compe&&on,)uncertain)mo&ves,)and) · pdf file(target+shim))...

Compe&&on,  Uncertain  Mo&ves,  and  Strategic  Communica&on  

Jonathan  Woon  (University  of  Pi>sburgh)  William  Minozzi  (Ohio  State  University)  

Lobbyists  influencing  legisla&on  

Interest  groups  guiding  agency  rules  

Li&gants  seeking  court  rulings  

Candidates  vying  for  office  

Elites  persuading  the  masses  

 How  do  experts  cra.  messages?  

Do  decision  makers  learn  the  truth?  

Nature  draws  Target  and  ShiMs      Receiver:  Target  T  ∈  [-­‐100,  100]      LeM  Sender:  ShiM  SL  ∈  [-­‐50,  0]      Right  Sender:  ShiM  SR  ∈  [0,  50]  

Senders  observe  T  and  privately  observe  own  Si    

Simultaneously  send  messages  mL,  mR  ∈  [-­‐150,  150]  

Senders  observe  T  and  privately  observe  own  Si    

Simultaneously  send  messages  mL,  mR  ∈  [-­‐150,  150]  

Receiver  observes  messages,  chooses  ac&on  A  ∈  [-­‐150,  150]    

Payoffs  =  100  -­‐  |A  –  (T  +  Si)|      

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)  

Messages  in  babbling  equilibria  

Le.  Sender   Right  Sender  

Messages  in  par&&on  equilibria  

Le.  Sender   Right  Sender  

Messages  in  jamming  equilibria  

Le.  Sender   Right  Sender  

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  

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

Ac&ons  and  Messages  

-150

-100

-50

050

100

Actio

n

-150 -100 -50 0 50 100Midpoint between Senders' Messages

Observed  ac&ons  

-100

-50

050

100

Action

-100 -50 0 50 100Target

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)  

Limited  strategic  sophis&ca&on  

T  

mL  =  T  -­‐  E  

T  +  SR  

Limited  strategic  sophis&ca&on  

T   T  +  SR  

mR    =  T  +  2SR  +  E  mL  =  T  -­‐  E  

Limited  strategic  sophis&ca&on  

T   T  +  SR  

mL  =  T  -­‐  E   mR    =  T  +  2SR  +  E  

Limited  strategic  sophis&ca&on  

T   T  +  SR  

mL  =  T  -­‐  E   mR    =  T  +  2SR  +  E  

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