Chapter 13 - Game Theory

Question 1

What is a game?

Answer 1

A game is any situation in which PLAYERS make strategic decisions.

A strategic decision is one that take the opponent into account

Question 1

What is “payoffs” to the players

Answer 1

We say that strategic decisions results in payoffs to the players. Outcomes that generate rewards or benefits.

Question 2

What is a strategy?

Answer 2

A strategy is a rule or a plan of action for playing the game.

Question 3

What is the “optimal strategy”?

Answer 3

optimal strategy is the one that results in maximized expected payoff.

Question 4

Any assumption regarding game theory?

Answer 4

Rational players who try to maximize profits

Question 5

Name the types of broad general different games firms can play

Answer 5

Cooperate and non cooperative. The distinction lies in ability to contract the coop.

Question 6

What is a dominant strategy?

Answer 6

A dominant strategy is one that is optimal no matter what the opponent does.

Question 7

What can we do to show the outcomes of different choices for 2 firms?

Answer 7

Create a payoff matrix

Question 8

Can both players in a game have the dominant strategy?

Answer 8

Yes. Dominant strategy is only about being best in all cases, not necessarily being better than the competitor.

Question 9

When every player has a dominant strategy, what do we call it?

Answer 9

We call the outcome of the game an “equilibrium” in dominant strategies.

Question 10

elaborate on “placing ourselves in the position of our competitor”

Answer 10

We have to consider if the opponent has a dominant strategy. if he has, then we know that the player will follow it. For instance, the dominant strategy could be to advertise no matter what. therefore, we know that our opponent will adervertise, and thus can respond to this.

Question 11

If we are in a dominant stategy equilibrium, are we in a Nash equilibrium?

Answer 11

Yes, but they are not the same.

Dominant strategy equilibrium means that “I am doing the best regardless of what you are doing” and “You are doing the best you can regardless of what I am doing”.

Nash is “I am doing the best I can GIVEN what you are doing” and “You are doing the best you can GIVEN what I am doing”.

Question 12

Can you always achieve nash equilibrium?

Answer 12

No

Question 13

Name a consequence of the Nash equilibrium

Answer 13

No player will deviate from the current position

Question 14

Is nash equilibrium the most profitable?

Answer 14

No

Question 15

What is “maximin strategy”?

Answer 15

Maximizing the minimum gain that can be earned. For the cautious firm.

Question 16

If you are unsure about what the opponent will do, but can assign probabilties to the possible choices, what kind of strategy are we then doing?

Answer 16

Maximizing expected payoff using expected value.

Question 17

In the prisoners dilemma, is there any dominant strategies?

Answer 17

Confessing happens to be a dominant strategy for both prisoners (firms).

Question 18

Are dominant strategies connected to maximin strategies?

Answer 18

Yes, dominant strategies are also maximin strategies.

Question 19

What is a “pure strategy”?

Answer 19

A pure strategy refers to a game where players makes a specific choice or takes a specific action. For instance, advertise or dont advertise.

Question 20

What is a tit for tat strategy?

Answer 20

tit for tat is a repeated game strategy in which a player responds to an opponents play by equalling it. If the opponent increase price, we increase price. If he lower price, we lower price.

this strategy create cooperation if the opponent is cooperative and it retaliates against uncooperative opps.

Question 21

If we consider a game of finite amount of periods, how will we treat it?

Answer 21

We will not undercut until the last period. At the last period, we undercut as it will increase our profits. The reason we wait until the last period, is that the opponent will not have a change of undercutting back. However, the opponent knows this, and will do the same. Therefore, we start considering the second to last period. Given that there will be no cooperation in the last period, we might attempt to undercut the second to last period.
This cause a ripple effect through to the first period, which results in the rational decision of charging low prices every month.

However, in practice, we usually dont know the amount of periods.

Question 22

What is a strategic decision?

Answer 22

A strategic decision is a decision that take the opponent views and actions into account.

Question 23

According to lecture, what is a game?

Answer 23

a game is a situation where payoff for players depend on each others decisions

Question 24

Accoridng to lecture, what is a strategy?

Answer 24

A strategy is a plan detailing action in each posible contingency

Question 25

What is a nash equilibrium?

Answer 25

A strategy combination constitutes a nash equilibrium iff NO PLAYER regrets the choice of strategy given the strategy choices of all other players. In nash equilibrium each player maximize own payoff given the other players’ sstrategy choices.

Question 26

If we say “equilibrium in dominant strategies” what does this mean?

Answer 26

It means that both competitors are following a dominant strategy, and the outcome is the equilibrium.

Since a dominant strategy equilibrium is like this: “I am doing the best I can regardless of what you do, and you are doing the best you can regardless of what I do” we easily see that dominant strategy equilibrium is a special case of nash equibrlium.

Question 27

Can we have multiple nash equilibria?

Answer 27

YES. Nash equilibrium only refers to a state where both competitors are doing the best they can given what the other is doing. Thus, no one has any incentive to change.

Question 28

What is “normal form”?

Answer 28

Normal form refers to the game matrix that show different combinations of strategeis/choices and results.

Question 29

What are dynamic games?

Answer 29

Dynamic games are games where players make decisions after having observed decisions of other players

typically represented by a game tree, not a game matrix, as there is no longer just a single choice.

Question 30

What is a pure strategy?

Answer 30

A pure strategy is a strategy where a player makes a specific choice without any randomness from among all avaiable options.

in contrast with mixed strategies, that use a random choice based on a set of probabilities.

Question 31

What is sequential games?

Answer 31

Sequantial games are games where each player move in turns, responding to each others actions.

Question 32

How is a game tree structured?

Answer 32

Nodes represent players. Edges represent actions.

Game trees are used in sequential games, typically between 2 players. Each player will take turns. First player 1, then player 2 etc…

At each player node, we create children for each possible action that the player can take.

At the leaf nodes, we indicate the payoff per player.

The game tree aims to capture all possible game states.

Question 33

What is a subgame?

Answer 33

A subgame is a part of a game that meets some criteria:

1) Singleton root
2) All successors to nodes in the subgame must also be in subgame

Question 34

Elaborate on subgame perfect equilibrium (SPE)

Answer 34

The case there every future state of the game will be a nash equilibrium.