(4) Bayes-Nash Equilibrium

Question 1

What is a perfect/ imperfect information game?

Answer 1

Perfect Information:

• I know perfectly where I am
• Player 2 knows the decision of Player 1

Imperfect Information:
- I don’t know where exactly I am

• Simultaneous move games are always imperfect
• Sequential move games can be perfect or imperfect

Question 2

What is a complete/ incomplete information game?

Answer 2

Complete Information:
- All players are fully informed about the structure of the game tree, including all actions, information sets and payoffs

Incomplete Information:

• Structure of the game tree is not fully known by everyone
• Nash Equilibrium cannot be applied
• “I don’t know the complete tree”

Question 3

What is the problem of an incomplete information game?

Answer 3

The Nash EQ in not applicable because the common knowledge assumption is violated.

Question 4

Harsanyi Transformation - Definition

Answer 4

• Turns an incomplete in an imperfect information game by assigning a probability to the type of a player
• Nature moves first and chooses the typ of the first player
• Solution Concept = Bayes Nash Equilibrium

Question 5

Bayes Nash Equilibrium

Answer 5

• Models limited information by adding nature to the game tree
• Nature’s moves resolve the uncertainty (specific probabilities that are common knowledge)
• Not all players can directly observe nature’s choices