Home » Second Price sealed bid-auction: Assume n players are bidding in an auction in order to obtain an indivisible object.

# Second Price sealed bid-auction: Assume n players are bidding in an auction in order to obtain an indivisible object.

Second Price sealed bid-auction: Assume n players are bidding in an auction in order to obtain an indivisible object. Denote by vi the value player i attaches to the object; if she obtains the object at the price p her payoff is vi −p. Assume that the players’ valuations of the object are all different and all positive; number the players 1 through n in such a way that v1 > v2 > · · · > vn > 0. Each player i submits a (sealed) bid bi . If player i’s bid is higher than every other bid, she obtains the object at a price equal to the second-highest bid, say bj , and hence receives the payoff vibj . If some other bid is higher than player i’s bid, player i does not obtain the object, and receives the payoff of zero. If player i is in a tie for the highest bid, her payoff depends on the way in which ties are broken. A simple (though arbitrary) assumption is that the winner is the player among those submitting the highest bid whose number is smallest (i.e. whose valuation of the object is highest). (If the highest bid is submitted by players 2, 5, and 7, for example, the winner is player 2.) Under this assumption, player i’s payoff when she bids bi and is in a tie for the highest bid is vi − bi if her number is lower than that of any other player submitting the bid bi , and 0 otherwise.

(a) Formulate this situation as a strategic (normal-from) game.

(b) Find a pure strategy Nash equilibrium in which player 1 obtains the object.

(c) Find a pure strategy Nash equilibrium in which player n obtains the object.

(d) Show that bidding own valuation is a weakly dominant strategy for each player.

(e) Find ALL pure strategy Nash equilibria of this game when n = 2.

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.