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1

Define complete information games.

What are the two types? Define them.

Complete information games are where the player who turns it is to move knows at least as much as the last player who moved.

-Perfect information games: Players know the full history of the game and they know the moves made and the payoffs.

-imperfect information games: Players are unaware of the actions of others.

However, they do know who the other players are, their strategies and the payoffs of the other player.

2

Define incomplete information games.


Given two topic examples.

Players may not know about the information of the other players.

1) Bayesian Games
2) Principal-Agent relationships.

3

How do you find a bayesian-nash equilibrium?

it is the generalisation of the Nash equilibrium for incomplete information games.

1) turn the game from incomplete to imperfect information.
2) using an extra player 'nature' as a proxy for the state of the world for one player.
3) Then use the Nash concept to solve the game.

4

What are the probabilities associated with nature's move?

They are subjective probabilities.

They are subjective for the player that is facing the uncertainty of the other player's type.

5

In a bayes-nash game, how do you know which strategy the unpredictable player will play?

Because it is likely that they will have a dominant strategy in each game.

So then you can assign p to one state and 1-p to the other.

You then know what the payoff for the predictable player will be from the other state because the other player will play their dominant.

6

What is the assumption of common prior?

It is where the unpredictable player knows the estimate of p from the predictable player.

7

Explain the assumptions behind the extensive form game in Bayes-Nash

-Dean knows what type he is.
-James' nodes are connected, he doesn't know what game type is being played.
-Dean knows this about James.

8

Describe the concept behind auctions.

Describe the private value model and the pure common value model.

There is asymetric information in auctions

Each player's bid is a function of their own information.

Players will maximise their payoff given the strategies of others and their beliefs of the other player's information.


Private value model is where each bidder knows how much they value the item for sale.

Pure common value model is where bidders have different private information about the actual value. But the actual value is the same for everyone.

9

Explain the different types of auctions.

First price Sealed bid: The highest bid wins

Second price sealed bid: highest wins but pays second highest.

English: Price ascends for highest bidder

Dutch: Price falls until someone bids.

10

Explain moral hazard and principle agent

What is optimal for the agent may not be optimal for the principle. The principle is not on hand to monitor the other.

The principle needs to design a contract that incentives T to work in a way that benefits P.

P wants to maximise utility subject to contrasints about T's behaviour.

11

What are the two constraints in the principle-agent problem.

-Participation: T will only participate if he gets the reservation utility.

-Incentive Compatibility: T chooses the best contract out of all of P's offers.

12

What are the assumptions for a principal agent?

Ua=W(e)-e
U[=R(e)-w(e)
E=H,L

13

Write down the incentive compatibility constraint

Write down the participation constraint.


What about if the game has asymmetric information?

w(h)>w(l)+h-l

W(h)-h>0
or L

E(Uh)>E(UL)

E(Uh)>0

14

When is the Principle-Agent game a social optimum outcome?

What actually is the social optimum outcome?

It is where P & T are both risk neutral.

P offers, T accepts and puts forth H effort.

15

When will a risk adverse agent not accept an offer?

If the constraint depends on them acheiving some target revenue.

This is because a contract of this type will expose him to risk.

If P is risk neutral, he must insure risk adverse T against unlucky outcomes.

This leads to a loss of efficiency.

Therefore not the social optimum.

16

What is meant by a rational player?

A player who is aware of their own, payoffs,preferences and constraints w/r to their own actions.

They then will aim to get maximal payoff according to their own criteria.

17

What is strategic thinking?

It is where you take into account what the other player is thinking. You must also take into account that they are considering what you are thinking.

18

Draw out the first form of Prisoner's dilemma. What concept would you try to explain by using this game

You can show an IEDS solution by using this game. See notes for game and solution.

19

What is meant by a dominant strategy.
Just remember to use the opposite for a dominated strategy.

A strategy that is strictly or weakly preferred over all other strategies, regardless of the strategy choice of the other players.

20

Draw the game of the Battle of the Sexes, What is this game usual for illustrating?

See Notes for game. You can show that there are two Nash Equilibria in the game.

Note that there is no Dominant Strategy equilibria.

21

What is the name for strategies which survive IEDS? What is important to remember about them?

They are called rationalizable strategies. However, this is only if they are strictly dominant strategies.

22

Give an overview of the IEDS assumptions.

-Both players are rational.
-Player 1 knows that player 2 is rational.
-Player 2 knows that player 1 is rational.
-Player 1 knows that player 2 knows that player 1 is rational.
-visa versa.
-Player 1 knows that player 2 knows that player 1 knows that player 2 is rational.

For every extra elimination, there is an extra level of assumption.

It is called the layers of rationality

This means:
Each Player's strategy is consistent with their rationality.

They will maximise their payoff with conjectures to other player's strategies.

If i conjectures that j will play sj with a positive probability, sj will maximise j's payoff with respect to a conjecture made by j about other player's payoffs.

23

What is a Nash equilibrium?

A strategy combination is a nash equilibrium if each player's strategy is choice is a best response against the opponent's choice in that combination.

24

When is a strategy choice a best response?

A strategy choice is a best response if it yields the highest possible payoff against the opponent's choice.

25

Will a Nash always exist?

Yes, but sometimes it will only exist if it is in a mixed-strategy context.

26

What is the relationship between Nash Equilibria and Dominant Strategy Equilibria?

What is important about this?

Every DSE is a Nash but not all Nash are DSE.

This means when you are choosing between Nash you can simply discard the weakly dominated strategies.

27

How can you choose between Nash Equlibria?

-Preplay negotiate: make negotiations before you play

-Convention: If you have played the game before and have decided on a certain Nash, you are likely to reach that Nash again.

-Focal Point: If one nash equilibria gives a higher payoff as opposed to another then the higher payoff may achieve the necessary convergence of expectations.

28

What is the conjecture of players in the Bertrand-Nash game>

Each firm assumes that the other will act in a way to keep the price that they sell at fixed.

29

Derive bertrand solutions under
-homogenous goods
-differentiated goods

Draw the bertrand curve

see notes
hint: equal prices, half of the market.

See notes

30

How can you solve the reaction functions to find the Nash solution for bertrand and cournot>

What do Cournot set and what is the graph?

What do bertrand set and what is that graph?

Cournot:

Set quantity; Qa=QB

Graph hits both axis


Bertrand:
Set Price Pa=Pb

Graph is on one axis and then moves out.