Lecture: Game Theory and Auctions

Introduction to Game Theory in Auctions

• Game theory helps in determining optimal strategies in strategic decisions.
• Auctions are a common scenario where strategic bidding is applied.

Types of Auctions

1. English Auction

   • Open outcry auction.
   • Price increases until only one bidder remains.
   • The last standing bidder wins and pays their bid amount.

2. Dutch Auction

   • Reverse of the English auction.
   • Price decreases until a bidder stops the auction.
   • The stopping bidder wins and pays the current bid amount.

3. Sealed Bid Auctions

   • Bidders submit bids privately and simultaneously.
   • Two types:
     • First-Price Sealed Bid: Winner pays their bid amount.
     • Second-Price Sealed Bid: Winner pays the bid amount of the second-highest bidder.

Strategic Bidding Example

• Participants: Tony, Spencer, Wu, Tasha.
• Willingness to Pay:
  • Tony: $500
  • Spencer: $450
  • Wu: $300
  • Tasha: $250
• Assumed everyone knows each other's max willingness to pay.

Auction Outcomes

• English Auction: Tony wins, pays slightly over $450.
• Dutch Auction: Tony wins, stops auction slightly under $450.
• First-Price Sealed Bid: Tony bids slightly over $450, wins, pays slightly over $450.
• Second-Price Sealed Bid: Tony bids $500, wins, pays $450.

Revenue Equivalence Theorem

• Under certain conditions, all auction types yield the same revenue.
• Pareto Optimal: Efficient for Tony to win for about $450.

Strategic Considerations

• With complete information:
  • Tony is less stressed in an English auction or second-price sealed bid.
• With incomplete information:
  • English Auction: Tony still wins easily.
  • Dutch Auction: Best to bid his maximum willingness ($500).
  • First-Price Sealed Bid: Tony bids his max willingness, ends up paying around $500.
  • Second-Price Sealed Bid: Pays $450.

Preferences

• Auctioneers: Prefer Dutch auctions and first-price sealed bids.
• Bidders: Prefer English auctions and second-price sealed bids.
  • eBay uses second-price format to attract buyers.
  • Fundraisers favor first-price sealed bids for higher donations.

Conclusion

• Game theory and strategic thinking can be applied to various life situations.
• Consider how strategic thinking might change your approach in different areas.