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Travelers’ Types
Pablo Brañas-Garza, María Paz Espinosa, Pedro Rey-Biel
To cite this version:
PII: S0167-2681(11)00004-7 DOI: doi:10.1016/j.jebo.2010.12.005
Reference: JEBO 2650
To appear in: Journal of Economic Behavior & Organization
Received date: 23-12-2008 Revised date: 6-12-2010 Accepted date: 21-12-2010
Please cite this article as: Bra˜nas–Garza, P., Espinosa, M.P., Rey–Biel, P., Travelers’ Types, Journal of Economic Behavior and Organization (2008), doi:10.1016/j.jebo.2010.12.005
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Travelers’ Types
Pablo Brañas–Garza
María Paz Espinosa
Pedro Rey–Biel
December 6, 2010
Abst ract
T his paper uses subj ect s’ diverse self-report ed just i…cat ions t o explain discrepancies between observed het erogeneous behavior and t he unique equilibrium predict ion in a one-shot t raveler’s dilemma experiment . Princi-pal component s analysis suggest s t hat it erat ive reasoning, aspirat ion levels, compet it ive behavior, at t it udes t owards risk and penalt ies and focal point s may be behind di¤erent choices. Such reasons are coherent wit h same sub-ject s’ behavior in ot her t est s and experiment s in which t hese part icular issues are prominent , and t hus, we ident ify " t ypes" of subject s. Overall, we conclude t hat subject s’ self-j ust i…cat ions in complex st rat egic sit uat ions
We t hank Jose Apest eguia, Miguel A . Ballest er, Jordi Br andt s, Vincent P. Crawford, Teresa García, Ignacio Palacios-Huert a, Albert Sat orra, two edit ors, a referee and seminar part icipant s at t he ESA Meet ings 2006, Barcelona JOCS, Univer sit y of St ockholm and Universit at Aut onoma de Barcelona for t heir comment s. We are indebt ed t o Ramón Cobo-Reyes and Rafael López del Paso for t heir help in running t he experiment s and t o A ndere Bot as and Pedro Ser rano for coding sub-ject s’ comment s. Financial support from Minist erio de Educación y Ciencia (SEJ2007-62081/ ECON, ECO2009-09120, ECON2009-0716, ECO2010-17049 and Consolider-Ingenio CSD2006-00016), Junt a de A ndalucía (P07-SEJ-02547), Gobierno Vasco (IT -313-07), I. Muj er (2007.031) and t he Bar celona GSE Research Net wor k and of t he Government of Cat alonia (2009SGR-00169).
Pablo Brañas-Garza. Depart ament o de Teoría e Hist or ia Económica. Facult ad de CC. Ecónomi-cas. Univer sidad de Granada. Campus Universit ario de La Cart uja. E-18011, Granada (Spain). Tel: (+ 34) 958 24 61 92. E-mail: [email protected]
Maria Paz Espinosa. Depart ament o de Fundament os del A nálisis Económico I I. Facult ad de Ciencias Económicas y Empresariales. Universidad del País Vasco. A venida Lehendakar i Aguirre, 83. 48015, Bilbao (Spain). Tel: (+ 34) 946013781. E-mail: [email protected]
Pedro Rey-Biel. Univer sit at Aut ònoma de Bar celona. Depart ment d ´ Economia i d´ Hist oria Econòmica. 08193, Bellat erra. Barcelona (Spain). Tel: (+ 34) 935812113. E-mail: [email protected]
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T he t raveler’s dilemma (T D) is one of t he classic examples used t o highlight discrep-ancies bet ween t he concept of rat ionalit y in Game T heory and t he way real individuals t ake st rat egic decisions. A s such, it s int uit ive out come and t he game t heoret ic pre-dict ion do not coincide. I t was …rst int roduced by Basu (1994) t o point out t hat discrepancies between game t heoret ic reasoning and act ual behavior may not only oc-cur due t o problems wit h backwards induct ion, as it also may ococ-cur in single shot games.1T he original formulat ion of t he T D is as follows:
“ T wo t ravelers lose t heir luggage during a ‡ight . Each t ravelers’ luggage cont ains exact ly t he same obj ect . To compensat e for damages, t he airline manager asks each t raveler t o independent ly make a claim for t he value of t he lost object bet ween and To discourage false claims, t he manager o¤ers t o pay each t raveler t he minimum of t he t wo claims, plus a reward of t o t he lowest claimant and minus a penalt y of t o t he highest claimant .”
All st andard game t heoret ic solut ion concept s predict t hat bot h players will select t he lowest possible choice and t hus, t he predict ed out come will be ( ). T his is t he unique Nash equilibrium, t he unique st rict equilibrium, t he unique st rong equilibrium and t he only rat ionalizable equilibrium. Yet , it seems int uit ive t hat subj ect s may play di¤erent ly since, for example, if t hey believe ot hers will make high claims, choosing higher s is bene…cial for bot h subj ect s. Previous experiment al evidence (Capra et al. 1999, Goeree and Holt 2001, Cabrera et al. 2007, Becchet t i et al. 2009 and Basu et al. fort hcoming) shows t hat a signi…cant proport ion of experiment al subject s
1“ T he t raveler’s dilemma seems t o be one of t he purest embodiment s of t he paradox of r at ionality
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choose values which are higher t han t he equilibrium predict ion and t hat t he size of t he penalt y ( ) in‡uences choices. I n part icular, lower penalt ies are associat ed wit h higher choices. Becker et al. (2005) show t hat even a large proport ion of expert s in Game T heory do not choose according t o t he Nash predict ion when playing an anonymous elect ronic version of t he T D among t hem. T herefore, ignorance on how t o reason in game t heoret ic t erms cannot be t he only reason behind t he observed het erogeneous choices in T D experiment s. Previous t heoret ical at t empt s have focused on explaining convergence t o t he Nash predict ion aft er repeat ed play in t he T D.2Since in t his paper we are int erest ed in t he underlying mot ivat ions behind subj ect s’ int uit ive and het erogeneous choices, we focus on init ial play.3 Rubinst ein (2006), in a one-shot not rewarded T D experiment wit h an ext ensive sample, st udies subject s’ t ime responses under t he hypot hesis t hat more cognit ive demanding choices t ake longer t o be t aken. Result s con…rm t his hypot hesis, alt hough most non-ext reme choices remain unexplained. We t ake a complement ary approach t oo underst and het erogeneit y in behavior.In games where t he equilibrium predict ion holds empirically, individuals’ het ero-geneit y does not play a role. T hus, we focus on a game where players do not play according t o t he unique equilibrium predict ion, t he T D, and t herefore t heir choices may reveal t he underlying mot ivat ions for st rat egic play. Our main int erest in t his paper is t o use t he observed het erogeneit y in behavior and in t he reasons behind such behavior in order t o check consist ency among individuals’ behavior across st rat egic and cognit ive t asks. Our experiment s wit h t he T D can be considered as a …rst st ep in t his line of research: what are t he fact ors in‡uencing behavior when t he Nash predict ion is not expect ed t o hold? We search for such fact ors in players’ self-report ed mot ivat ions and …nd t hat t he “ t ype of player” (as de…ned by self-report s) predict s behavior in t he T D. We t hen see whet her t he ident i…ed fact ors are informat ive for predict ing behavior in di¤erent sit uat ions. T he fact ors we ident ify or even t heir relat ive weight should not be considered as t he de…nit e fact ors det ermining behavior unt il more ext ensive research has been undert aken, because t hese fact ors or t heir relat ive weight could be in‡uenced by t he design. Furt her research should reveal whet her ot her fact ors should be included
2For example, Capra et al. (1999) rat ionalize observed behaviour in repeat ed versions of t he game
t hrough a lear ning process in a probabilist ic choice model in which players updat e t heir beliefs about rivals while using a noisy best response.
3Crawford (2002) argues t hat by foregoing repet it ion as a t eaching device, one-shot exper iment s
place a heavier burden on subj ect s’ underst anding, wit h a premium on simplicit y and clarit y of design.
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ent choices in t he T D are also consist ent ly het erogeneous. Given such het erogeneity, t he T D is an ideal candidat e t o st udy di¤erent mot ivat ions behind subject s’ experimen-t al choices. We use independenexperimen-t research assisexperimen-t anexperimen-t s experimen-t o codify subjecexperimen-t s’ self-reporexperimen-t s inexperimen-t o variables and we t hen use principal component s analysis (PC) in order t o rat ionalize choices in t he T D and classify subject s according t o t heir most prominent ly alleged reasons. We …nd t hat some classic experiment al issues such as cognit ive complexity, payo¤ aspirat ions, social preferences, risk and penalt y aversion and focal point s are closely relat ed t o alleged reasons in our T D experiment .We also t ook independent measures of same subj ect s’ personal charact erist ics and behavior in ot her t asks and experiment s. I n part icular and wit h respect t o subject s’ charact erist ics, we considered subject s’ scores in a GRE-t ype mat h t est , subject s’ self-evaluat ion in academic act ivit ies and gender. W it h respect t o experiment al measures, we obt ained how much t hey give in a dict at or game experiment and t heir choices when facing uncert aint y in t wo di¤erent t asks. Given t he int uit ive relat ionship bet ween sub-ject s’ self-report ed just i…cat ions in t he T D and t hese ot her measures, we check whet her subj ect s prominent ly mot ivat ed by one part icular feat ure in t he T D also score high in t he part icular t ask or experiment designed t o check such feat ure. For example, we st udy whet her subject s report ing more cognit ively complex reasoning procedures in t he T D score high in t he GRE-t ype t est or whet her subject s using ant isocial just i…cat ions in t he T D give less in dict at or games. We obt ain coherent and consist ent relat ionships bet ween bot h types of measures. Overall, we conclude t hat t here exist s di¤erent types of subj ect s whose …rst int uit ive responses t o a st rat egic sit uat ion are driven by di¤erent mot ivat ions and t hat such mot ivat ions are relat ively consist ent across t asks. T herefore, we show t hat subj ect s’ self-report in st rat egically complex sit uat ions such as t he T D cont ain informat ional value which can be useful t o predict behavior in ot her simple
4See A ust in and Delaney (1998), Crut cher ( 1994) and Er icsson and Simon (1993).
5T here exist s however an increasing t endency in Economics t o use subject s’ self-report s t o explain
laborat ory choices and go beyond using t his informat ion as just anecdot al evidence. A successful example is A pest eguia et al. (2007).
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relat ed t asks and st rat egic sit uat ions.Basu et al. (fort hcoming) also used subject s’ self report s in a t raveler’s dilemma experiment . T hey …nd a set of report ed st rat egies which up t o some point nicely correspond t o our principal component s, alt hough t he relat ive weight of each of t he alleged reasons di¤ers and t hey do not group st at ement s in principal component s. T he research object ive of t heir paper di¤ers from ours, since Basu et al. (fort hcoming)’s main int erest are t he reasons behind choices in t he T D and t hey focus on how changes in t he sizes of each subject ’s penalt y in‡uence choices in t he T D. Our paper aims at ident ifying t ypes of players and on st udying whet her self-report s help predict ing behavior in ot her t asks and experiment s.
T he paper is organized as follows. Sect ion 2 int roduces t he experiment al design and describes subj ect s’ choices in t he T D. Sect ion 3 explains how principal compo-nent s (PCs) were ext ract ed from subject s’ self-report ed comment s. Sect ion 4 shows how PCs explain subject s’ choices in t he T D. Sect ion 5 st udies t he relat ionship be-t ween PCs and subjecbe-t s’ choices in obe-t her be-t asks and experimenbe-t s. Secbe-t ion 6 concludes. Appendices available online include addit ional calculat ions (Appendix A ), inst ruct ions for t he T D experiment (Appendix B), inst ruct ions given t o dat a codi…ers (A ppendix C) and descript ive st at ist ics not included in t he paper (Appendix D).
T he complet e set of experiment al dat a report ed in t his paper was collect ed during t he spring semest er 2005 in several sessions wit h …rst year Economics st udent s at Univer-sidad de Granada (Spain). Subj ect s were informed t hat t he number of experiment al point s obt ained during each of t he sessions in which t hey would part icipat e cont ribut ed t o t heir …nal grade in t heir M icroeconomics I course in t he following way. Subject s belonged t o four di¤erent sect ions of around sixt y subject s each. T he t ot al number of experiment al point s obt ained by a subj ect during t he course were added t o det ermine his/ her posit ion wit hin his/ her sect ion’s ranking. T he subject wit h t he highest number of experiment al point s added t hree ext ra grade point s (out of a maximum of t en) t o his/ her …nal grade. For each posit ion below, grade point s were calculat ed as a funct ion of t he dist ance from t he winner:
5
2
Exp er im ent al D esi gn, Pr ocedur es and R esult s
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(end of A pril), and t he session det ailed below cont aining four t asks (June). Dat a from all sessions were gat hered and added t o an ongoing dat abase at Universidad de Granada which cont ains informat ion about subj ect s’ behavior across experiment s and t heir academic performance.T he …nal experiment al sessions referred above (June) cont ained t he t raveler’s dilemma experiment and are t hus t he main focus of t his paper. I n t hese sessions subj ect s per-formed four t asks: ) predict t heir relat ive performance in t he …nal Microeconomics I exam wit h respect t o ot her st udent s in t heir class; ) decide bet ween a binary lot t ery and t he out come of a 2x2 game in which t hey played; ) choose a number in a T D and give an explanat ion for t heir decision and ) predict t heir overall performance in t he courses t aken during t hat t erm.
Experiment al procedures for t hese …nal sessions were as follows: Once in t he class-room and during t he usual t ime slot for Microeconomics I , st udent s were handed in-st ruct ions for t he four t asks. T hey were asked t o perform t he t asks in no part icular order. W it h respect t o t he T D, t hey were informed t hat t hey had been randomly mat ched wit h anot her st udent from t he same group. T hey were handed inst ruct ions and asked t o choose a number in t he int erval t o which we will refer as t heir choice ( ). T hey were also asked t o volunt arily provide writ t en comment s -on t he same answer sheet - on how t hey had reached t heir decision. A ft er one hour, st udent s handed back t he answer sheet s for all four t asks and left . St udent s were informed about t heir performance in all experiment al sessions at t he end of t he course and graded accord-ingly, once all experiment s had …nished.
T he T D was framed as t wo …rms compet ing in prices, such t hat t he cont ent of t he experiment could be used t o explain oligopolist ic compet it ion in subsequent
Microeco-6Grade rewards were used in all experiment s carried out wit h t hese subj ect s. Administ rat ive and
…nancial const raint s prevent ed us from using monet ary incent ives. Rubinst ein (2006) report s a similar percent age of non-equilibrium choices t o previous T D experiment s wit h monet ary incent ives in a T D experiment wit h no rewards.
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nomics courses.7 Not ice t hat at t he t ime of t he experiment , subj ect s had received no lect ures on oligopolist ic compet it ion nor on Game T heory. I t is t rue t hat t he frame of …rms …xing prices may have not only a¤ect ed subject s’ choices but also t heir reason-ing process, and t hus t he reasons behind our result s may not perfect ly apply t o ot her experiment s wit h t he T D in which no frame or a di¤erent frame is used. In any case, result s below show t hat t he dist ribut ion of het erogeneous choices was clearly similar t o t he usually obt ained result s in T D experiment s wit h neut ral frame.T here were 243 subject s part icipat ing in t he experiment al sessions cont aining t he T D; 241 t urned in an answer for t he T D game, alt hough t hree subject s answered wit h an int erval inst ead of a number so t hat t hese t hree observat ions were eliminat ed, leaving 238 valid observat ions of t he T D.
T here were two t reat ment s varying in t he size of t he penalt y in t he T D. St udent s in t hree groups (184 subject s) were assigned t o t he t reat ment wit h penalt y size , while st udent s in t he fourt h group (54 subj ect s) faced a penalt y .8
Figure 1 shows t he dist ribut ion of subj ect s’ choices in t he T D for t he t wo penalt y sizes.
Alt hough a signi…cant percent age of subject s made Nash Equilibrium choices ( = 20), a higher proport ion of subject s in bot h t reat ment s made di¤erent choices ( wit h
, wit h ). T he dist ribut ion of choices maint ains t he same propert ies as previous experiment al t est s of t he T D.9 First , t here are choices all around t he in-t erval. Second, in-t he disin-t ribuin-t ion shows in-t hree peaks: t he Equilibrium predict ion ( ), choices around t he average of t he int erval ( ), and t he highest possible number ( ). W it h respect t o previous research, our dist ribut ion shows
7T he game is similar t o a Bert rand duopoly in which …rms have t o choose prices from a given
set . T he analogy is not perfect since in our game, t he …r m choosing t he lowest price does not sell t o t he whole market . However, it is su¢ cient ly close t o a duopoly model in which t here is some product di¤erent iat ion. I n any case, few subject s ment ioned t he market framing and subj ect s’ explanat ions indicat e t hat t hey underst ood t he st rat egic sit uat ion t hey were facing.
8Pr evious experiment s wit h t he T D show t hat t he Nash equilibrium is a relat ively bet t er pr edict ion
wit h high incent ives ( high ). Our highest penalt y ( 20) provides relat ively lower incent ives t han t he highest penalty in previous experiment s designed t o st udy how behavior changes wit h t he penalty size (Capra et al., 1999). We did so expect ing t o obt ain more het erogenous choices in t he T D.
9Capra et al. (1999), Goeree and Holt (2001), Cabrera et al. (2007), Becker et al. (2005),
Rubinst ein (2006 and 2007), Basu et al. ( 2008) and Becchet t i et al. (2009).
7 p p p i b i i i i i = 20 = 5 65% = 5 71% = 20 ) = 20 ) = 70 ) = 120
Figur e 1 about her e
b
p p
b b
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own explanat ions of t heir behavior t o st udy whet her t here were also het erogeneous reasons driving t hese choices.Our aim was t o use an independent , syst emat ic and j udgement -free met hod t o codify in a st andard response format t he comment s volunt arily writ t en by subj ect s aft er t hey had played t he T D. We asked t wo independent research assist ant s t o help us in t his t ask.
First , we st art ed by reading subj ect s’ comment s. We de…ned t ernary variables t aking values and referring t o t he cont ent in subject s’ comment s and it s sign. I f a subj ect ’s comment did not cont ain any informat ion on a part icular variable, such variable would t ake value zero, while it would t ake value if t he comment cont ained it and it s e¤ect went in one direct ion and if t he comment cont ained it but it s e¤ect went in t he opposit e direct ion. For example, t he variable would t ake value if t he subject expressed t hat her decision was mot ivat ed t o avoid risk, while it would t ake value if it expressed t hat she was willing t o t ake risks. T he variable would t ake value
if risk was not ment ioned.12
Second, our t wo independent research assist ant s (RAs) received inst ruct ions on how t o codify subject s’ comment s int o variables.13 RA s were not informed of t he object ive
10Suet ens and Pot t ers (2007) review t he experiment al evidence on Bet rand duopoly and …nd t hat
Bert rand produces mor e collusive behavior t han Cournot .
11Capra et al. (1999) show changes in t he dist r ibut ion when varying t he penalt y size, but penalty
changes wer e much more pronounced (fr om 5 unit s t o 80 unit s, when choices could be made in t he int erval ). Rubinst ein (2006) uses a single hypot het ical $5 penalt y when choices are made in a int erval.
12Variables and were binar y (0 or 1), as it s cont ent could not t ake di¤erent direct ions. 13T he de…nt ion of variables and writ t en inst ruct ions given t o RAs can be found in A ppendix C.
8 26 0 1 2 1 2 1 2 0 f ; ; g Ri sk
3
Pr incipal Com ponent s A naly sis
3.1
Codi …cat ion of sub j ect s’ com m ent s i nt o var i ables
[80 200] [180 300]
; ;
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of our st udy.14 T hey were explicit ly t old t hat t heir t ask was t o capt ure and classify what had been said rat her t han t o int erpret or rat ionalize subject s’ choices.15 Bot h RAs worked separat ely and independent ly and only met at t he t ime of receiving inst ruct ions. T here were no requirement s on t he number of variables used for each subj ect and RAs were allowed t o creat e new variables if t hey t hought t hey were necessary, alt hough t hey did not do so. RA s ret urned t wo spreadsheet s associat ing subject s’ comment s t o variables.No e¤ort was made t o force agreement bet ween coders. One of t he coders was more prone t o classify comment s int o variables t han t he ot her. W hile coder gave a posit ive value t o ent ries ( out of ent ries), coder gave a posit ive value t o ent ries ( ). I n any case, t he degree of agreement bet ween bot h coders was relat ively high. Taking t he average over t he value of all original t ernary variables for all subj ect s, bot h coders assigned t he same value ( , or ) t o of t hem.16 Coders never disagreed on t he direct ion of t he original t ernary variables.
Once t his informat ion was collect ed, we duplicat ed t he number of variables by t ransforming t he t ernary variables (0, 1 or 2) int o dummy variables (0 or 1) re‡ect ing t he direct ion of t he comment t hat t he variable capt ures. For example, t he variable , became t wo variables: (1 if want ing t o avoid risk, 0 if it did not refer t o risk) and (1 if want ing t o t ake risks, 0 if it did not refer t o risk).17
Our analysis below shows t hat t his codi…cat ion of subject s’ self-report s proved useful in explaining subject s’ choices in t he T D.
Table shows t he percent age of subject s whose comment s were re‡ect ed in our dummy variables ( ) at least according t o one of t he coders. T he t able cont ains a brief de-script ion of t he meaning of t he variables. Variables are classi…ed in …ve groups. T he names used t o describe t hese groups are only orient at ive and should help t he reader, but t hey were never used in t he analysis.
14T he RAs hold a BSc in Physics (coder 1) and a BSc in M at hemat ics (coder 2). At t he t ime, t hey
were enrolled in a PhD. progr am in Quant it at ive Finance.
15Our met hods closely followed t he met hodology in Brandt s and Cooper (2007) and Cooper and
K agel (2005).
16Maximum agreement was reached in variables and while minimum agreement
occurred in variable .
17De…nit ions for t he t er nary variables appear in t he I nst ruct ions for coders in A ppendix C, and
from t hem it is inmediat e t o obt ain t he dummy variables.
9 1 843 13 62% 238 26 = 6188 2 525 8 48% 0 1 2 92 26% 1 2 1 : : : Ri sk Ri sk Ri sk x ¤
3.2
D escr ipt ive st at ist ics of sub j ect s’ com m ent s
CutR F ai r Z er o :
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reasoning.ST RAT EGY refers t o own decisions: choosing t he middle of t he int erval or one of t he ext remes, undercut t ing t he predict ed rival’s choices, or choosing (or not ) a high value.
RIVALS refers t o beliefs about rivals’ choices: whet her t hey ment ioned a possible dist ribut ion for rivals’ choices or had point beliefs, t hought t heir rival would choose a high value, a higher value t han t heir own, et c.
INT ERDEPENDENT PREFERENCES includes variables re‡ect ing equit y consid-erat ions, appreciat ion for fairness or desire t o compet e.
Variables which bot h coders t hought were absent were eliminat ed.18 Not ice t hat no subj ect ment ioned choosing a number due t o it being “ an equilibrium” neit her explicit equilibrium reasoning was found in subject s’ comment s. No individual ment ioned imit at ing t heir rival. I n cont rast , some of t hem t ried t o coordinat e –t ypically on .
T here exist s not able het erogeneit y on t he explanat ions given by subj ect s for t heir choices in t he T D. Some reasons were ment ioned by a low percent age of subj ect s. We eliminat ed from t he following analysis t hose variables ment ioned by less t han 5% of t he subject s. T his leaves us wit h t he 23 variables t hat appear wit h a sign in Table 1.19
18T his was t he case for variables , , , , , _ , _ , and .
was eliminat ed for being redundant .
19Qualit at ive result s form t he remaining of t he paper were maint ained when all variables were
included in t he analysis.
10
120
+
P enalt y L ose Cut Cut R F ai r Coor d T heor y
2 2 2 2 2 20 2 120 2 2
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Table 1: Subj ec t s Ex pl an at i o ns o f Ow n Ch o ic es in t he t d x x Ri sk Aver age Ri sk Aver age Z er o Z er o W i n W i n Coor d Cut P enal ty CutC Si ze CutC Si ze CutR Lose Low Low Aspi Aspi P r ob P r ob Cal c H i gh H i gh Theor y H i gher H i gher E r r or Aver ageRN olog Aver ageR
N olog
Soci
E r mean F ai r
E r mean Soci
% Cont ent % Cont ent
CONCERNS STRATEGY
13.4 Risk averse 19.3 Average 4.6 Risk loving 5.5 Average
32.8 Win zero averse _ 1.3 Focal Point 20 0.4 Win zero like _ 5.0 Focal Point 120 9.7 Win loving
1.3 Win aversion 1.7 Coordinat e 10.5 Undercut rival 6.3 Penalty averse 5.0 Undercut 1 unit 0.4 Penalty high 3.4 Undercut 1 unit 0.8 Penalty low 0.8 Undercut twice
7.6 Loss aversion 17.6 Choice is low 5.0 Choice is high 7.6 Aspirat ion low RIVALS
5.0 Aspirat ion high 28.6 Probabilit y beliefs
REASONING 0.4 Point beliefs
20.2 Calculations 14.7 Beliefs high 2.5 Beliefs low 8.4 Economic t heory 13.9 Beliefs higher
0.4 Beliefs lower 8.8 Errors
2.9 Beliefs average 0.8 Solvable 0.4 Beliefs not average 6.3 Unsolvable INT ERDEPENDENT PREFERENCES
3.4 Equit y 10.1 Average is 70 0.4 Fairness 4.2 Average not 70 12.2 Compet it ive
As it is frequent ly argued in prot ocol analysis, our variables may j ust be a subset of t he reasons t hat could have in‡uenced subject s’ choices. I n any case, t here are a number of argument s which were prominent and syst emat ically repeat ed in subject s’
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informat ion about t heir subject ive probability dist ribut ion on rivals’ choices ( ), and/ or st at ed beliefs indicat ing t hat rivals may choose high values or higher values t han t heir own ( and ). Finally, subject s indicat ed a preference for earning more t han t heir rivals ( ). Not ice t hat more alt ruist ic forms of social preferences such as fairness or equit y concerns ( ) were barely ment ioned.20To convert t he above informat ion int o a more t ract able dat a set , for each variable we creat ed an variable adding up t he value of t he dummies assigned by each of t he t wo coders ( and ).
Our variables t ake value if no coder t hought t he subject ’s comment referred t o such variable, value if one of t he coders t hought it did and value if bot h coders t hought t he variable was ment ioned. Given t he lack of complet e agreement among coders, our index may be int erpret ed as re‡ect ing t he degree of int ensit y in t he cod-i…cat ion of each variable. Out of a possible t ot al of ent ries ( subject s dummy variables), t here were zeros ( ), one’s ( ) and two’s ( ). An alt ernat ive would have been t o have let dat a decide which of t he t wo coders was more e¤ect ive and use only such coder’s classi…cat ion. However, we favour having independent classi…cat ions and a measure of int ensit y.
Next we explain how we t urned t he index variables int o Principal Component s (PC).
20T his may be part ially induced by using grade point s as rewards which depend on t he overall
relat ive performance across all exper iment s and t asks.
12 Prob1 High1 Hi gher1 Soci2 Fai r1, Soci1 index
3.3
Conver t i ng V ar iabl es int o I ndex es
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3.4
P r i nci pal Com p onent s A nal ysis
Given t he nat ure and lengt h of our dat a set , t he use of PC analysis was nat ural: ) we were int erest ed in summarizing t he informat ion obt ained t hrough codi…cat ion in a more t ract able format ; and ) several variables may have conveyed t he same informat ion. For example, we were uncert ain a priory about t he possible relat ionship bet ween
and .
T he most salient feat ures of PC analysis are precisely t hat ( ) it t he number of variables and ( ) it in t he relat ionships bet ween t hem, i.e., it s according t o t heir cont ent . We ext ract ed Principal Component s explaining of t he variance.21 A ppendix A (available online) shows t he mat rix of rot at ed component s wit h t heir sat urat ion level.
Table shows t he indexes associat ed t o each of t he PCs and t heir sat urat ion level. We ident i…ed which indexes are predominant in each new PC t hrough t heir sat urat ion level. Our select ion crit eria was t o assign each original index t o t he component in which it shows it s highest value as long as t his value is clearly highest for one PC.22 We assign an orient at ive name t o each of t he PCs (Name) and we brie‡y remind t he cont ent of t he indexes t hat form each PC (Explanat ion). T he last column shows t he scoring of each index in it s component and t he direct ion of it s part icipat ion (it s sign).
21We did not prede…ne t he number of ort hogonal component s, rat her we used as ext ract ion crit erion
an eigenvalue higher t han 1 ( ); we also did not limit t he number of comput at ional it erat ions. To st udy t he signi…cance of each component , we rot at ed t he new variable using t he Varimax-K aiser procedure. I nit ially we got nine component s including t hree wit h only one variable which did not cont ribut e much in t erms of int erpr et at ion or explained variance.
22I ndexes , and , dissapear of t he analysis as t hey score low and similar values
in more t han one PC.
13 i i i ; loss r isk aversi on reduces detects structure
classi…es var iable
Zero1 T heor y1 Nolog1
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P C1Rival chooses higher 0.673 Uses probability 0.619 _ Rival chooses 120 0.562 Rival chooses high 0.560 PC2 Considers own choice as high 0.800 Aspires t o high value 0.692 PC3 Want s t o earn more t han rival 0.801 Want s t o beat rival 0.760
PC4 Expects low value 0.663
Risk averse 0.634 Choice is low 0.503 Hat es to earn less t han rival 0.395
PC5 Mean is 70 0.637
Chooses not mean 0.582 Chooses the mean 0.444
PC6 Penalty averse 0.454
Writ es calculat ions -0.477 Errors calculat ing payo¤s -0.653
T he indexes grouped under each PC and present ed in Table 2 suggest consist ent argument s for making a choice and it is st raight forward t o derive a behavioral predict ion from subject s classi…ed under each PC, as we lat er do in t able 4.23
T he set of indexes cont ained in indicat es t hat t here is a number of subject s who reason in t erms of probabilit y dist ribut ions on choices ( ) and believe t hat t his dist ribut ion has more weight on high values ( , _ ). Given t hese beliefs subj ect s show some level of it erat ive reasoning as t hey best respond by
23Using a di¤erent number of PCs does not yield a di¤erent r esult . For example, wit h 9 PCs t he
…rst four ar e ident ical and t he …ft h and sixt h are very similar.
14 H i gher
P r ob H i gh Aspi r ati ons L ow
A spi Competi ti ve Soci W i n Ri sk aver si on A spi Ri sk L ow L ose Aver age E r mean
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Undercutting
A spirations
Competi tive
Risk aversi on.
Average
L1
L2 Cut2, CutC2 CutR2
t he choice t hey expect from t heir rivals ( , ).24 Accordingly choices made by subj ect s scoring high in t his component should be made in t he high part of t he int erval, but should be lower t han t he highest value ( 120), as subject s un-dercut on t heir rival. Depending on t he exact expect at ion subj ect s may have on t heir rivals’ choice, t heir choice may be spread along t he int erval. Undercut t ing behavior may t hus cont ribut e t o t he dispersion of choices. T he second component , , in-cludes indexes re‡ect ing high payo¤ aspirat ions ( ) and, consequent ly high choices ( ). We t hus label PC2 as . Subject s scoring high in PC2 should made choices in t he high part of t he int erval. re‡ect s behavior. I n part ic-ular, indexes scoring high in t his PC correspond t o mot ivat ions such as earning more t han rivals ( ), or desire t o beat t hem ( ). T he indexes cont ained in PC3 sug-gest t hat subject s should choose t he lowest possible number (20) in order t o beat t heir rival and prevent him/ her from earning more t han t hem. refers t o choices part ly mot ivat ed by I ndexes scoring high in t his PC re‡ect desire t o avoid risks ( , ) and t hus, acknowledgement of low values chosen ( ) and low aspirat ion values ( ). Since subject s scoring high in PC4 indicat e t heir desire t o avoid risk and losses and acknowledge and expect t o obt ain low numbers, t hey should choose t he lowest possible number (20). cont ains indexes relat ed t o comment s made about t he of t he int erval. For example, st at ing it s value ( ) or j ust ifying choices due t o precisely being in t he average of t he int erval ( ) or close t o it , but not being t he average ( ). T herefore, we should expect choices from subject s scoring high in PC5 t o be in t he middle of t he int erval (around ). Finally, includes two t ypes of variables: subject s who are averse t o being penalized ( ) and subject s who make calculat ions ( ) or make mist akes in calculat ing payo¤s ( ). T here exist no clear a priory relat ionship among t he indexes grouped in PC6.T herefore, t he predict ion of choices made by subject s scoring high in PC6 is not so clear cut . Aversion t o being penalized should drive subj ect s t o make low choices, but ot her indexes in PC6 do not allow t o make clear predict ions. As such, we expect t hese choices t o be spread along t he int erval.
T here are t wo import ant remarks concerning t he int erpret at ion of principal com-ponent s:
24Not ice t hat subj ect s scor ing high in PC1 j ust ify t heir choices following a similar reasoning t o
t he cognit ive level as de…ned by St ahl and Wilson (1994 and 1995). Few subject s just i…ed t heir choices using higher levels of it erat ive reasoning such as , since variables like and
were rarely codi…ed.
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i i i i i i : :Regarding choice predict ions, Figure 2 below shows t hat choice predict ions for sub-ject s scoring high in each component were relat ively well ful…lled. Not ice t hat PC3 and PC4 predict t he same choice as t he unique Nash equilibrium of t he T D. A lt hough peo-ple using equilibrium reasoning may be mot ivat ed by some of t he variables cont ained in t his PCs, not ice t hat no subj ect just i…ed t heir choice wit h equilibrium argument s.
In t he next sect ion we check whet her t he di¤erent t ypes help us in predict ing choices in t he T D.
We now check coherence bet ween subject s’ comment s, summarized in t he PCs, and t heir choices. Given t he indexes cont ained in each of t he PCs we conj ect ure t hat : ) PC1( ) and PC2 ( ) have a posit ive impact on choices. ) PC3 ( ), PC4 ( ) and PC6 ( ) have a negat ive impact . ) PC5 ( ) drives choices t owards t he average of t he int erval.
Table 3 below shows t he result of Tobit censored regression and a simult aneous quant ile regression (SQR) of each subj ect ’s choice in t he T D wit h t he 6 principal component s as regressors. I n our T D, t he posit ion of t he choice along t he dist ribut ion is not t rivial. T herefore, a proper analysis by quant iles seems t o be appropriat e. T he SQR t echnique est imat es a regression for each quant ile and produces a vect or of correct ed errors (VCE) via boot st rapping, where t he VCE includes bet ween-quant ile blocks. T he int erpret at ion of t he coe¢ cient s of t he QSR in t able 3 are as in any regression model. T he comparison bet ween bot h est imat ions (t obit and SQR) shows coe¢ cient s of t he same sign and order of magnit ude, which allows us t o conclude t hat t he informat ion of t he dist ribut ion does not have import ant e¤ect s. P-values are equal t o zero in all cases, apart from t he coe¢ cient of PC5 which equals
16
4
Pr edi ct ing T D choices t hr ough P r incipal Com
-ponent s
Undercutting Aspirations
Competiti ve Risk Aversi on Penalty
Average
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Table 3:
Figure2 ab out here
PCs d r i v i ng T D c h o ic es (t o bit r eg r essio n ) ( N = 238) PC Name (Tobit ) (QSR) 56.71 PC1 12.16 PC2 11.51 PC3 -8.35 PC4 -12.87 PC5 3.28 PC6 -9.09
Not ice t hat all PCs are signi…cant (p-values of virt ually and have t he expect ed sign).
Figure 2 shows t he di¤erences bet ween act ual and …tt ed choices. I nt erest ingly, low and int ermediat e values are bet t er …tt ed t han high ones, which are underest imat ed.
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5
T y pe Coher ence A cr oss Tasks
per so n al c h ar ac t er i st i cs
G RE
PC4 20.83 28.33 17.77
PC5 23.61 67.46 9.76
PC6 18.06 39.55 31.49
Overall, we have been able t o ident ify di¤erent t ypes of subject s whose het eroge-neous choices in t he T D are j ust i…ed by het erogeeroge-neous reasons. Subject s self-report ing similar reasons make similar choices which coincide wit h our init ial conj ect ures. T he most import ant reasons driving choices in t he T D are relat ed t o st rat egic and it erat ive reasoning (PC1), high payo¤ aspirat ions (PC2), compet it ive preferences (PC3), at t i-t udes i-t owards risk and losses (PC4) and focal poini-t s such as i-t he average of i-t he ini-t erval (PC5).25 I n t he following sect ion we check whet her t hese ident i…ed t ypes are consist ent wit h some of subject s’ personal charact erist ics and t heir choices in independent t asks and experiment s.
T he following variables were obt ained from t he same sample of subject s performing di¤erent t asks in t he experiment al sessions det ailed in Sect ion 2. T he number of observat ions ( ) was not t he same across t asks, as some individuals were absent from cert ain experiment al sessions and some answers were erroneously report ed in t he session cont aining t he T D (June session).
We …rst describe t he variables relat ed t o subj ect s’ or at t it udes:
A dummy variable ( male, female).
Subj ect s’ scores in a -t ype mat h t est cont aining 25 mat hemat ics quest ions.
25A s previously ment ioned, PC6 , which capt ures t he lowest percent age of t he variance, has a less
clear int erpret at ion.
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Self-evaluat ion: Opti mi sm: Sel…sh: Ri sk-love:Lott er y-aver si on:
Proport ion of correct answers subject s expect ed t o get in t he -t ype -t es-t .
Average grade subject s expect ed t o obt ain in t he second t erm exams minus average grade obt ained in t he …rst t erm.
We now describe t hose variables which re‡ect ’ in ot her exper-iment s:
A dummy variable indicat ing how much subj ect s gave compared t o t he me-dian of t he subj ect s in t heir t reat ment playing t he same dict at or game ( gave less, gave equal or more).26
A variable in t he int erval indicat ing how much a subj ect has t o be paid t o avoid playing a 2x2 game wit h uncert ain out come. T his variable may re‡ect t he degree of individuals’ st rat egic risk–love.
A variable in t he int erval which re‡ect s t he average degree of risk–aversion showed by individuals playing four di¤erent lot t eries.27
First we explore t he correlat ions among t he variables regarding personal charac-t erischarac-t ics charac-t ogecharac-t her wicharac-t h charac-t he Principal Componencharac-t s. Table 5 reporcharac-t s Pearson- t est s among bot h t ypes of variables. T he number in parent hesis indicat es p-values while t he number on bracket s shows t he number of observat ions available for each of t he personal charact erist ics. Numbers in bold indicat e signi…cant coe¢ cient s at t he 10% level or bet t er. T he last line in t he t able shows correlat ions bet ween choices in t he T D and personal charact erist ics.
26We cr eat ed t his variable because di¤erent groups played dict at or games wit h di¤erent init ial
allocat ions.
27A s described in Brañas-Garza et al. (2008) .
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0.12 0.12 -0.11 -0.11 0.10 0.18 0.11 0.12 -0.10 b old PC2 Aspi rati onsPC3 Competiti ve PC4 Risk aversi on PC5 Average PC6 Penalty T D Choice GRE PC1 Self-evaluation
self-evaluati on PC2 Aspi rati ons
self-evaluation PC4 0.07 (0.30) (0.06) (0.10) (0.08) [180] [224] [176] [238] 0.10 (0.17) 0.07 (0.25) -0.02 (0.79) -0.04 (0.50) [180] [224] [176] [238] -0.10 (0.16) (0.09) 0.03 (0.65) (0.10) [180] [224] [176] [238] -0.05 (0.47) 0.04 (0.55) 0.05 (0.44) (0.00) [180] [224] [176] [238] 0.01 (0.88) -0.02 (0.68) -0.00 (0.92) -0.04 (0.52) [180] [224] [176] [238] 0.10 (0.17) (0.09) (0.10) (0.10) [180] [224] [176] [238]
* (p-value) and [sample size]. Numbers in indicat e st at ist ical signi…cance.
Our variable measures mat hemat ical skills, which may be relat ed t o subject s’ analyt ical and cognit ive abilit ies, and t hus we may expect t hat subject s using more cognit ively demanding j ust i…cat ions for t heir T D choices may be t hose who score high in t he GRE-t ype mat h t est .28 Table 5 indicat es t hat individuals’ mat h abilit ies are posit ively correlat ed t o .
may capt ure how con…dent subject s feel about t heir abilit ies. Con-…dent subject s may t hus expect t o obt ain high payo¤s, and in part icular t hey may aspire t o a high payo¤ in t he T D. T herefore t he posit ive relat ionship observed bet ween and ( ) was t o be expect ed. Addit ionally, t he negat ive correlat ion bet ween and may indicat e t hat con…dent subject s are not concerned about t he st rat egic uncert ainty in t he T D, as t hey may feel assured t hey will obt ain high payo¤s.
28Not ice t hat unercut t ing rivals’ choices is a cognit ively demanding r easoning process according t o
t he lit erat ure on K -level t hinking ( st art ing wit h St ahl and Wilson 1994).
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Optimi sm
optimi sm PC4
Gender men undercut
PC1 aspirations PC2
ri sk PC4
average PC5
Self-evaluati on Opti mism
Gender
types of subjects
sel…shness
risk-lovi ng lot tery-aver sion
may relat e t o t he expect at ion of get t ing bet t er out comes t han previously obt ained. T his opt imism may drive subject s t o hold high aspirat ions in t he T D, which would explain t he posit ive correlat ion bet ween and .
We also observe some e¤ect s. I n t he T D, are more likely t o
t heir rivals ( ) and have higher ( ). On t he cont rary, women express more concerns about ( ) and t end t o ment ion choosing values because of t heir proximit y t o t he of t he int erval ( ).
Finally, we …nd t hat t he analysis nicely ext ends t o t he correlat ion bet ween personal charact erist ics and choices in t he T D. We …nd t hat and
are posit ively correlat ed (at t he 10% level) wit h choices in t he T D, which may be explained by self-con…dent and opt imist ic subject s expect ing t o obt ain higher payo¤s in t he T D and t hus making high choices. W it h respect t o gender e¤ect s, we …nd negat ive correlat ion bet ween and choices in t he T D, which, as we explained below, may be due t o higher risk aversion among women..
Now we check t he possible relat ionship bet ween choices in di¤erent experiment s. T he het erogeneit y observed in t he di¤erent j ust i…cat ions of subject s’ act ions in t he T D, makes it an ideal candidat e t o st udy t he t ranslat ion of subj ect s’ mot ivat ions across t asks. In such case, we would expect PCs t o be able t o capt ure subject s’ int rinsic mot ivat ions not only in T D but in ot her experiment al t asks, and t hus t here may exist an int rinsic component in de…ning , which may not be complet ely t ask-dependent . For example, we want t o check whet her t hose individuals ment ioning risk concerns in t he T D are t hose behaving as risk averse when facing lot t eries. Table 6 report s regressions of dict at or game choices ( ), choices under uncert aint y involving st rat egic risk ( ), and lot t ery choices ( ) on t he six PCs obt ained from t he T D. T herefore, we should observe signi…cant coe¢ cient s for t hose PCs capt uring t he most relevant feat ure for each t ask.
Not ice t hat t he t ranslat ion of t he mot ivat ions capt ured by PCs t o ot her t asks may not be perfect . For example, subj ect s in t he T D may have ment ioned only a subset of t he mot ivat ions driving t heir choices. However, we should expect t hat self-report s may reveal t he most prominent mot ivat ion underlying T D choices, and t hus, our exercise may show meaningful result s. Table 6 shows t hat most of t he signi…cant coe¢ cient s in our regressions have t he expect ed sign and are easy t o int erpret . Below we discuss t he signi…cant coe¢ cient s for each of t he PCs.
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-0.23 0.03 PC3 Competi ti ve PC4 Ri sk Aver sion PC5 Average PC6 Penalty PC4 ri sk-love lotter y-aversi on PC1Undercutti ng insurance lot tery-aver sion
PC2 Aspi rati ons sel…shness).
lottery-aversi on
sel…shness
risk-lovi ng
lottery-aversi on
sel…shness risk-lovi ng, lott ery-aver sion
0.07 (0.43) 0.08 (0.46) -0.00 (0.60) -0.03 (0.71) (0.02) (0.02) -0.07 (0.46) 0.03 (0.77) 0.00 (0.70) 0.04 (0.69) 0.09 (0.40) -0.00 (0.84) -0.44 (0.00) 5.40 (0.00) 0.48 (0.00) * (p-value).
T he most salient result s appear in bold in Table 6. We now describe a possible int erpret at ion of t he result s:
First , subj ect s report ing t heir choices were mot ivat ed by a desire t o avoid risks ( ) are precisely t hose who also avoided st rat egic risk ( ). Consist ent ly, t hey are also t hose who are more risk averse ( ).
Second, subj ect s just ifying t heir T D choices using argument s cont ained in ( ) less prone t o buy in lot t eries ( ), which may be relat ed t o t he fact t hat t hose who choose high values in t he T D may underest imat e t he risk of obt aining bad out comes. T his same behavior would lead t hem t o buy less insurance in ot her uncert ain sit uat ions such as lot t eries.
Finally, Subj ect s ment ioning argument s cont ained in ( ) aims t o obt ain a high payo¤ in t he T D. T his same behavior would lead t hem t o keep everyt hing for t hemselves in dict at or games ( Such subject s are also more prone t o buy insurance ( ), possibly also in order t o maint ain t heir payo¤s.
We …nally performed regressions of t he dict at or game choice ( ), t he choice under uncert aint y involving st rat egic risk ( ), and t he lot t ery choices (
) on t he choice in t he T D. A lt hough coe¢ cient s have t he expect ed signs (posi-t ive for ( and negat ive for ), t hey are not st at is-t ically signi…canis-t ais-t sis-t andard levels. A lis-t hough is-t his resulis-t may seem disappoinis-t ing ais-t …rst , not ice t hat if in t his paper we have focused on self-report s, grouped under PCs, it is precisely because t hey indicat e a unique driving mot ivat ion behind choices in t he
22 constant
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T D. On t he ot her had, t he same choice in t he T D may be driven by several mot ivat ions which may not be re‡ect ed in t he simples t asks and experiment s we are correlat ing t hem wit h (dict at or game, st rat egic risk and lot t eries). T herefore, we should not expect t hat behavior would t ranslat e across t asks as well as mot ivat ions do.T his paper st art s by providing reasons behind observed het erogeneous behavior in a part icular version of a one-shot t raveler’s dilemma experiment .
Our experiment s were part of a larger t ournament compet it ion among st udent s used t o mot ivat e learning during a Microeconomics course. T hus, we used a part icular relat ive performance incent ive st ruct ure and a part icular frame (…rms …xing prices). Our version of t he T D maint ains t he same t heoret ical propert ies and a similar empiri-cal dist ribut ion of het erogeneous choices as more st andard versions of t he T D. We use subj ect s’ self-report ed just i…cat ions for t heir behavior and we …nd t hat t heir claims t urn out t o be coherent and consist ent reasons for making di¤erent choices in t he T D. Among t he most prominent argument s, we …nd t hat di¤erent levels of st rat egic sophis-t icasophis-t ion, hesophis-t erogeneous beliefs on opponensophis-t s’ choices, payo¤s aspirasophis-t ions, compesophis-t isophis-t ive preferences, di¤erent degrees of risk and loss aversion and focal point s such as t he average of t he int erval are behind one-shot choices in our T D.
Alt hough self-report ed explanat ions are obt ained using no incent ives and t hey may only be a subset of t he possible reasons leading t o het erogeneous choices in t he T D, we …nd t hat t hey are useful in underst anding behavior. T hus, our paper is in line wit h recent experiment s using a variet y of sources easily available in t he laborat ory t o obt ain higher explanat ory power t han relying only in choices made in t he laborat ory. Similar recent approaches have successfully st udied subject s’ sequence of payo¤ look-ups t o ident ify reasoning processes (Cost a-Gomes and Crawford 2006), elicit ed beliefs of opponent s’ choices (see Cost a-Gomes and Weizsäcker 2008), recorded communicat ion among subj ect s (Brandt s and Cooper 2007) or measure response-t imes (see Rubinst ein 2006) t o explain laborat ory behavior.
T he t raveler’s dilemma is an ideal game t o st udy het erogeneous mot ivat ions behind behavior since t he t ypical dist ribut ion of choices is het erogeneous. However, if we want t o st udy how consist ent t hose mot ivat ions are across di¤erent t asks, using only t he act ions observed in a T D experiment might not be enough. T he reason is t hat we show
23
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sic t o subject s. T hus we observe t hat mot ivat ions are coherent wit h choices by t he same subj ect s in ot her t asks for which such mot ivat ions should be prominent . Alt hough our result s are limit ed t o t he number of t asks and experiment s available using t he same subj ect s, our paper is a …rst promising st ep t owards ident ifying types of subject s in a given populat ion. We have shown t hat it may be possible t o predict subj ect s’ be-havior in di¤erent t asks using subject s’ self-report ed reasoning in ot her t asks. Furt her research aiming t o ident ify t he relat ionship bet ween di¤erent t ypes of individuals and t heir st rat egic behavior should follow.Page 25 of 278
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Ericsson, K . A., Simon, H. A., 1993. Prot ocol analysis: Verbal report s as dat a MI T Press, Cambridge, MA.
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St ahl, D., W ilson, P., 1994. Experiment al evidence on players’ models of ot her players. Journal of Economic Behavior and Organizat ion 25, 309-327.St ahl, D., W ilson, P., 1995. On Players’ Models of Ot her Players: T heory and Experiment al Evidence. Games and Economic Behavior 10, 218-254.
Suet ens, S., Pot t ers, J., 2007. Bert rand colludes more t han Cournot . Experiment al Economics 10, 71-77.
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A ppendix
A pp endi x A : M at r ix of r ot at ed com p onent s
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A pp endi x C: I nst r uct i ons t o Classi …er s
In t his t est you must decide on prices. A ssume t hat YOU are a …rm compet ing in a market wit h only t wo …rms. Now we will explain t o you who is t he ot her …rm and what your t ask is.
Your compet it or is a clasmat e in your Micro I sect ion. T he mat ching will be made such t hat everyone has a single part ner.
Task : You must …x a price in t he int erval [ 20, 120 ], bot h ext remes included. Since you compet e wit h a rival …rm you must consider t hat :
I f t he ot her company …xes a price lower t han yours, t hen you will earn what t he ot her has …xed minus a 20 point penalt y (she will earn her price plus 20 ext ra point s).
if t he ot her company …xes a price higher t han yours, t hen you will earn what you have …xed plus 20 ext ra point s (she will earn your price minus a 20 point penalt y
if bot h prices coincide t hen BOT H of you will earn t he price you have …xed.
T he price t hat I choose is: _ _ _ _
You can use t he following space for what ever you may need. Please indicat e how you have come up wit h your decision.
Your t ask consist s in classifying t he comment s made by t he 242 subj ect s who part ic-ipat ed in t he experiment . We have creat ed t he variables list ed below and you must codify t he writ t en informat ion provided by subj ect s in t hese variables. Your t ask does not consist in int erpret ing why t he subj ect s writ e what t hey writ e, but only in ac-curat ely at t est ing what t hey writ e. Our object ive is t o …nd out regularit ies on what subj ect s writ e, so please be careful when classifying comment s, you should re‡ect only what subject s wrot e.
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T he forms are in t he same order t hat t he names in t he Excel …le you will be working on. Please, st art by reading t he name of t he subj ect and his/ her comment . Next , move along t he row corresponding t o t hat subject and …ll up t he cells you t hink should be …lled.You must use " ones" (1) and " t wos" (2) t o …ll up t he cells, according t o t he expla-nat ion for each variable provided below. I n t he cases in which t he subject ’s comment s do not convey any informat ion on a part icular variable, please do not change t he ent ry in t he corresponding cell (leave t he " zero" ).
Consider t he cells as independent : …lling up a cell wit h a number does not imply anyt hing about t he number you ent er in anot her cell.
Finally, you can add columns of variables if you t hink t hat our variables do not allow you t o re‡ect what a subject writ es. I n t hat case, please, writ e your codi…cat ion syst em in a Word document similar t o t he t able " VARI ABLES" shown below.
Please, before you st art reading subj ect s’ comment s, have a look at t he list of variables and t heir codi…cat ion below. You will need t o check t he codi…cat ion again while you …ll up t he Excel …le, specially wit h t he …rst subj ect s. Please, be pat ient and do it carefully.
T he inst ruct ions of t he experiment appear in each subj ect s’ forms. Please, before you st art make sure t hat you underst and t he experiment and t he payo¤ mechanism.
T hank you very much for your help.
Does not like / Does not want t o t ake risks
Says does not want / does not like t o t ake risks / t akes a decision because implied risk is low or moderat e
Says want s / likes t aking risks Does not ment ion t his issue
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Explanat ion: “ 1” if: “ 2” if: Leave “ 0” if: Lose F Explanat ion: Size G Explanat ion: “ 1” if: “ 2” if: Leave “ 0” if: Calc H Explanat ion: “ 1” if: Leave “ 0” if: T heor y I Explanat ion: “ 1” if: “ 2” if: Leave “ 0” if: Err or JWant s t o avoid being penalized Says want s t o avoid being penalized Says want s t o be penalized
Does not ment ion t his issue
Want s t o avoid having less point s t han rival
“ 1” if: Says does not want t o lose / t o have less point s t han t he rival “ 2” if: Says want s t o lose / t o have less point s t han t he rival
Leave “ 0” if: Does not ment ion t his issue
Decision depends on size of t he penalt y Says penalt y is " high" and t hat it a¤ect s decision Says penalt y is " low" and t hat it a¤ect s decision
Does not ment ion t his issue
Writ es calculat ions on sheet T here are calculat ions writ t en on sheet
T here are no calculat ions on sheet
Gives an economic explanat ion of decision
Comment explains an economic t heory (correct or not ) / t alks about …rms/ uses t erms like " undercut t ing" , et c.
Comment does not cont ain economic t heories or about how …rms compet e, et c.
Does not ment ion t his issue
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Explanat ion: “ 1” if: Leave “ 0” if: Prob K Explanat ion: “ 1” if: " 2" if: Leave " 0" if: Ermean L Explanat ion: “ 1” if: " 2" if: Leave " 0" if: Nolog M Explanat ion: “ 1” if: “ 2” if: Leave “ 0” if: High N Explanat ion: “ 1” if: “ 2” if: Leave " 0" if: Higher O Explanat ion: “ 1” if: " 2" if: Leave “ 0” if:M akes mist akes when calculat ing payo¤s
Comment s show subject does not underst and payo¤ mechanism
Underst ands payo¤ mechanism or it is not possible t o infer whet her t he payo¤ mechanism has been underst ood
T hinks t hat t he rival can choose di¤erent values
Says t hat cert ain values will be chosen wit h probabilit y / are likely / most probably / a high percent age of t imes / in t he maj orit y of cases
Says t hat rival will choose some value for sure
Does not say anyt hing about t he probabilit y of values chosen by rival
Does not know how t o calculat e t he int erval ’s mean Says mean is di¤erent from 70
Says mean is 70
Does not ment ion t he value of t he int erval’s mean
Does not t hink it is possible t o choose using reasoning Says it is not possible t o choose using reasoning / chooses randomly Says it is possible t o choose using reasoning
Does not ment ion “ reasoning”
T hinks rival will choose a high value Says rival will choose a high value
Says rival will choose a low value Does not ment ion rival’s value
T hinks t hat rival will choose higher value t han self Says rival will choose higher value t han self
Says rival will choose lower value t han self Does not ment ion rival’s value
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Cut C P Explanat ion: " 1" if: " 2" if: Leave “ 0” if: Cut R Q Explanat ion: " 1" if: " 2" if: Leave " 0" if: Fair S Explanat ion: “ 1” if: " 2" if: Leave “ 0” if: Soci T Explanat ion: “ 1” if: “ 2” if: Leave “ 0” if: A verage O Explanat ion: “ 1” if:Chooses a value lower t han rival’s expect ed value Says chooses j ust one unit less t han rival’s expect ed value
Says chooses a somewhat lower value (5, 12, " a lit t le lower" ) t han rival’s expect ed value
Does not ment ion value rival will choose
T hinks rival will undercut and undercut s even more Says undercut s just one unit t o t he rival’s undercut value
Says chooses a somewhat lower value (5, 12, " a lit t le lower" ) t han rival’s undercut value
Does not ment ion rival’s value
Chooses a value for being " fair"
Says choice is mot ivat ed t o make payo¤ dist ribut ion fair / t alks about " fairness"
Says choice is mot ivat ed t o make payo¤ dist ribut ion unfair Does not ment ion payo¤ dist ribut ion fairness
Cares about rival´ s payo¤s
Says want s bot h players t o earn more or less t he same Want s t o earn more t han rival
Does not ment ion payo¤ dist ribut ion
Chooses an average value
Says chooses a value so t hat it is average (or int ermediat e)
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" 2" if: Leave “ 0” if: A verageR V Explanat ion: “ 1” if: “ 2” if: Leave " 0" if: 20 W Explanat ion: " 1" if: " 2" if: Leave " 0" if: 120 X Explanat ion: " 1" if: " 2" if: Leave " 0" if: Coord Y Explanat ion: “ 1” if: " 2" if: Leave " 0" if: W in Z Explanat ion: “ 1” if: “ 2” if: Leave “ 0” if: A spi A A Explanat ion: “ 1” if: " 2" if:Says chooses a value for not being t he average (above, below...) Does not ment ion choosing average value or not
Rival / Rivals will choose average value
Says rivals will probably choose/ on average an average value
Says believes rivals will choose / probably/ on average anot her value Does not ment ion rival’s value
Rival / Rivals will choose 20
Says rival will choose / probably/ on average 20
Says t hinks rivals will choose / probably/ on average anot her value Does not ment ion rival’s value
Rival / Rivals will choose 120
Says rival will choose / probably/ on average 120
Says t hinks rivals will choose / probably/ on average anot her value Does not ment ion rival’s value
Want s t o coordinat e wit h rival Says want s t o coordinat e value wit h rival´ s
Says does not want t o coordinat e value wit h rival´ s Does not refer t o coordinat ion
Want s t o beat rival Says want s t o beat rival
Says does not want t o beat rival
Does not ment ion whet her want s t o win or not
A ims t o / Expect s / A ccept s a value Says aims t o low value
Says aims t o high value
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Leave “ 0” if: Does not ment ion t he size of own value
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A pp endi x D : D escr ipt ive St at ist ics
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Subject 15 El precio que yo elijo es: 20 Tienes este espacio para lo que necesites: He elegido el precio de 20 así como mínimo voy a ganar 20. Hay varios casos que puedo tener: Yo→20, otro →20 →Los dos nos llevamos 20Otro→n>20, yo→20 → Yo me llevo 40 el otro cero.
Si no se escogiera esta opción podría darse la posibilidad de que la otra empresa cogiera un precio menor que el mío, como por ejemplo 20, y yo me llevaría cero. The price that I choose is: 20 You have this space for whatever you need: I have chosen the price of 20, in this way I will at least win 20. There are several cases: Me→20, other →20 →we both win 20
Other→n>20, me→20 → I win 40 the other zero.
