Mixed strategies

Question 1

What is a mixed strategy for a player i in a normal form game (S1, …, Sn ; u1, …, un)?

Hint: first, give the definition of “simplex” over a set A.

Question 2

When a strategy si belongs to the support of a mixed strategy σ*?

Question 3

Expected payoff of player i when he chooses the pure strategy si and his opponents play the mixed strategy σ−i.

Question 4

Expected payoff of player i when he chooses the mixed strategy σi and his opponents play the mixed strategy σ−i.

Question 5

When is a mixed strategy profile σ* = (σ1, …, σn) considered to be a Nash Equilibrium for each player i?

Question 6

If σ* is a NE, and both si and si’ are in the support of σi*, then what is a fundamental property of the utility functions of these two strategies?

Question 7

Do Nash Equilibriums survive IESDSm?

Question 8

Nash Theorem (intro)

Answer 8

Every game with finite Si’s has at least one Nash equilibrium (possibly involving mixed
strategies)

Question 9

What is a belief of a player i?

Question 10

The Nash theorem (definition)