Nash Equilibrium과 Best Responce의 관계

Nash Equilibrium

=NE

 

If the game and players' rationality are common knowledge & each player's belief θ₋ᵢ is commonly known and correct,

the players are in Nash Equilibrium.

 

There can be no NE in pure strategies (such as Matching Pennies)

so we should look for the mixed strategies.

 

Pure strategy NE is not always unique: there may be several or none.

NE reflects a situation of mutually consistent beliefs among rational players; it does not prescribe where these beliefs should come from. (내쉬 균형은 합리적 참가자들 사이에서 상호 일관된 신념의 상황을 반영한다. 이러한 믿음(belief)은 어디서 왔는지 규정되는 것은 아니다.)

 

 

Best Responce=BR

 

내쉬균형 그리고 최적대응:(s₁*, s₂*)가 NE일 때, s₁* ∈ BR₁(s₂*)이고

s₂* ∈ BR₂(s₁*)이다.