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:

• 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?