Auctions Flashcards
Revenue Equivalence Theorem
Applies to IPV auction. Assume that:
- no collusion
- exogenous number of bidders
- Risk-neutral bidding
- Private values
- Values drawn from same distribution
- Rational bidding
- -> All auctions where the object goes to the person with the highest valuation and where the person with the lowest possible valuation expects zero payoff yield the same revenue.
RET Violations
Risk aversion:
Because FPSB auctions allow for trade-off between expected payoff and probability of winning, risk-averse bidders will bid more.
Asymmetric values:
Under asymmetric values, the FPSB raises more generally (because, if the highest bidder is drawn from a different, higher distribution, then the possible value derived from his valuation is higher than that derived from the second highest valuation).
Efficient Multi-Unit auction for unit demand and homogeneous goods
Natural extension of the second price sealed bid: K+1 Price sealed bid. For K goods the first K bidders get the objects to the price of the K+1’st bid.
Efficient Multi-Unit auction for unit demand and heterogeneous goods
SAA is efficient. Heterogeniety –> Bidders have different valuations for different lots, so they must be able to bid for whichever they have the highest valuation for.
Efficient Multi-Unit auction for multi-unit demand but no complementarities
Separate one-unit auctions. Bidders will, knowing the outcomes of the previous auctions, bid optimally for the next good according to their values. Is more efficient than SAA because in SAA they must condition winning on other’s behaviour. Problems emerges with complementarities. Assume A values {1,2,3} but B only values {2,3}. A wins {1}. Then B wins {2,3}. Now A has inefficiently obtained {1}. Under no complementarities, valuations are independent so, after initial one-unit auctions, no bidder has any desire to reverse the previous bids. They are manifested and efficient.
Revenue and Efficiency in Single-Units
Single-Unit auctions can generally be efficient and revenue maximising. Lot goes to bidder with highest value (necessary condition of revenue equivalence) and such an auction will lead to highest revenue possible assuming reserve price. Thus, efficiency and revenue maximisation are aligned.
Multi-Unit Problems
Demand Reduction:
Downplay your valuation (bids) to attain lower prices at the loss of some objects. Tradeoff only possible because you don’t lose all lots (compared to single-unit).
Exposure Problem:
Bidders afraid to bid for element of a complementary bundle out of fear of not getting the other component. Thus, will bid less (low revenue). Can be alleviated through combinatorial bidding. However, combinatorial bidding reduces efficiency (Only because one bidder has highest valuation for bundle does not mean he has highest valuation for every element in bundle)
Tacit Collusion:
Collusion through signalling. Problem in multi-unit auctions because there is not necessarily competition, unlike for one good. Collude tacitly through signals if lower price from collusion is preferable to more units from competition. Only works in SAA as opponent’s reactions are observable. In Sealed-bid there is the incentive to break collusive agreement.
Revenue vs Efficiency in Multi-Units
Trade-off problems.
Combinatorial bids: increase revenue by alleviating exposure problem but allow for inefficient allocation of individual goods
Collusion:
FPSB decreases chances of collusion (increasing revenue) but decreases efficiency as bidders cannot alter their bidding patterns to adjust for relative valuation of specific lots
FPSB vs Ascending Common values:
In common value asymmetric ascending auctions imply that the bidder with slightly higher valuation will always win. In sealed bid auctions the other bidders have a realistic chance as well. This increases revenue but is inefficient (chance of object going to person with lower valuation).
Winner’s Curse
Only applies when valuation is uncertain (not in IPV case). Winner’s curse states that winner was bidder with highest valuation so he most likely overvalued the object. More specifically:
Value of object only relevant when winning auction. So payoff must be valuation conditional on winning. Valuation conditional on winning is lower than unconditional valuation because it suggests that all others valued it lower. Therefore Bayesian updating during auction is necessary.
Common Value Sealed Bid
If both signals are drawn from the same distribution then it makes sense to bid own signal. Reason: again, what is the value of the object subject to winning the auction?
Slightly Asymmetric Common Value Ascending
Assume that
v1 = z1+z2+e
v2=z1+z2
Situation is asymmetric. Bidder 1 will always be in a better situation than bidder two. So it makes no sense for bidder two to bid above (z2) since, for anything he bids, bidder 1 will be able to bid more. If Bidder 1 again bids two times value he can now bid 2(z1+1). This increases winner’s curse if Bidder 2 actually wins so Bidder 2 bids less aggressively. Symmetric bidding rule breaks down and, in equilibrium, bidder 2 bids z2.
Example: toehold. Bidders with toehold win more often and at lower prices.
Entry Problems
Often arise with common value auctions. If a “strong bidder” almost certainly has a higher valuation and there are bidding costs then other bidders won’t compete at all.
Improving Entry
Single-Unit:
FPSB is better than ascending, especially in common-value contexts. It prevents aggressive bidding
Multi-Unit:
Weak bidders are better off with uniform auctions versus discriminatory ones because they don’t set the price which gives players with less information a chance.
General:
Number Units > Number of strong competitors –> Weak competitors enter and drive up price for all (UK 3G Auction)
Arguments for Uniform Auction
- “Fairer” as in more level playing field
- Information less valuable so again better for weak bidders
- Bidding therefore easier for small bidders
- Therefore more entry and so less collusion
- More efficient and more informative
Arguments for Discriminatory
- No free riding on information
- Less implicit collusion possible
