5.1 This problem makes clear the connection between a pair of numbers (, ) that maximizes both payoff functions and a Nash equilibrium. Suppose that we have a two-person game with payoff functions ui(q1, q2), i = 1, 2. Suppose there is a pure strategy pair (, ) that maximizes both u1 and u2 as functions of the pair (q1, q2).
(a) Verify that (, ) is a Nash equilibrium.
5.1.a Answer: Since (, ) maximizes both u1 and u2, we have
for every , . Thus, (, ) automatically satisfies the definition ...