B(x)≠∅ isn’t equivalent to x being Nash.
Suppose Alice and Bob are playing prisoner’s dilemma. Then the best-response function of every option-profile is nonempty. But only one option-profile is nash.
x∈B(x) is equivalent to x being Nash.
B(x)≠∅ isn’t equivalent to x being Nash.
Suppose Alice and Bob are playing prisoner’s dilemma. Then the best-response function of every option-profile is nonempty. But only one option-profile is nash.
x∈B(x) is equivalent to x being Nash.