ECON 1108 Lecture Notes - Lecture 5: Nash Equilibrium, Renting, Extensive-Form Game

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limeimpala505

6 Mar 2019

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Any finite strategy game has a nash equilibrium. If there is no pure strategy, then it is a mixed strategy equilibrium. The arrows point to whichever strategy player 1 or 2 should use. To show a strategy is nash you have to show the payoffs for all players in that strategy. To show a strategy isn"t nash you only need to show one payoff that is higher for one player. When a strategy has to be a complete plan of action that just means you have to pick one. But strategy becomes more complicated when its no longer simultaneous play. First thing we want to do is take a game of perfect information. An entrant firm wishes to enter movie rental business. There is one incumbent firm in the market. I makes threat if you enter i will increase my advertising budget, lower my prices, and smash you . Incumbent on its own is a monopoly, doesn"t want to share.

Related Questions

The correct statements are [mark all that apply]:

A. The concept of best response strategy played in equilibrium by all players and no unilateral deviation are applicable for Bayesian games.

B. A game, where there are one firm 1 and two types of firms 2 (strong or weak) but firm 1 knows that firm 2 is strong with probability 0.7, can be described as a game of incomplete information.

C. A Bayesian Nash equilibrium is totally different from a Nash equilibrium in Bayesian games.

D. To be uncertain about others players' payoff functions is equivalent to saying that player 1 may be uncertain about the types of the other players.

QUESTION 1

Stackelberg duopoly game is also known as the ________ model. If we change the Stackelberg ______ competition game to a simultaneous-move game, we get the ______ game results.

	A.	leader-follower, quantity; Cournot
	B.	Competitive fringe; price; backward induction
	C.	leader-follower, quantity; Bertrand
	D.	entry, price; Cournot

QUESTION 2

Comparing Stackelberg and Cournot competition results, we can say that the _____ is better off while the ______ is worse off under Stackelberg than under Cournot results. This result show that there is _______________ advantage.

	A.	entrant, incumbent, investment
	B.	leader, follower, first-mover
	C.	follower, leader, a size
	D.	incumbent, entrant, first-mover

QUESTION 3

Mark all the FALSE statements

	A.	An equilibrium is a collection of strategies (and a strategy is a complete plan of action), whereas an outcome describes what will happen only in the contingencies that are expected to arise, not in every contingency that might arise.
	B.	In games of complete but imperfect information, backward induction is still the strongest process to solve the model to get unique equilibrium.
	C.	All subgame perfect Nash equilibria (SPNE) are Nash equilibria (NE), but not all Nash equilibria is SPNE
	D.	We cannot apply the notion of Nash equilibrium to dynamic games of complete information if we allowed a player s strategy to leave unspecified actions in some contingencies.
	E.	A game can be of perfect information whenever Nature or Luck does not play, each information set does not necessarily need to have a single node.

QUESTION 4

True or false. Mark the correct sequence:
I. Simultaneity of moves means that these games have imperfect information.
II. Dynamic games of complete and perfect information do not necessarily need that a player observes all the previous moves, just part of them are fine.
III. Backward induction and subgame perfect equilibrium concept lead to the same result in games of incomplete information.
IV. Any game in extensive form is a subgame itself.

	A.	TFFT
	B.	TTTF
	C.	FTFF
	D.	TTFT

QUESTION 5

The subgame perfect Nash equilibrium is the equilibrium associated with ____________ outcome. Subgame perfect equilibrium ________ non-credible threats.

	A.	Maxmin; involves
	B.	the backward induction; does not involve
	C.	Iterative deletion of weakly dominated strategies; rules out
	D.	the backward induction; includes

(Please show as much work as possible)

1. You are bidding in a second-price auction for a painting that you value at $800. You estimate that other bidders are most likely to value the painting at between $200 and $600. Which of these is likely to be your best bid?

a. $1,000

b. $800

c. $600

d. $400

2. Which of the following is true about different ways of conducting a private-value auction?

a. A first-price auction is strategically equivalent to a second-price auction.

b. A first-price auction is strategically equivalent to an English auction.

c. A second-price auction is strategically equivalent to an English auction.

d. None of the above

3. Suppose that five bidders with values of $500, $400, $300, $200, and $100 attend an oral auction. Which of these is closest to the winning price?

a. $500

b. $400

c. $300

d. $200

4. In the above auction, if the bidders with the first- and third-highest values ($500 and

$300) collude, which of these is closest to the winning price?

a. $500

b. $400

c. $300

d. $200

5. If a seller is concerned about collusion among bidders, which of the following changes to the auction, should the seller make?

a. Hold frequent, small auctions instead of infrequent large auctions.

b. Conceal the amount of winning bids.

c. Publically announce the name of each auction's winner.

d. Hold a second-price instead of a first-price auction.

6. You're holding an auction to license a new technology that your company has developed. One of your assistants raises a concern that bidders' fear of the winner's curse may encourage them to shade their bids. How might you address this concern?

a. Release your analyst's positive scenario for the technology's future profitability.

b. Release your analyst's negative scenario for the technology's future profitability.

c. Use an oral auction.

d. All of the above

7. In a first-price auction, you bid ________ your value, and in a second-price auction you bid _________ your value.

a. at; above

b. below; above

c. below; at

d. below; below

8. You hold an auction among three bidders. You estimate that each bidder has a value of either $16 or $20 for the item, and you attach probabilities to each value of 50%. What is the expected price? If two of the three bidders collude, what is the price?

9. In Sweden, firms that fail to meet their debt obligations are immediately auctioned off to the highest bidder. (There is no reorganization through Chapter 11 bankruptcy.) The current managers are often high bidders for the company. Why?

10. When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, representatives of other museums that have no chance of winning are actively wooed by the auctioneer to attend anyway. Why?

11. The deities Mars and Venus often do battle to create the weather conditions on Earth. Venus prefers extreme temperatures (especially heat), while Mars prefers temperate conditions. The payoffs (expressed in Points of Wrath) are given below.

		Venus
		Warm	Chill
Mars	Warm	20 , 0	0 , 10
Chill	0 , 90	20 , 0

What is the unique mixed-strategy equilibrium of the above game?

(Let p be the probability of "Warm" for Mars, and q the probability of "Warm" for Venus.)

a) p=9/10, q=1/2

b) p=1/2, q=1/10

c) p=1/2, q=1/2

d) p=1/10, q=1/10

Player 2

		H	D
Player 1	H	0 , 0	4 , 1
D	1 , 4	2 , 2

12. The above game is the title of the hawk-dove game and used by evolutionary biologists to describe evolutionary processes. It is also used to model how a business should grow. In the above game, what is the Nash equilibrium in pure strategies and mixed strategies.?

Assume the cost of producing the goods is zero and that each consumer will purchase each good as long as the price is less than or equal to value. Consumer values are the entries in the table.

	Good 1	Good 2
Consumer A	$2,300	$1,700
Consumer B	$2,800	$1,200

13. Suppose the monopolist only sold the goods separately. What price will the monopolist charge for good 1 to maximize revenues for good 1?

a. $2,300

b. $2,800

c. $1,200

d. $1,700

14. What is the total profit to the monopolist from selling the goods separately?

a. $4,500

b. $6,300

c. $7,000

d. $6,000

15. What is a better pricing strategy for the monopolist? At this price, what are the total profits to the monopolist?

a. Bundle the goods at $2,800; Profits = $5,600

b. Bundle the goods at $4,000; Profits = $8,000

c. Charge $2,800 for good 1 and charge $1,700 for good 2; Profits = $4,500

d. Charging the lowest price for each good individually is the best pricing strategy; Profits = $7,000

16. The prisoners' dilemma is an example of

a. a sequential game.

b. a simultaneous game.

c.a shirking game.

d. a dating game

17. Nash equilibrium

a. is where one player maximizes his payoff, and the other doesn't.

b. is where each player maximizes his own payoff given the action of the other player.

c.is where both players are maximizing their total payoff.

d. is a unique prediction of the likely outcome of a game.

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ECON 1108 Lecture Notes - Lecture 5: Nash Equilibrium, Renting, Extensive-Form Game

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