LIT5: Carmichael, F. (2005). A Guide to Game Theory. Prentice Hall. Chapter 1 & 2

Question 1

What is strategic independence? (Carmichael) Game Theory

Answer 1

This is called strategic interdependence and such situations are commonly known as games of strategy

Question 1

What is Game Theory (Carmichael)

Answer 1

Game theory is a technique used to analyse situations where for two or more individuals (or institutions) the outcome of an action by one of them depends not only on the particular action taken by that individual but also on the actions taken by the other
(or others).

Question 2

What is the equilibrium in game theory? Carmichael

Answer 2

The equilibrium of a game describes the strategies that rational players are predicted
to choose when they interact.
If the players choose their equilibrium strategies they are doing the best they can given the other players’ choices.
And equilibrium strategy: a ‘best’ strategy for a player in that it gives the player his
or her highest pay-off given the strategy choices of all the players.

Question 3

What are Static and Simultaneous-move games?

Answer 3

Games in which players move at the same time or their moves are hidden are called simultaneous-move or
static games.

Games in which the players move in some kind of predetermined order are call sequential-move or
dynamic games

Question 4

What is a dominant strategy in Game Theory (carmichael)

Answer 4

A dominant strategy is a strategy that is a best response to all the possible
strategy choices of all the other players.

So a player will choose this strategy regardless of what the other player does.

Question 5

What are the two kinds of dominant strategies (Carmichael - Game Theory)

Answer 5

There are two kinds of dominant strategies:
1) Strongly dominant strategy: in a two-player game the pay-offs to a player from choosing a strongly dominant strategy are higher than those from choosing any other strategy in response to any strategy the other player chooses.

So the pay-off to the player from choosing that strategy is better than that from any other strategy in response to any strategy the other player picks.

2)
Weakly dominant strategy: in a two-player game the pay-offs to a player from choosing a weakly dominant strategy are (i) at least as high as those from choosing any other strategy in response to any strategy the other player chooses and (ii) higher than those from choosing any other strategy in response to at least one
strategy of the other player.

So the pay-off to the player from choosing that strategy is at least as good as any other strategy and better than some in response to whatever strategy the other player picks

Question 6

What is the
iterated-dominance equilibrium. (Carmichael-Game Theory)

Answer 6

A two-person game that doesn’t have a dominant-strategy equilibrium may have an iterated dominance equilibrium if one of the players has either a strongly or weakly dominant strategy

If one of the players in a two-player game has a dominant strategy then even if the other player doesn’t the game may still have an iterated-dominance equilibrium.

Question 7

What is the Nash Equilibrium?

Answer 7

In a Nash equilibrium the players in a game choose strategies that are best responses to each other.

Every dominant strategy and iterated-dominance equilibrium must also be a Nash equilibrium

But not every Nash equilibrium is also a dominant strategy equilibrium or even an iterated dominance equilibrium. Consequently there are games that have no dominant strategy or iterated-dominance equilibrium but do have a Nash equilibrium.

Question 8

How to identify a Nash Equilibrium (Carmichael - Game Theory)

Answer 8

The way we will do this here is by underlining the pay-offs corresponding to each player’s best response to each of the strategies of the other.

Let’s start by considering Pin’s position:
If Chip chooses lower price then Pin’s best response is to offer a free printer, so underline 4.
If Chip chooses free printer then Pin’s best response is to lower price, so underline 4 in the second column.
If Chip chooses to offer an extended guarantee then Pin’s best response is to also offer an extended guarantee, so underline Pin’s pay-off of 6 in the last row of the third column.

Now follow the same procedure for Chip’s best responses to Pin’s choices:
If Pin chooses lower price then Chip’s best response is also to lower price, so
underline 4 in the first cell of the top row.
If Pin offers a free printer then Chip’s best response is to also offer a free printer and so I have underlined Chip’s pay-off of 4 in the middle row of the second column.
If Pin offers the extended guarantee then Chip’s best response is to also offer the extended guarantee, so underline the second 6 in the last row of the third column.

The only cell with two underlinings is the third cell of the bottom row and so this is the Nash equilibrium