GraduateGameTheoryLecture-SignalingGames - Game Theory...

Game Theory Lecture 7
Signaling Games
Prof. John Patty
1

Classical Signaling Games:
● Sender: knows Receiver’s preferences state of nature ω , chooses
message , m
● Receiver: knows Sender’s preferences, distribution of ω
Observes message,
Infers state of nature,
Chooses action, x .
Set of players: N = { S,R }
2

Ω : set of state of nature
F : distribution function governing ω M : set of messages ( M ≥ Ω )
X : set of receiver’s actions
Payoff function for i ∈ { S,R } :
u
i
∶ Ω × M × X →
R
3

Equilibrium Analysis of Signaling Games
● m
*
∶ Ω → Δ ( M ) : equilibrium strategy of sender
● x
*
∶ M → Δ ( X ) : equilibrium strategy of receiver
● μ
*
∶ M → Δ ( Ω ) : equilibrium beliefs of receiver
1st Key Equilibrium Condition: Incentive Compatibility :
● For each ω ∈ Ω ,
u
S
( ω,m
*
( ω ) ,x
*
( m
*
( ω )) ≥ u
S
( ω,m
′
,x
*
( m
′
)
4

Equilibrium Analysis of Signaling Games
● m
*
∶ Ω → Δ ( M ) : equilibrium strategy of sender
● x
*
∶ M → Δ ( X ) : equilibrium strategy of receiver
● μ
*
∶ M → Δ ( Ω ) : equilibrium beliefs of receiver