior as we move from Almost-Common Knowledge (generations 1– 5 of the Public-Advice Treatment) to C ommon Knowledge (generations 6 –9 of the Public-Advice treatment) was unex- pected but extremel y su gg estive of what t y pe of information ma y be needed to g et p eo p le to coo p erate . T h ese exper i ments are extreme l y suggest i ve, i mp l y i ng t h at w h en we want groups o f people to act in a coordinated manner in situations where the y need to trust each o ther, the form in which the advice given is crucial. Private advice tends to make t hi ngs worse – peop l e a d v i se t h e i r o ff spr i ng not to b e suc k ers an d to watc h out f or n umero uno. Public advice can help but onl y when it is common knowled g e and all h ave faith that each other has not only heard the public advice but knows that others h ave h ear d i ts an d t h at ot h ers k now t h at t h ey k now t h at i t was h ear d a d i n fi n i tum . 7 . CO N C LU S I O N T his paper has surve y ed a number of papers all of which have investi g ated the i mpact of advice on decision-making. In general, this advice is offered by decision m a k ers w h o are on l y s li g h t l y more exper i ence d i n t h e tas k at h an d t h an are t he people the y advise. We call such advice “naïve”. Despite this lack of expertise we find a number of results . Fi rst peop l e ten d to f o ll ow t h e a d v i ce o ff ere d to t h em. T hi s i s seen i n a num b er o f wa y s. For example, in Ultimatum and Trust Games the amounts of mone y sent A dvice Onl y N o Ad v ic e VBB Ad v i ce+H i stor y Public Ad v ic e 0 1 2 3 4 5 6 7 Minimum Chosen G enerat i ons T reatments Ad v i ce On ly N o A d v i ce VBB A dvice+History P ublic Ad v ice Figure 6 . Behavior of the Minimum Across All Treatments . [...]... are prevalent: business- to -business suppliers supply in the present and expect to be paid in the future; credit card issuers rely on credit card holders to pay for their purchases 249 A Rapoport and R Zwick (eds.), Experimental Business Research, Vol II, 249–260 d ( © 2005 Springer Printed in the Netherlands 250 Experimental Business Research Vol II These are just two examples Whether a business or an... 43.8 56.5 45.2 55.4 49.5 4 55.8 47.2 60.7 51.2 53.4 42.7 56.7 46.5 55.3 49.6 5 56.0 47.3 60.0 50.8 53.5 42.2 56.5 45.6 55.0 49.4 256 Experimental Business Research Vol II Table 4 Equilibrium price demands π→ 0.00 0.01 0.05 0 .10 0.50 H→ Period 45 10 45 10 45 10 45 10 45 10 1 95 60 95 55 55 55 55 55 55 55 2 95 60 95 55 55 55 55 55 55 55 3 95 60 95 55 95 55 55 55 55 55 4 95 60 95 55 95 55 95 55 55 55 5... 83–4 Auctions 9 10, 16, 30, 36, 90, 103 –9, 111, 113–14, 117–20, 123–31, 133–6, 138– 40, 146–8 Absolute 108 , 117–18, 120 Auction revenue 110 13, 115, 120 Bidding strategy 6 Common value auctions 131, 133–6, 138, 140 Internet auction 103 , 106 , 127, 146 eBay 104 , 106 , 119, 123–5, 131 Hard close 123– 4, 127, 129–30 Late bidding 123–4, 130–1 Soft close 123–4, 127–30 Sniping 124 Minimum bid 104 , 107 –11, 114,... = 45 than when H = 10 2 For π = 0.50, the price demand in each period should be the same no matter whether H = 45 or H = 10 3 For π = 0.01, 0.05, and 0 .10, the price demands are generally lower in the earlier periods than in the later periods (they go up from 55 to either 60 or 95) Table 3 Mean medians price demands π→ 0.00 0.01 0.05 0 .10 0.50 H→ Period 45 10 45 10 45 10 45 10 45 10 1 56.8 46.8 61.1... Levin, D 104 –5, 115, 119, 138, 213 Luft, J 151–3, 155, 161–2, 166–8 Marrese, M 187–8, 195–6 Maskin, E S 2, 5, 54 Maurer, S 84, 90, 92, 95–6 McAfee, R P 103 –5, 118–9 262 Experimental Business Research Vol II McMillan, J 104 –5, 119 Merlo, A 240–1 Milgrom, P 6, 152, 186, 191, 197 Mitani, S 48, 55–8, 73–5, 79–80 Mori, T 188, 195–6 Moser, D V 151, 154, 158, 167 Muench, T 186, 193, 196 Samuelson, W F 104 –5,... demand by the conditions of the experimental design, except that we collapse the data from periods 2 to 5 The goal FAILURE OF F BAYESIAN UPDATING N 257 Table 5 Correlations between search behavior and price demands π→ 0.00 0.01 0.05 0 .10 0.50 H→ Period 45 10 45 10 45 10 45 10 45 10 2–5 0.300 0.297 0.286 0.187 0.271 0.235 0.156 0.364 0.203 0.087 1 0.442 0.413 0.504 0. 510 0.330 0.457 0.440 0.563 0.474... Michigan 107 5 Beal Avenue Ann Arbor, MI 4 8109 -2112 yanchen@umich.edu James C Cox Department of Economics and Economic Science Laboratory Eller College of Management University of Arizona Tucson, AZ 85721- 0108 jcox@eller.arizona.edu 266 Experimental Business Research Vol II Rachel Croson Department of Operations and Information Management The Wharton School University of Pennsylvania Philadelphia, PA 1 9104 -6340... received from the Hong Kong Research Grants Council for this research (Project Number: CUHK4076/98H) NOTES 1 2 $100 Hong Kong dollars The exchange rate between Hong Kong and US dollars is approximately 7.8 to 1 The amount of the cash prize was very attractive to students considering that the hourly wage for an on-campus job was about $50 260 Experimental Business Research Vol II REFERENCES Camerer, Colin... 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Mean me d ians price d eman ds π → 0 . 00 0 . 01 0 . 0 5 0 . 10 0 .5 0 H → 4 5 10 4 5 10 4 5 10 4 5 10 4 5 10 P erio d 1 56.8 46.8 61.1 52.6 51.2 43.2 56.0 46.6 53.6 4 9 .1 25 6. 5 4 5 .8 59 . 9 4 9 . 95 1.8. Rapoport and R . d Zwick ( e ( ( ds. ) , E x p erimental Business Researc h , Vol. II , 24 9 –2 60. 2 5 0Ex p erimental Business Research Vol. I I Th ese are j ust two examp l es. W h et h er. b etween 0 an d 100 ca ll e d t h e i r d ec i s i on num b er. T h ey were to ld t h at t h ey were p l ay i ng aga i nst a computer i ze d 240 Ex p erimental Business Research Vol. I I p artner