Week 4

Question 1

What is the definition of a mixed Nash-equilibrium?

Answer 1

If for all i in N, and for all sigma.i in delta.i: U.i(sigma.i, sigma.-i) ≥ U.i(sigma.i, sigma.-i*)

Question 2

What are the critical assumptios of the Nash equilibrium?

Answer 2

1. Expected utility functions
2. Consistent preditions (i.e. all players make the same prediction)
3. Flawless utility maximization (no typing errors)

Question 3

What is level-k reasoning?

Answer 3

Way of thinking where you assume the that the opponent thinks k-1-levels deep

Question 4

What is the principle of insufficient reason?

Answer 4

If you know nothing apply uniform

Question 5

What is the definition of the Quantal Response Equilibrium?

Answer 5

For i in N, for all a.i in A.i: sigma.i(a.i) = QR(a.i, sigma.-i; lambda)

Question 6

What is Brouwer’s Fixed Point Theorem?

Answer 6

Let X (subset) R^m be a non-empty, compact, and convex set. Every continuous function f: X –> X admits a fixed point x* in X.