Definition Best Response

definition admitted

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Lean declarations

def IsBestResponse EconCSLib @ cef01c7, EconCSLib.GameTheory.StrategicGame.BestResponse

def IsBestResponse (G : StrategicGame N U) (σ : G.Profile) (i : N) : Prop :=
  ∀ s' : G.strategy i, G.payoff (deviate σ i s') i ≤ G.payoff σ i

Modules: EconCSLib.GameTheory.StrategicGame.BestResponse

Best Response

A strategy $\sigma_i$ is a best response for player $i$ to the profile $\sigma$ if no unilateral deviation can improve $i$'s payoff:

$$\forall s'_i \in S_i, \quad u_i(\sigma[i \mapsto s'_i]) \le u_i(\sigma).$$

References

[MSZ, Chapter 2, Section 2.4] Maschler, Solan, and Zamir, Game Theory. Definition of best response.

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