Question

Suppose that we have the following auction scheme. There are two bidders, and an item to be allocated to them. Each bidder submits a bid. The highest bidder gets the good, but both bidders pay their bids. Consider the case in which bidder 1 values the item at 3, while bidder 2 values the item at 5; this is commonly known. Each bidder can only submit one of three bids: 0, 1 or 2. If player i bids more than player j, player i gets the good and both pay. If both players bid the same amount, each gets the item with probability 0.5, but again, both pay. (a) Write down the game in matrix form. Which strategies survive IESDS? (b) Find the NE of the game.

Answer #1

a.Both Player i and Player j should use strictly dominating strategy to Survive IESDS.

b.If two players i and j choose strategies A and B, (A, B) is a Nash equilibrium if i has no other strategy available that does better than A at maximizing her payoff in response to j choosing B, and j has no other strategy available that does better than B at maximizing his payoff in response to i choosing A.

Consider a first-price sealed-bid auction as the one analyzed in
class. Suppose bidders' valuations are v1=10 and v2=10. Suppose
bidder 2 submits a bid b2=10. Then, in a Nash equilibrium in pure
strategies bidder 1 must be submitting a bid equal to __ . In this
Nash equilibrium, bidder 1's payoff is equal to __ (please, enter
numerical values only, for example: 4).

Consider an auction where n identical objects are offered, and
there are {n + 1) bidders. The actual value of an object is the
same for all bidders and equal for all objects, but each bidder
gets only an independent estimate, subject to error, of this common
value. The bidders submit sealed bids. The top n bidders get one
object each, and each pays the next highest bid. What
considerations will affect your bidding strategy? How?

In the following auction:
• There are three bidders, and there are two identical items for
sale.
• Reservation prices are drawn independently from a uniform
distribution on [0, 1].
• The high and middle bidders each get one of the items and pay
their own bids. The low bidder pays nothing.
Suppose your opponent (who is not very strategic) makes the
mistake of using the strategy “bid half your reservation price”.
What is your optimal strategy against him? What...

Consider an auction where n identical objects are offered and
there are n+ 1 bidders. The true value of each object is the same
for all bidders and for all objects but each bidder gets only an
independent unbiased estimate of this common value. Bidders submit
sealed bids and the top n bidders get one object each and each pays
her own bid. Suppose you lose. What conclusion might you draw from
losing? How will this affect your bidding strategy?...

Consider 45 risk-neutral bidders who are participating in a
second-price, sealed-bid auction. It is commonly known that bidders
have independent private values. Based on this information, we know
the optimal bidding strategy for each bidder is to:
A. bid their own valuation of the item.
B. shade their bid to just below their own
valuation.
C. bid according to the following bid function: b
= v − (v −
L)/n.
D. bid one penny above their own valuation to ensure...

There are two bidders bidding for one object. Each one’s value
of the object is his private information and independent of the
other’s, with their values at v1=500 and v2=600. They
simultaneously submit their bids b1 and b2. The one with the higher
bid wins the auction but pays the loser’s bid (the second highest
price). If b2=500, should bidder 1 try to win or lose? and how much
should bidder 1 bid?

Professor Nash announces that he will auction off a $20 bill in
a competition between two students, Jack and Jill at the beginning
of their game theory lecture. Each student is to privately submit a
bid on a piece of paper; whoever places the highest bid wins the
$20 bill. In case of a tie, each student gets $10. Each student
must pay whatever he or she bid, regardless of who wins the
auction. Suppose that each student has only...

1.
There are many sellers of used cars. Each seller has exactly one
used car to sell and is characterised by the quality of the used
car he wishes to sell. The quality of a used car is indexed by θ,
which is uniformly distributed between 0 and 1. If a seller sells
his car of quality θ for price p, his utility is p − θ 2
. If he does not sell his car, his utility is 0....

Answer the following questions about oligopolistic markets for a
simultaneous game in which Microsoft and Apple decide whether to
advertise or not.
Players: Apple and Microsoft (MS)
Strategies: Advertise (A) or No-Ads (NA)
Payoffs:
If both choose to A, Apple gets $8 billion revenue and MS gets
$16 billion revenue;
If Apple choose A and MS choose NA, Apple gets $15 billion and
MS gets $12 billion;
If Apple choose NA and MS choose A, Apple gets $10 billion and...

Please answer the following Case
analysis questions
1-How is New Balance performing compared to its primary rivals?
How will the acquisition of Reebok by Adidas impact the structure
of the athletic shoe industry? Is this likely to be favorable or
unfavorable for New Balance?
2- What issues does New Balance management need to address?
3-What recommendations would you make to New Balance Management?
What does New Balance need to do to continue to be successful?
Should management continue to invest...

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