Emulation in Teams and Families

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(1)2009s-04. Emulation in Teams and Families Daniel Leonard, Ngo Van Long. Série Scientifique Scientific Series. Montréal Mars 2009. © 2009 Daniel Leonard, Ngo Van Long. Tous droits réservés. All rights reserved. Reproduction partielle permise avec citation du document source, incluant la notice ©. Short sections may be quoted without explicit permission, if full credit, including © notice, is given to the source..

(2) CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d’une subvention d’infrastructure du Ministère du Développement économique et régional et de la Recherche, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Québec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the Ministère du Développement économique et régional et de la Recherche, and grants and research mandates obtained by its research teams. Les partenaires du CIRANO Partenaire majeur Ministère du Développement économique, de l’Innovation et de l’Exportation Partenaires corporatifs Banque de développement du Canada Banque du Canada Banque Laurentienne du Canada Banque Nationale du Canada Banque Royale du Canada Banque Scotia Bell Canada BMO Groupe financier Caisse de dépôt et placement du Québec DMR Fédération des caisses Desjardins du Québec Gaz de France Gaz Métro Hydro-Québec Industrie Canada Investissements PSP Ministère des Finances du Québec Power Corporation du Canada Raymond Chabot Grant Thornton Rio Tinto Alcan State Street Global Advisors Transat A.T. Ville de Montréal Partenaires universitaires École Polytechnique de Montréal HEC Montréal McGill University Université Concordia Université de Montréal Université de Sherbrooke Université du Québec Université du Québec à Montréal Université Laval Le CIRANO collabore avec de nombreux centres et chaires de recherche universitaires dont on peut consulter la liste sur son site web. Les cahiers de la série scientifique (CS) visent à rendre accessibles des résultats de recherche effectuée au CIRANO afin de susciter échanges et commentaires. Ces cahiers sont écrits dans le style des publications scientifiques. Les idées et les opinions émises sont sous l’unique responsabilité des auteurs et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners.. ISSN 1198-8177. Partenaire financier.

(3) Titre Emulation in Teams and Families Daniel Leonard*, Ngo Van Long † Résumé / Abstract Nous présentons un modèle où la distribution de la valeur du succès d'un agent dépend non seulement de son aptitude et de son effort, mais aussi des objectifs qui lui sont fixés par le principal. L'agent choisit son effort en tenant compte de son utilité et du coût percu de l'effort. Ce coût est inversement proportionel à une 'fonction d'émulation' qui dépend des objectifs fixés à ses rivaux. Dans une première partie, nous analysons les choix d'entraineurs d'athlètes rivaux et celui de l'entraineur d'une équipe. Nous pouvons parfois ordonner leurs résultats. Une deuxième partie analyse le cas des familles qui, contrairement aux entraineurs, ne considèrent pas leurs enfants comme de parfaits substituts. Nous démontrons que souvent le processus d'émulation aboutit à des résultats contraires à une intuition naïve. Il y a maintenant deux voies distinctes pour pousser les enfants vers le succès : une voie directe par la formation, et une voie indirecte s'appuyant sur la rivalité entre frères et soeurs. Mots clés : émulation, fixation des objectifs, relation entre un principal et des agents.. We present a model where the probability distribution over the space of an agent's achievements depends not only on her ability and effort, but also on the goals set for her. The agent chooses her effort according to her utility net of perceived cost of effort. This cost is inversely proportional to an `emulation function' that depends on the training undertaken by rival agents. The principal also incurs costs in setting goals. In the first part of the paper we analyse the cases of coaches setting goals for rival athletes and that of a coach in charge of a team. We can sometimes rank the outcomes. In the second part of the paper we turn our attention to families where parents do not treat their children as perfect substitutes, as coaches did. We show that in many circumstances the emulation process reverses our naive intuition. There are now two distinct ways of prodding children to success: direct coaching, and emulation through sibling rivalry. Keywords: emulation, goal setting, principal-agent relationship. Codes JEL : D1, D23. *. Flinders School of Business, Flinders University, Adelaide, Australia. Email: daniel.leonard@filnders.edu.au. † CIRANO and CIREQ, Department of Economics, McGill University, 855 rue Sherbrooke Ouest, Montréal, Québec, H3A 2T7, Canada. Email: ngo.long@mcgill.ca..

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(68) E96 D:8? :D 2=D@ ?682E:G6 &?=J :7 :D G6CJ =2C86 4@>A2C65 E@ 2?5 2?5 C642== E92E

(69) 42? E96 56C:G2E:G6 36 A@D:E:G6 ? 2== @FC 6I2>A=6D :E :D ?682E:G6 2?5 H6 E2<6 E9:D E@ 36 E96 O?@C>2=O C6DF=E. *96C67@C6 O?@C>2==JO. 2?5 . . ? E9:D 4@?E6IE 7@C LI65 , E96 >@DE 72G@FC65 49:=5 :D D6E 2 9:896C 8@2= H96? E96 EH:?D 2C6 92C56C E@ >@E:G2E6 *96 C6G6CD6 :D ECF6 H96? E96 EH:?D 2C6 <66? E@ 6I46=. E D66>D E92E E96 5:S4F=EJ @7 65F42E:?8 E96D6 49:=5C6?. 6I246C32E6D E96:C 5:T6C6?E EC62E>6?E :? E9:D 42D6 F?2>3:8F@FD=J E@H2C5D E96 72G@FC65 EH:? *96 EFC?:?8 A@:?E :? E96 23@G6 5:28C2> 4@CC6DA@?5D E@ E96 4C:E:42= G2=F6 2DD@4:2E65 H:E9 C6G6CD2= 2?5 :D 9:896C E96 =2C86C :D @C E96 DEC@?86C 6>F=2E:@? H@C<D. 4 *96 LCDE @C56C 4@?5:E:@? :D .

(70) .

(71) S. S1*. T. ȕy/2(1-ȕ). :CDE 4@?D:56C E96 42D6 H96C6 2?5 + E 42? 36 HC:EE6? 2D. . . ECF6 :7 2?5 @?=J :7 , , R (642== ,. . . . . . . . H:49 :D. *96C67@C6 H96? ) 2?5 + :7 2?5 @?=J :7 , , J 4@?E:?F:EJ E9:D 2=D@ ECF6 7@C ) ?62C ? @C56C E@ EC246 E96 3@F?52CJ 36EH66? E96 C68:@?D H96C6 2?5 :? E96 + ) DA246 H6 FD6 E96 LCDE @C56C 4@?5:E:@? 6G2=F2E65 2E . . . . . . . . . + *#!'! & . . -6 @3E2:? 7@C E96 3@F?52CJ. . . ) &. . . ) ). *9:D 3@F?52CJ 42? 36 A=@EE65 7@C D6=64E65 G2=F6D @7 2?5 & E :D A@DD:3=6 E92E E96 ?F>6C2E@C 2?5 E96 56?@>:?2E@C 2C6 @7 5:T6C6?E D:8?D :? H9:49 42D6 @?6 @7 E96 8@2=D :D 2=H2JD 23@G6 E96 @E96C.

(72) . E :D 62DJ E@ D9@H E92E. .

(73) Where the (S,S) boundary doesn't exist 6 5 4. t. S2*<S1* 3 2 1 S2*>S1* 0 0. 0.5. 1. 1.5. 2. n, NOT-x t=(2-n)/n or n=2/1+t. t=n/(2-n), or n=2t/1+t. :?56A6?56?E=J @7 E96 G2=F6 @7 *96 ?F>6C2E@C 92D E96 D:8? @7 &. ) 2?5 E96 56?@>:?2E@C E92E @7 & ) ). C@> E9:D C6DF=E H6 42? 5C2H E96 7@==@H:?8 5:28C2> E92E :?5:42E6D E96 C6=2E:G6 G2=F6D @7 2?5 2?5 , C6=2E:G6 E@ H96C6 @?6 @7 E96 8@2=D 2=H2JD 5@>:?2E6D *9:D 92AA6?D H96? , :D ?@E E@@ 72C 7C@> , 2?5 2?5 ?@E E@@ 4=@D6 E@86E96C. *96 3@F?52CJ C@E2E6D 2?E: 4=@4<H:D6 2D :?4@>6 :?4C62D6D -96? , :D 4=@D6 E@ , E96 3@F?52CJ :D 2=>@DE 2 DEC2:89E =:?6 2E ) 2?5 G2=:5 7@C 2 G6CJ D>2== :?E6CG2= @7 ) G2=F6D 2D 6IA64E65 7C@> :8FC6

(74) 23@G6.

(75) .

(76) 8. 7. 6. t. 5. 4. 3. 2. 1. 0 0. 0.5. 1. 1.5. 2. x Boundary (b) Low y. Boundary (b) High y. . Boundary (b) Very High y. 2.5.

(77) Region II Sm<Sl. Region I. Tm<Tl. Sm>Sl Tm>Tl. Region III Sm>Sl Tm<Tl Region III” Region I”. Region II”. Sm>Sl. Sm<Sl. Tm>Tl. Tm<Tl. Sm>Sl Tm<Tl. ? E96 + ) DA246 H6 :==FDEC2E6 9@H E96 3@F?52CJ G2C:6D H:E9 :?4@>6 , *96 3@F?52CJ C@E2E6D 2?E: 4=@4<H:D6 2D :?4@>6 :?4C62D6D -96? , :D 4=@D6 E@ , E96 3@F?52CJ :D 2=>@DE 2 DEC2:89E =:?6 2E ) 2?5 G2=:5 7@C 2 G6CJ D>2== :?E6CG2= @7 ) G2=F6D 2D 6IA64E65 7C@> :8FC6

(78) 23@G6. ? @C56C E@ F?56CDE2?5 E96 A2CE:E:@??:?8 @7 E96 + ) DA246 =6E FD C6E9:?< @FC 56D4C:AE:@? @7 O9:89 :?4@>6O E >62?D , , *9:D :D >@C6 =:<6=J E@ @44FC H96? 6>F=2E:@? :D DEC@?8 3642FD6 :? E92E 42D6 , :D D>2== )@ =6E FD ?@H C676C

(79).

(80) E@ D:EF2E:@?D @7 O9:89 :?4@>6O 2D D:EF2E:@?D @7 ODEC@?8 6>F=2E:@?O -6 92G6 56A:4E65 E96 42D6 @7 H62< 6>F=2E:@? =@H :?4@>6 :? :8 ):I C68:@?D 2C6 :56?E:L65 *96 ?@E2E:@?D 2?5 C676C E@ >@C6 8:7E65 49:=5 2?5 =6DD 8:7E65 C6DA64E:G6=J 2D 5@ 2?5 ? C68:@? 49:=5 :D >@C6 8:7E65 2?5

(81) 2=D@ 96?46 ? C68:@? 49:=5

(82) :D >@C6 8:7E65 2?5 . DE:== 2=D@ 96?46 2D H6== ? C68:@?. 7@C :?DE2?46 . 2?5 2D H6== 2D D@ H6 92G6 2?5 ):>:=2C. C6=2E:@?D 2C6 565F465 7C@> :8FC6 7@C 2== D:I C68:@?D @7 :8 :CDE ?@E6 E92E C68:@?D 2?5 . 2?5. 6E4. 2C6 9@>6@>@CA9:4 :? E96 E6C>:?@=@8J. @7 O>@C6 8:7E65O 2?5 O=6DD 8:7E65O E96:C 56L?:E:@?D 2C6 :56?E:42= 2D 42? 36 D66? @? E96 5:28C2> *96 E6C>:?@=@8J @7 49:=5

(83) 2?5 49:=5 H9:=6 FD67F= :? E96 42=4F=2E:@?D >FDE ?@H 8:G6 H2J E@ E96 >@C6 C6=6G2?E 5:DE:?4E:@? @7 23:=:EJ. *96 :?E6CAC6E2E:@? @7 E96 C6DF=ED :D 2D 7@==@HD -96? 6>F=2E:@? :D H62< 2 49:=5 H9@ :D 3@E9 >@C6 8:7E65 2?5 >@C6 5:S4F=E H:== 2EEC24E >@C6 4@249:?8 C68:@? E9:D :D 6IA64E65 H96? A2C6?EDO AC676C6?46D 7@==@H 23:=:EJ *9:D H:== 9@=5 ECF6 6G6? :7 E96 >@C6 8:7E65 49:=5 :D 2 =:EE=6 62D:6C E@ >@E:G2E6 &?=J :7 @?6 49:=5 :D @?=J D=:89E=J >@C6 8:7E65 2?5 >F49 >@C6 5:S4F=E E@ >@E:G2E6 H:== A2C6?ED D6E 9:> @C 96C 2 =@H6C 8@2= C68:@?. *96J 2C6 E96? FD:?8 E96. @E96C 49:=5 E@ =@H6C E96 4@DE @7 6T@CE E@ E96 >@C6 8:7E65 2?5 AC676CC65 @?6 E9C@F89 6>F=2E:@? *9:D :? E96 + ) DA246 D66>D E@ 92AA6? =6DD 7C6BF6?E=J. -6 ?@H EFC? E@ E96 9:89 3F586E DEC@?8 6>F=2E:@? 42D6 D66 :8 *96 3@F?52CJ 92D C@E2E65 4@F?E6C 4=@4< H:D6 7C@> E96 =@H 3F586E D:EF2E:@? 2?5 C68:@?D. 2?5. 92G6 5:D2AA62C65 H96? E96 3@F?52CJ >@G65 :?E@ E96. ) =:?6 (68:@?D , 2?5 , 92G6 6>6C865 *96J 2?5 C68:@?D. 2?5. . ?@H 5@>:?2E6 E96 5:28C2> -96? E96 6>F=2E:@? AC@46DD :D >F49 DEC@?86C 9:89 3F586E E96 D:EF2E:@? :D C6G6CD65 A2C6?ED FD6 E96:C 4@?D:56C23=6 3F5 86E E@ 96=A E96 72G@FC65 49:=5 :?5:C64E=J 3J =@H6C:?8 E92E 49:=5OD 6T@CE 4@DE E9C@F89 6>F=2E:@? 2?5 4@2I:?8 9:> @C 96C :?E@ 9:896C 6T@CE 3J 4@249:?8 E96 =6DD 72G@FC65 49:=5 >@C6 D C6>2C<65 62C=:6C H6 4@F=5 2=D@ G:6H E96 D:EF2 .

(84) E:@? 2D @?6 H96C6 A2C6?ED 92G6 6I9F2DE65 E96:C 5:C64E :?MF6?46 @? E96 >@C6 8:7E65 49:=5 E9C@F89 255:E:@?2= 4@249:?8 2?5 ?@H C6G6CE E@ :?5:64E 4@2I:?8 3J =@H6C:?8 E96 49:=5OD 6T@CE 4@DE E9C@F89 6>F=2E:@?. 5 6C6 H6 DFAA@D6 E92E A2C6?ED 72G@FC E96 =6DD 8:7E65 49:=5. *96 LCDE @C56C 4@?5:E:@? :D . -6 AC@4665 2D :? 42D6 4. *96 6IAC6DD:@? 7@C E96 3@F?52CJ :D + H96C6 2?5 2C6 2D 23@G6. E :D 62DJ E@ D9@H E92E :?56A6?56?E=J @7 E96 G2=F6 @7 E96 ?F>6C2E@C 2?5 E96 56?@>:?2E@C 2C6 @7 E96 D:8?D @7 ) & 2?5 @7 & C6DA64E:G6=J. ) ) *96C67@C6 E96 K@?6D :? & ) DA246 H96C6 2?5 2C6 :?G6CE65 4@>A2C65 E@ 42D6 4. *96 3@F?52CJ C@E2E6D 4=@4<H:D6 2D :?4@>6 :?4C62D6D -96? , :D 4=@D6 E@ , E96 3@F?52CJ :D 2=>@DE 2 DEC2:89E =:?6 2E ) 2?5 G2=:5 7@C 2 G6CJ D>2== :?E6CG2= @7 ) G2=F6D 2D 6IA64E65 7C@> :8FC6

(85) 23@G6. %@H A2C6?ED 72G@FC E96 49:=5 H:E9 E96 =@H6C 23:=:EJ ? 2?2=JD:D @7 E96 5:28C2> 2=@?8 E96 =:?6D @7 H92E H2D 5@?6 :? 42D6 4 C6G62=D 2 DE2CE=:?8 724E. -96? 6>F=2E:@? :D H62< =@H :?4@>6 :? 42D6 5 E96 3C@25 D92A6 @7 E96 3@F?52CJ 2?5 E96 6I24E 56L?:E:@? @7 E96 C68:@?D >2E49 E96 C6DF=ED @7 42D6 4 H96? 6>F=2E:@? :D DEC@?8 @?G6CD6=J DEC@?8 6>F=2E:@? H:E9 AC676C6?46 7@C E96 =6DD 23=6 49:=5 >2E49 E96 C6DF=ED @7 H62< 6>F=2E:@? H:E9 AC676C6?46 .

(86) 8. 7. 6. t. 5. 4. 3. 2. 1. 0 0. 0.5. 1. 1.5. 2. x Boundary (c) Low y. Boundary (c) High y. . Boundary (c) Very High y. 2.5.

(87) 7@C E96 >@C6 23=6 49:=5 *9:D @3D6CG2E:@? 3C:?8D @FE 2 762EFC6 @7 E96 >@56=. E :D ?@E E96 23:=:E:6D :7 E96 49:=5 E92E 5C:G6 E96 C6DF=ED :E :D E96 A2C6?EDO AC676C6?46D 7@C H92E6G6C C62D@?. 6 6C6 . H:E9 2D 367@C6 ) . ) 2?5 . -6 2=D@ FD6 E96 ?@E2E:@? , - :? E9:D 42D6. ) ) ) ) ) *96 LCDE @C56C 4@?5:E:@? :D H:E9 2?5 96?46 . E =6E FD DFAA@D6 E92E H9:49 H@F=5 :>A=J . *9:D >62?D ) ) ) @C @C . - - )- ) ). 6G6=@A:?8 2?5 D:>A=:7J:?8 - - ) ) @C. , - @C , , . . . ) ) . ) ) . -96? , :D =2C86C E92? E96 7C24E:@? @7 , 56L?65 23@G6 E96 =62DE 72G@FC65 49:=5 H9@ :D 2=D@ E96 62D:6C @?6 E@ >@E:G2E6 :D D6E 2 9:896C 8@2= *92E 7C24E:@? @7 , :D =2C86C E96 =2C86C :D 2?5 E96 D>2==6C ) :D E92E :D E96 DEC@?86C 6>F=2E:@? :D 2?5 E96 =6DD 5:T6C6?46 E96C6 :D 36EH66? E96 D:3=:?8D -96? , :D D>2==6C E96 @C56C:?8 @7 8@2=D :D C6G6CD65. .

(88) 'FEE:?8 :E 2?@E96C H2J H96? A2C6?ED 72G@FC E96 >@C6 5:S4F=E 49:=5 2?5 6>F=2E:@? :D H62< E92E 49:=5 C646:G6D >@C6 4@249:?8 E9:D :D >@C6 =:<6=J E@ 92AA6? H96? 6>F=2E:@? :D DEC@?8 7. E96 C6DE :D 2D :? 6 ) ) ) 2?5 %@H 6C6 . -6 7@==@H 2 AC@465FC6 D:>:=2C E@ 42D6 6 E@ D9@H E92E . C6BF:C6D - - ) ) @C. , - . . ) ) . -96? , :D D>2==6C E92? E96 7C24E:@? @7 56L?65 23@G6 E96 >@DE 72G@FC65 49:=5 H9@ :D 2=D@ E96 62D:6C @?6 E@ >@E:G2E6 :D D6E 2 9:896C 8@2= *92E 7C24E:@? @7 :D =2C86C E96 D>2==6C 2?5 ) 2C6E92E :D E96 H62<6C 6>F=2E:@? :D 2?5 E96 =6DD 5:T6C6?46 E96C6 :D 36EH66? E96 D:3=:?8D -96? , :D =2C86C E96 @C56C:?8 @7 8@2=D :D C6G6CD65 H9:49 42? 2=D@ 36 DE2E65 2D -96? , :D =2C86C E92? 2 7C24E:@? @7 E96 =62DE 72G@FC65 49:=5 H9@ :D 2=D@ E96 92C56C @?6 E@ >@E:G2E6 :D D6E 2 9:896C 8@2= *9:D >2<6D :E 62D:6C E@ 4@>A2C6 H:E9 E96 C6DF=E @7 42D6 6 E96 7C24E:@? @7 E9@F89 ?@H 564C62D6D H:E9 .

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