compe&&on,)uncertain)mo&ves,)and) · pdf file(target+shim))...
TRANSCRIPT
![Page 1: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/1.jpg)
Compe&&on, Uncertain Mo&ves, and Strategic Communica&on
Jonathan Woon (University of Pi>sburgh) William Minozzi (Ohio State University)
![Page 2: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/2.jpg)
Lobbyists influencing legisla&on
Interest groups guiding agency rules
Li&gants seeking court rulings
Candidates vying for office
Elites persuading the masses
![Page 3: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/3.jpg)
![Page 4: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/4.jpg)
![Page 5: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/5.jpg)
How do experts cra. messages?
Do decision makers learn the truth?
![Page 6: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/6.jpg)
Nature draws Target and ShiMs Receiver: Target T ∈ [-‐100, 100] LeM Sender: ShiM SL ∈ [-‐50, 0] Right Sender: ShiM SR ∈ [0, 50]
![Page 7: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/7.jpg)
Senders observe T and privately observe own Si
Simultaneously send messages mL, mR ∈ [-‐150, 150]
![Page 8: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/8.jpg)
Senders observe T and privately observe own Si
Simultaneously send messages mL, mR ∈ [-‐150, 150]
![Page 9: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/9.jpg)
Receiver observes messages, chooses ac&on A ∈ [-‐150, 150]
Payoffs = 100 -‐ |A – (T + Si)|
![Page 10: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/10.jpg)
How would you play this game?
1. Nature chooses Targets and ShiMs 2. Senders both observe Target, but privately observe ShiMs,
then send Messages 3. Receivers observe both Messages (but not Targets or ShiMs)
and choose an Ac&on Payoffs decreasing in distance from Ac&on to own ideal point (Target + ShiM)
![Page 11: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/11.jpg)
Messages in babbling equilibria
Le. Sender Right Sender
![Page 12: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/12.jpg)
Messages in par&&on equilibria
Le. Sender Right Sender
![Page 13: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/13.jpg)
Messages in jamming equilibria
Le. Sender Right Sender
![Page 14: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/14.jpg)
Equilibrium predic&ons
• Mul&ple equilibria: Babbling, Par&&on, Jamming
• Any equilibrium depends on all players having mutually correct expecta&ons of other players’ strategies
• Messages convey only limited informa&on – Senders must be careful not to reveal too much – Receivers must commit to ignoring some informa&on – Equilibria vary in the ways in which senders limit their informa&on
• Predic=on: Messages and ac=ons will only be weakly correlated with targets
![Page 15: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/15.jpg)
Observed messages
-150
-100
-50
050
100
150
-100 -50 0 50 100 -100 -50 0 50 100
Left Sender Right SenderM
essa
ge
TargetGraphs by Type
![Page 16: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/16.jpg)
Ac&ons and Messages
-150
-100
-50
050
100
Actio
n
-150 -100 -50 0 50 100Midpoint between Senders' Messages
![Page 17: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/17.jpg)
Observed ac&ons
-100
-50
050
100
Action
-100 -50 0 50 100Target
![Page 18: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/18.jpg)
Limited strategic sophis&ca&on
• Instead of equilibrium, suppose subjects a>empt to reason about how to play best responses
• Conjecture that Receivers split the difference
• Form beliefs or expecta&ons about the other sender’s message (through iterated reasoning/level-‐K or experience)
![Page 19: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/19.jpg)
Limited strategic sophis&ca&on
T
mL = T -‐ E
T + SR
![Page 20: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/20.jpg)
Limited strategic sophis&ca&on
T T + SR
mR = T + 2SR + E mL = T -‐ E
![Page 21: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/21.jpg)
Limited strategic sophis&ca&on
T T + SR
mL = T -‐ E mR = T + 2SR + E
![Page 22: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/22.jpg)
Limited strategic sophis&ca&on
T T + SR
mL = T -‐ E mR = T + 2SR + E
![Page 23: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/23.jpg)
![Page 24: Compe&&on,)Uncertain)Mo&ves,)and) · PDF file(Target+ShiM)) Messages)in)babbling)equilibria) ... mustbe)careful)notto)reveal)too)much) – Receivers)mustcommitto)ignoring)some)](https://reader031.vdocuments.mx/reader031/viewer/2022020315/5aaa27327f8b9a9a188dd97b/html5/thumbnails/24.jpg)
Summary
• Equilibrium theory predicts behavior poorly
• Senders engage in exaggera&on consistent with limited strategic sophis&ca&on (but they also underexaggerate)
• Offseing exaggera&on by compe&ng Senders allows the Receiver to learn more about the Target than in any equilibrium