Biased Sender S knows realization of rv iased Sender S knows realization of rv Receiver R takes action a Informed R chooses a But S ideal is a For any realization that S reports R will believe true ID: 895735
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1 Comparative Cheap TalkArchishman Chakrab
Comparative Cheap TalkArchishman Chakrabortyand, forthcoming Biased Sender S knows realization of r.v. iased Sender
2 S knows realization of r.v. Receiver R
S knows realization of r.v. Receiver R takes action a Informed R chooses a = But S ideal is a = For any realizati
3 on that S reports, R will believe true
on that S reports, R will believe true So S must exaggerate even more and R compensates even moreSo communication b
4 reaks down and R just chooses a=E[S rec
reaks down and R just chooses a=E[S receives expected payoff of only receives expected payoff of only S]= -Var[Whi
5 ch is less than if S told truth! hich is
ch is less than if S told truth! hich is less than if S told truth! S]= -b Uncertainty over quality of a good -selle
6 r tells buyer its Uncertainty over pro
r tells buyer its Uncertainty over prospects for a stock analyst says its Uncertainty over whether a spending pr
7 ogram is worthwhile administrator says
ogram is worthwhile administrator says its essentialUncertainty over quality of a job applicant Good A is bette
8 r than BStock A is better than BPropos
r than BStock A is better than BProposal A is better than BStudent A is better than BComparative statements are p
9 ositive along one Cant exaggerate!But
ositive along one Cant exaggerate!But still might have an incentive to invert the ordering Professor (S) has N st
10 udents to recommend to employer Employe
udents to recommend to employer Employer hires a student if expected quality Professor wants a student to be hired
11 if CSequilibrium in one dimension if
if CSequilibrium in one dimension if (sorting condition), so any ordering is an equilibrium. Rankings become mo
12 re informative as number of issues incre
re informative as number of issues increases 1 0.75 0.5 0.25 0 10 7.5 5 2.5 0 N=3N=2Distribution of top-ranked issue
13 For given N, partition cheap talk outper
For given N, partition cheap talk outperforms ordinal cheap talkfor small For given b, ordinal cheap talk outperforms
14 partition cheap talkfor large As befor
partition cheap talkfor large As before let aj:Nbe Rs best action for issue ranked jfrom the bottom. And let a(kki
15 s known. For each q(0,1), by the Gliven
s known. For each q(0,1), by the Glivenko-CantelliTheorem= F¹(q) a.s.where F(k) is distribution of each kTherefore f
16 or i=S,R,limjkkSo in the limit as the nu
or i=S,R,limjkkSo in the limit as the number of issues increases, the sender reveals allinformation and sender and re
17 ceiver payoffs are equivalent E[N=2: E
ceiver payoffs are equivalent E[N=2: E[[È2:2]=2/3N=3: E[[È2:3]=2/4, E[È3:3]=3/4N=4: E[[È2:4]=2/5, E[È3:4]=3/
18 5, E[È4:4]=4/5N=5: E[[È2:5]=2/6, E[È
5, E[È4:4]=4/5N=5: E[[È2:5]=2/6, E[È3:5]=3/6, E[È4:5]=4/6, E[È5:5]=5/6Partial ordering:N=3: E[[È{2,3}:3N=4:
19 E[{1,2}:44È{3,4}:4]=7/10N=5: E[{1,2}:5
E[{1,2}:44È{3,4}:4]=7/10N=5: E[{1,2}:55È{3,4,5}:5 Interdependent actionsCan only hire one personMust buy goods
20 in bundleSender and receiver take actio
in bundleSender and receiver take actions, e.g. Private receiver information, e.g. auctionsNon-additive payoffsRe