Term 1 Lecture 2

Question 1

Whats a game in extensive form?

Answer 1

A game in extensive-form captures information about the order of moves, which is ignored in the strategic-firm model of a game in the previous section

Question 2

Whats a game tree?

Answer 2

Diagram that describes the details of the sequence of decisions and actions players take when they play a game
- tree must have a unique initial node and a unique path from the initial node to every successor node

Question 3

Why is ‘Nature’ included?

Answer 3

We want to allow for the possibility that there is some randomness in the game, so we introduce nature with node name 0 into the game tree

Question 4

What is a pure strategy?

Answer 4

An instruction book for a player on how to play the game, must be complete and tell the player what to do at every point at which he/she makes a move
- even include apparently redundant instructions for when other players make mistakes

Question 5

Whats a mixed strategy?

Answer 5

A random choice of a pure strategy for player
- player 1 -> (p,q,r, 1-p-q-r) for example
- key feature is that the randomisation occurs before the game is played and they stick to it

Question 6

Whats a behavioural strategy?

Answer 6

When a player chooses probabilities for actions at each decision point
- key feature: randomisation happens at each decision node

Question 7

Games so far have what property about information

Answer 7

Everyone playing the game knows everything about past events in the game

Question 8

Whats an information set?

Answer 8

An information set is a collection of nodes with the property that, each node in the set has the same player’s name, each node in the set has the same actions available
- can be used to describe situations where a player’s past actions are hidden from others - like simultaneous
- IS can be used to describe situations where a player has private information
- IS can be used to describe situations where a player forgets what they knew previously

Question 9

Existence of IS changes the definition of pure strategies:

Answer 9

A pure strategy for an incomplete information extensive form game is just an instruction for every info set where it must make a move
- player cant distinguish between decision nodes, so player must choose the same action for all nodes in the same information set

Question 10

Backwards induction
- what it works for
- what it provides
- what it proves

Answer 10

• works for all finite, perfect info games and can be used to find credible NEs
• once we work through an extensive form game to find NE, have created pure strategy for every player in the game, called SPNE
• proves existence of NE in a finite perfect info game - called Zermelo’s theorem

Question 11

Not all NE are reasonable

Answer 11

Sometimes the given NE can be based on a non-credible threat
- so SPNE might be a better solution concept as players play optimally at every decision point