Game Theory: An item is going up for auction. There are two bidders, and each can be one of two types, Rich and Poor. We know the following about the…

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Game Theory:

An item is going up for auction. There are two bidders, and each can be one of two types, Rich and Poor. We know the following about the bidders:

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  • A Rich bidders is willing to pay $120.
  • A Poor bidders is willing to pay $100.
  • Poor bidders make up 60% of the bidders.

If the item is sold using an Ascending Auction:

  • Describe the dominant bidding strategy for each player.
  • Assuming a Rich bidder is in the auction, what would be the probability of a that Rich bidder winning the auction? 
  • What would be the expected payment of a Rich bidder? 
  • What would be the expected surplus of a Rich bidder?
  • Assuming a Poor bidder is in the auction, what would be the probability of that Poor bidder winning the auction? 
  • What would be the expected payment of a Poor bidder? 
  • What would be the expected surplus of a Poor bidder?

If the item is sold using an Descending Auction:

  • Describe the dominant bidding strategy for each player.
  • Assuming a Rich bidder is in the auction, what would be the probability of a that Rich bidder winning the auction? 
  • What would be the expected payment of a Rich bidder? 
  • What would be the expected surplus of a Rich bidder?
  • Assuming a Poor bidder is in the auction, what would be the probability of that Poor bidder winning the auction? 
  • What would be the expected payment of a Poor bidder? 
  • What would be the expected surplus of a Poor bidder?

 

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