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Polling + Auctions
Anna Karlin
Agenda
- An application of The Central Limit Theorem – Polling
- A glimpse of auction theory
Polling + Auctions Anna Karlin Agenda An application of The - - PowerPoint PPT Presentation
Polling + Auctions Anna Karlin Agenda An application of The - - PowerPoint PPT Presentation
Polling + Auctions Anna Karlin Agenda An application of The Central Limit Theorem Polling A glimpse of auction theory Magic mushrooms Yesterday, Oregonians are voting on whether to legalize the therapeutic use of magic
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Magic mushrooms
Yesterday, Oregonians are voting on whether to legalize the therapeutic use of “magic mushrooms”. If you take a "heroic" dose, supposedly, “the ego dissolves and the user feels inseparable from the rest of the universe.”
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CLT à Polling on magic mushrooms
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The Central Limit Theorem
Consider i.i.d. (independent, identically distributed) random vars X1, X2, X3, … Where Xi has μ = E[Xi] and σ2 = Var[Xi] As n → ∞, Restated: As n → ∞,
Mn = 1 n
n
X
i=1
Xi → N ✓ µ, σ2 n ◆
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The Standard Normal CDF
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Suppose want to use CLT to estimate Pr(28 ≤ 𝑌 ≤ 30 ) when X is Binomial (100, 0.3) Issue: Binomial is discrete, Normal is continuous.
The Continuity Correction (Idea)
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Auctions
- Companies like Google and Facebook make most of their
money by selling ads.
- The ads are sold via auction.
○ Advertisers submit bids for certain “keywords”
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An auction is a …
- Game
○
Players: advertisers
○
Strategy choices for each player: possible bids
○
Rules of the game – made up by Google/Facebook/whoever is running the auction
- What do we expect to happen? How do we analyze
mathematically?
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Special case: Sealed Bid single item auction
- Say I decide to run an auction to sell my laptop and I
let you be the bidders.
- If I want to make as much money as possible – what should
the rules of the auction be? Some possibilities:
- First price auction: highest bidder wins; pays what they
bid.
- Second price auction: highest bidder wins; pays second
highest bid.
- All pay auction: highest bidder wins: all bidders pay
what they bid.
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sealed bid single item auction
Some possibilities:
- First price auction: highest bidder wins; pays what they
bid.
- Second price auction: highest bidder wins; pays second
highest bid.
- All pay auction: highest bidder wins: all bidders pay
what they bid. Which of these will make me the most money?
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Bidder model
Each bidder has a value, say vi for bidder i. Bidder is trying to maximize their “utility” – the value of the item they get – price they pay.
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The Central Limit Theorem
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Normal random variables
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The Standard Normal CDF
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END PIC
Alex Tsun Joshua Fan