Game Theory and Auction Sales: An Economic Analysis

This essay analyzes auction sales using game theory principles, focusing on a case study involving Laura, a computer scientist, who is selling a new digital platform. The essay explores various auction mechanisms, including Dutch and sealed-bid auctions, and evaluates their effectiveness in maximizing revenue. It delves into strategic bidding, the advantages of sealed-bid second-price auctions, and the impact of the number of participants on revenue generation. The essay also considers the application of the Shapley value in determining the fair distribution of profits from a new investment based on the auction's proceeds. The analysis provides a comprehensive understanding of how game theory can be applied to real-world business scenarios, such as determining optimal selling mechanisms and investment strategies.

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Game Theory
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Game theory
Introduction
The determination of the sale of the product it holds in the available market is depended
on the value and the purpose it serves. For a new product in the market, the seller has to
determine a new price. It is dependent on production cost and demand (Hubbard & Parsec,
2016). For a new product, it might cost more to the producer due to maybe an advertisement and
so on. If a technical product is invented, the producer may receive some motivation incentives
from government or private companies which do so at their interest (Buschbom et al., 2018). For
more details about the new product in the market and price determination, a case of Laura, a
computer scientist, is considered. Laura is a computer scientist who had invented a new digital
platform.
Answering question one, the company has to choose the selling mechanism for this
platform. Considering external validation and enhanced buyer perception involved in auctioning,
it will fit best for this digital platform to use auctioned. Since Laura has a new product on the
market, then she can opt for auction, which will offer the maximum price possible. In this
auction selling mechanism, the buyer will express his or her capabilities, and the best buyer with

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the highest bid will be in a position to get the product. The company facilitating the sale of this
platform must consider the digital capability of the platform to attract more participants in the
auction period. The design must be based on the Dutch auction where bids are placed until no
one is willing to bid as per the given time of placing bids.
Question two, the sealed-bid second-price auction, is a type of auction that is sealed,
meaning the bid is hidden from the other bidders. It involves bidders submitting written bids.
The bidders do not know the bid of the other bidders in the auction (Milgram, 2004). The top
participant gains the opportunity to take the commodity. However, he pays the price equivalent
to that of the second-highest. The two most common auction is the sealed first and second prices
auction. The bid involves the bidder visiting the bidding website. The bidder sees only the under
auction (Guo et al., 2017). He or she places the bid but does not see the bid of the other bidders.
After placing the bid, it must rule until another high bid is placed. If the bids do not increase,
therefore the highest bid wins. He, therefore, pays the second prices below him and not his bid.
He pays to halve his or her bid. The strategic biding involves the bidder bids, not more than
once, to avoid the first bid from losing value. The exact bid depends on the other bids. The
strategy involves the following. Suppose the buyer valuation is V. And the current price is b.
Therefore b>v. Then, the buyer will, therefore, lose by raising his or her hand. If v>b, he can win
then let somebody win (Deck and Wilson, 2020). It is the dominant strategy as the winners
depended on the dominating bid. The payment of the winner is given by e (v) = 1/2v.
However, in question three, this mechanism follows the following strategy and design.
The strategy follows that suppose Diana is a bidder, and her bid valuation is a. Then, the rational
will follow. She should never bid more than a so that a will not lose value. If she bids exactly a,
she will neither gain to lose value? If she bids less than her valuation price, then she may have

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some positive gain, but the exact gain will depend on the bids of the other bidders (Hirshleifer
and Daniel, 2018). The challenge here is that Diana does not know the bids of others. The
highest bidders win, and he parts with the half of his or her bid.
Question four, the winner of the auction, will find the purchasing of the platform
profitable. It is because the other bidders contribute to the price of the platform. However, the
single highest bid wins, which is not the equilibrium cost of the platform (Zincenko, 2018). The
more the bids, the more gains to the owner of the platform. But the highest bidder wins the bid
by earning the platform at a relatively meager price.
Question five, the seller will benefit more from the sealed bid second price. The sealed
bid first price strategy requires the winner to pay half of his or her bid value. But, the sealed bid
second prize, the winner will pay the price of the second bidder (Qian et al., 2018). It is not
easily possible for half of the sealed bid first price to be greater than the sealed bid second price
(Krishna, 2009). Therefore it follows that the seller will benefit more from the sealed bid second
price strategy.
Question six requires to determine the amount that can be invested in the advertisement
to achieve ten more participants. Since the seller revenue is a third of the total sales, the buyer
has to consider the minimum amount or the reserved amount before investing in the market
advertisement. Here the companies with the highest bid valuation will be the most likely to win
the bid (Qian et al., 2018). The outcomes will be the profit to the seller. The seller revenue will
be one-third of the total earning. Therefore the other two-thirds of the money will be a benefit to
Laura. Laura should now use an amount less than a third to advertise the auction to achieve more
auctioning firms.

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Firm
s
1 2 3 4 5 6 7 8 9 1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
valua
tion
8
6
9
9
8
5
6
2
6
7
5
0
4
5
5
3
4
0
7
3
7
6
1
2
8
4
7
7
0
4
3
4
3
5
1
3
4
4
4
1
6
5
9
1
3
4
9
6
3
8
2
8
9
6
9
2
1
8
6
3
posit
ion
5 1 1
1
8 1
5
2
9
9 1
2
7 1
0
1
8
1
3
1
6
2
0
3 1
4
1
7
4 2 6
For the N bids
N=20
Expected revenue = The probability of this happening is f(x)(n 2)(2 F(x))F(x)n 2
The probability that x must be the highest bid is given by
H(x,n) = n(n1)f(x)(1F(x))F(x)n 2.
Expected value h(x,n) is given by
The lim0— 1000 xh (x, n) dx = n(n 2)ʃ0 1000 x(1/1000)(2 x/1000)(x/1000)n2 dx
We simplify this equation by:
ʃ0 1000 x (x, n) dx = (n (n 2)/ 1000n 2) ʃ0 1000 (x n 1 xn/1000) dx
= 1000 n (2/ n (n+2))

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Now
Calculating the revenues
The highest bid = 985
The second-highest bid = 921
When using the first bid sealed price auction, we divide the value of the highest bid by
two
= 985 / 2 = 492.5
However, when using the second bid sealed price, we take the second-highest bid
valuation which is 921
We do not need to calculate the probability since we have bid valuation for each firm
hence the total revenue = 921
On question seven, the sealed bid second price bid will be maintained since when the
number for participants increases the difference between the second and the first bid becomes
relatively small (Bergemann et al., 2017). The seller, therefore, will want more, and the highest
bid will win with the winner paying the amount equivalent to that of the second bidder.
Question eight is the scenario of a new investment using the funds obtained from the
digital platform auction sales. The shapely value is used as it involves the splitting of the capital
and the revenue earned. The scheme consists of the use of the fair distribution of a strategy

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method (Fuchs and Paningbatan, 2020). The delivery can reasonably be determined by the
number of ratios each group contributed. Since Laura has participated in the contribution of the
highest capital, she deserves a fair allocation of the profit earned. Hence shapely splitting will be
very honest.
Conclusion
Game theory is a critical theory applied in business and economic environments. Laura
has used a perfect auction mechanism, which simply can earn a lot of funds. The sales of the
digital platform have earned her capital worthy of starting another business. Game theory is a
suitable mechanism for making sales. Most nations use game theory through auction to generate
government revenue.
References

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BERGEMANN, D., BROOKS, B. & MORRIS, S. (20170. First‐Price Auctions With General
Information Structures: Implications for Bidding and Revenue. Econometrica, 85, 107-
143.
BUSCHBOM, S., DEHRING, C., DUNSE, N. & MUNNEKE, H. (2018). Sealed-Bid Auctions
and Fixed Price Sales: Seller Choice in Housing Markets. The Journal of Real Estate
Finance and Economics, 56, 525-545.
DECK, C. & WILSON, B. J. (2020). Auctions in near-continuous time. Experimental
Economics, 23, 110-126.
FUCHS, M. & PANINGBATAN, A. R. (2020). Correlation between Shapley values of rooted
phylogenetic trees under the beta-splitting model. Journal of Mathematical Biology, 80,
627-653.
GUO, Z., FU, Y. & CAO, C. (2017). Secure first-price sealed-bid auction scheme. Eurasip
Journal on information security, 2017, 16.
HIRSHLEIFER, D. A. & DANIEL, K. D. (2018). A Theory of Costly Sequential Bidding
(Presentation Slides). Forthcoming, Review of Finance, March.
Hubbard, T. P., & Paarsch, H. J. (2016). auctions. US: The MIT Press
Krishna, V. (2009). Auction theory (Second;2nd; ed.). Burlington, MA: Academic Press
Milgrom, P. R. (2004). Putting auction theory to work. Cambridge: Cambridge University Press
QIAN, X., FANG, S.-C., HUANG, M., AN, Q. & WANG, X. (2018). Reverse auctions with
regret-anticipated bidders. Annals of Operations Research, 268, 293-313.
ZINCENKO, F. (2018). Nonparametric estimation of first-price auctions with risk-averse
bidders. Journal of econometrics, 205, 303-335.

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