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← 14-28 Auction Question

Unit 14 28 Auction Question.mp4

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Showing Revision 1 created 11/28/2012 by Amara Bot.

  1. Let's examine a type of auction called the second price option.
  2. This is popular in various internet search and auction sites.
  3. The way it works is that we have a line of possible prices--
  4. higher prices at the top--and bids come in.
  5. Different players can bid whatever they want,
  6. and whoever bids the highest is the winner,
  7. but the price that they pay is the price of the second highest bidder.
  8. Now let's say you're participating in this auction,
  9. and something is for sale, and you place a value on that.
  10. We'll call that value "V", and say V is here.
  11. Your bid we'll call "b", and the highest other bid we'll call "c."
  12. Now the payoff to you if your bid is higher than all the others
  13. then the payoff is you get the value of the auction,
  14. because you won the item, and you get V,
  15. but you have to pay the second highest price, which is c.
  16. You get b minus c. Otherwise, you lose the auction.
  17. You don't get anything, and you don't pay anything.
  18. The value to you of the auction is zero.
  19. What I want you to do is fill in this chart to look at different strategies for different possible bids.
  20. We'll say that the value to you of the item for sale is V equals 10.
  21. You have the option of bidding, say, 12, 10, or 8,
  22. and we'll consider the cases where the highest other bid is 7, 9, 11, or 13.
  23. What I want you to do is fill in this chart with the value to you
  24. of this game according to your strategy and the strategies of the other players.
  25. Tell me if one of these strategies is a dominant strategy.
  26. Then tell me is that dominant strategy, if there is one, a truth revealing strategy?
  27. I should have one note about dominance.
  28. When we talked about it before, we glossed over the possibility of ties.
  29. If some policy is better everywhere than any other policy,
  30. then we say that that policy strictly dominates the others.
  31. On the other hand, if there are some ties and some places where its better
  32. but none where it's worse, then we say it weakly dominates.
  33. Either way, it's a case of dominance.
  34. Now I'll do the first entry to get you started.
  35. If you bid 12 and the highest other bid is 7,
  36. then you have the high bid, so you win.
  37. It's a second-price auction, so you pay 7.
  38. The value of the goods is 10, so the total value of the outcome is 10 minus the cost of 7 for 3.
  39. I want you to fill in the rest.