( ) H α iff α Pure and Impure Altruism C H,H S,T. Find the utility payoff matrix of PD if subjects all have utility u C D
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1 .8. Pure ad pure Altrus u x x x, ~ u P Altrus H,H S,T T,S L,L T H L S Fd the utlty payoff atrx of P f subects all have utlty u Altrus. (sol,, (, H ( T H S T, T S S, S T L (, L( Whe wll (, stll be the oly Nash equlbru? Whe wll (, be NE? (sol (, s NE ff ( S ( L T L ff (, s NE ff ( T ( H S H ff L S T L K T H H S K f K K : (, s NE K K (, s NE f K K : (, s NE K K (, s NE f K K : (, s NE (, s NE (, s uque Nash Eq. ff < { K K }. How uch Altrus expla corporato o [(, ] P? (sol f K, we ay susta (, as NE. K K, we ay susta (, ad (, as NE. f K K,
2 a u Altrus expla reecto ultatu aes? (sol Gve a offer ( a, a, u ( reect u ( accept a ( a r a a. Ths reures <, whch cotradcts the assupto a a ot spteful. that people are altrustc ( [Hoewor] a expla publc oods cotrbuto?.8. Gult-Equalty [Fehr ad Schdt (999] u ( x x ax ( x x, ax ( x x, ~ u, ( 不好意思 Fd the P's utlty payoff atrx?,where FS r (sol H, H S ( S T, T ( T S T ( T S, S ( S T S L, L Whe wll (, stll be NE? Whe wll (, be NE? (sol (, s NE ff ( L S ( S T L S ff K (ot evy eouh T S (, s NE ff ( H T ( T S T H ff K (fell bad eouh about ett too uch T S How ay equalty Averso expla corporato P? (sol As lo as people feel 不好意思 for ett too uch ( K sustaed. a u FS expla reecto ultatu aes? (sol Gve a offer ( a, a a 5,,where,(, s
3 u reect u accept a a a r r a or a a # a f a 5, eed a ( a possble a a 5 a u FS expla far offers proposed ultatu aes?,f a < 5 (sol Gve, belef s up ( a, a ( a P ( a,f a 5 ( a P ( a,f a 5 P P, wo't offer a 5; ( a P ( a, wo't pc a < ( Pc to ax P a P f P, Pc larest a 5 (f you feel ulty for ett too uch, propose 5-5 f, Pc sallest (Squeeze out as uch as possble, but P < a ( ε stll accept..8. Fehr & Schdt(999[otued] 6 a u FS also expla cotrbuto publc oods aes? (Sol Player cotrbuto [, y], G {,, } Ears x ( G y, where <
4 A th player s free rde ff for ve assue Wolo,, ax, ax, ax, ax, y y u G u [ ] free - rd always. supports the, f B Show that f th players free rde,, the everyoe free rdes. (Sol Assue, for soe. The cosder, [ ] <. By atheatc ducto,. Show people have < (free rde, others have & wll codto [ ] y, s a equlbru. (Sol Assue, osder, ( trval by A,
5 ( ( ( ( ( sce #.8. Other (Hoewor. Show that G-E (Fehr-Schdt 99' predcts, uder proposer copetto: ( Proposers offer alost everyth to espoder (depedet of # of proposers Uder espoder copetto, we have: ( espoders accept ay offer; Proposer offers ff P < hhest equato offer s as,, { } x. E: u ( x u x,. Show that x ( Offer betwee ad 5% dctator ae ( How ca G-E (F-S et ths cocavty? ( Ultatu: eect always. Never reect 5-5. eecto rate as % ad as pe sze (fx % Offer <5%, ctator results. ( players ultatu-dctator cobo: Allocato to the actve ecpet s ored (5 What's E's predcto for P ad PG?. osder PG wth pushet: After cotrbuto, aouces G Player ca push oe ut wth a pushet P at cost c<. ( Stadard Gae Theory predcts P. ad suffcetly ( f are suffcetly ulty ( * evos: c( ( c( ( eq. wth.8. ab (99: Faress Equlbru Two Players: & Stratey: a b th belef about other s stratey : ( b th belef about other s belef : c far π Kdess (of toward : ( b, a π ( b f a, b, π ax ( b π ( b π ( b possble
6 ax π π payoffs of ve b (belef about s acto equtable(ex: exclud Pareto doated f :d; f < :ea Perceved dess (of what th about s dess to her: far ~ π ( c, b π ( c f b, c ax π ( c π ( c Socal Utlty fucto(for ~ ~ u ( a, b, c π ( a, b f ( b, c f ( b, c f( a, b Eq. requres a b c ( a b c, a b c P, ε, 6 ¾, ¾ -½, 6 6, ε, 6, -½, f ε ax ax π, π ε, π, far ε far π (, π (, π ( 6( s excluded ε ε f (,, fɶ (,, ε ε ε u (,, ε ε ( ε 6 f (,, fɶ (,, u (,, u (,, 6 ε ε 6 6 (,, (, ε f fɶ, 6 ε ε ε ( ε u (,, ε u (,, ε ε ε ε ε 6 6 f,, fɶ,, u,, 6 u,, ε ε 6
7 8 * (, s a Faress Eq. f 6 (For ε, (, s F.E. f 6 ( ε ( ε.8. ab (99:F. E. (otued hce -, -, -, -, -½,, -½, ¾, ¾ ax ax far far π (, π (, π (, π (, π (, π ( f (,, fɶ (,, u u f (,, fɶ (,, (,, (,, (,, ( ( (,, u u f (, fɶ (,, fɶ (, f (,, u u u u (,, (,, (,, (,,. (, s F. E. f (. (, s F. E. f. (, s F. E. f (So s (,.8. Extesve For Faress Equlbru: Fal & Fschbcher(998 (TBA s stratey s belef about s choce: s belef about s belef about s choce: s
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