ECON 116A Lecture Notes - Lecture 2: Game Show Network, Nash Equilibrium, Strategic Dominance
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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 |
Consider the following game, which comes from James Andreoni and Hal Varian at the University of Michigan. A neutral referee runs the game.There are two players, Row and Column. The referee gives two cards to each:
2 and 7 to Row and 4 and 8 to Column. This is common knowledge. Then, playing simultaneously and independently, each player is · asked to hand over to the referee either his high card or his low card. The referee hands out payoffs- which come from a central kitty, not from the players' pockets- which come from a central kitty, not from the players' pockets-that are measured in dollars and depend on the cards that he collects. If row chooses his low card, 2, then row gets $2; if he choses his High card, 7 then Column gets $7. If column chooses his low card, 4, then column gets $4; if he chooses his high card, 8, then row gets $8.
(a) Show that the complete payoff table is as follows:
| Column | Column | ||
| low | high | ||
| row | Low | 2,4 | 10,0 |
| row | High | 0,11 | 8,7 |
(b) What is the Nash equilibrium? Verify that this game is a prisoners' dilemma.
Now suppose the game has the following stages. The referee hands
out cards as before; who gets what cards is common knowledge. At stage
I, each player, out of his own pocket, can hand . over a sum of money,
which the referee is to hold in an escrow account. This amount can be
zero 'out cannot 'oe negative. When both have made then Stage l choices,
these are publicly disclosed. Then at stage II, the two make their choices
of cards, again simultaneously and independently. The referee hands
out payoffs from the central kitty in the same way as in the single-stage
game before. In addition, he disposes of the escrow account as follows.
If Column chooses his high card, the referee hands over to Column the
sum that Row put into the account; if Column chooses his low card,
Row's sum reverts back to him. The disposition of the sum that Column
deposited depends similarly on Row's card choice. All these rules are
common knowledge.
(c) Find the rollback (subgame-perfect) equilibrium of this two-stage game.
Does it resolve the prisoners' dilemma? What is the role of the escrow account?
(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.
