Test 1 Definitions

Question 1

What is Game Theory?

Answer 1

Game Theory is the analysis of interaction among rational agents who behave in a strategic manner.

Question 2

What is meant by a rational player?

Answer 2

A rational player is one who is aware of their own; objectives, preferences, limitations and contraints on their own decisions. They will choose the best that they possibly can based on that criteria.

Question 3

If a game is asking for IEDs or to see if it is Dominance Solveable, what should you do?

Answer 3

You should remove all WEAKLY or STRONGLY dominated strategies.

Question 4

What is a weakly dominated strategy?

Answer 4

A weakly dominated strategy is one where it is dominated by a strategy that has a pay off that is at least as high as it.

Question 5

Should you include strategies in rationalizeable strategies if you have remove strategies that were only weakly dominated through IEDs?

Answer 5

No, because rationalizeable strategy sets should only include sets of strategies that result from a game where there has been a strong dominance elimination.

Question 6

What must a player do when they think strategically?

Answer 6

They must keep in mind the choices of the other player.

Question 7

What does simultaneous choice mean for each player?

Answer 7

It means that each player will make their choice without any idea of the choice of the other player.

Question 8

What are the payoffs for the prisoner’s dilemma game>

Answer 8

CC=-5,-5 DC,C=-6,0 and visa versa and DCDC= -1,-1.

Question 9

What is a dominant strategy?

Answer 9

A dominant strategy is any strategy that is always strictly or weakly better than every other strategy, regardless of the choices made by the other player.

Question 10

What is a dominated strategy?

Answer 10

It is a strategy that is always strictly or weakly worse than other strategies, regardless of the strategy choices of the other players.

Question 11

How many Nash are there in the Battle of the Sexes game? Which one is the most feasible?

Is the Battle of the Sexes game dominance solvable?

Answer 11

There are two Nash Equilibria in the game but no focal point. It would rely on historical information to improve the chances of the man and the women to converge on one point. So the feasibility information is not inside the game.

It is not, unless you remove dominated strategies at the same time, which is not common practice.

Question 12

When is a strategy rationalizable?

Answer 12

A strategy will be rationalizable when each player’s strategy is consistent with rationality conditions.
i.e: They will maximise their payoff with respect to a conjecture about the other player’s strategy.

Question 13

What do you need to assume when removing strategies in an IEDs game?

Answer 13

You know that Player 1 knows that player 2 kows player 1 will not play a certain strategy because that strategy is dominated. Player 1 knows that player 2 knows this and knows that player 2 will not play some strategies because of this fact. Player 2 knows that player 1 knows.

This assumes perfect information.

COMMON KNOWLEDGE ASSUMPTION:

Basically; Assume that all players are Rational and that all players know that all players are rational. Continued on and on. (Ad Infinitium)

Question 14

What is true about the existence and uniqueness of DSEs?

Answer 14

They don’t always exist, but when they do, they are always a unique equilibrium.

However a weakly dominated solved game will not always produce a unique outcome.

Question 15

What is the relationship between NE and DSE.

Answer 15

A DSE is always an NE but and NE is not always a DSE.

Question 16

What is a Nash Equilibrium?

Answer 16

A Nash equilibrium is where each player’s strategy choice is a best response to the other player’s choice of strategy.

Essentially you choose something which will maximise your utility with respect to the choice made by your opponent.

Question 17

What is a best response strategy?

Answer 17

A strategy choice that yields the highest possible payoff that the player can achieve against that choice.

Question 18

Will a Nash always exist?

Answer 18

With a finite number of players and a finite number of strategies, a Nash Equilibrium will exist. Do note that this may have to include mixed strategies.

Question 19

How do you choose the most likely among a multiple number of Nash Equilibria?

Answer 19

There are three ways to choose;

• ‘Cheap-Talk’: Is where the players will conduct negotiations prior to the play of the game. As a result of these negotiations they will converge on one of the Nash Equilibria.
• Convention; This is where they choose to an equilibrium tied to historical conventions. They do what they have always done and get what they always got. They may know another piece of information which will cause them to converge on this point.

Remember to mention in the writing that the Game setting is not able to convey this information.

• ‘Focal Point’; This is where one of the Nash Equilibria’s will offer the players a higher payoff than the others. Therefore they will converge on this point.

Basically, when choosing between Nash, choose the one which weakly dominates the others.

Question 20

What is a Focal Point?

Answer 20

A focal point is a point where players will converge their expectations to. When they have a common understanding of the game.

Question 21

What is the difference between Bertrand and Cournot competition?

Answer 21

Bertand Companies will focus on the setting the price. So you need to derive with respect to the price and solve for price.

Cournot looks at the quantity setting aspect of the business, so diff with respect to quantity.