Why are spectrum auctions held?
What are the goals? - CORRECT ANSWER 1 - *Missing* markets e.g. radio spectrums are
rarely traded
2 - Demand for some
... [Show More] frequency bands typically *exceeds* supply at low prices
3 -*Uncertainty* about
• Value
• Amount and quality required by users
4 -Other assignment properties e.g. lotteries
• Historically susceptible to *process
interference* (lobbying & corruption)
• *litigation* (challenging decisions)
• *reneging* on promises (non-credible)
• Assignments may not *reflect value*
5- help allocate resources to those that can use them most valuably
Define a mechanism - CORRECT ANSWER an economic instrument which incentives agents to
be truthful
What does a well-design spectrum auction look like? - CORRECT ANSWER about finding the
right mechanism
Take competition for a radio spectrum
Private valuation of the bidders (type space ϴ)
Desire to *maximise social welfare*
• Spectrum should be used by those contributing most to society
• Social choice function f(ϴ) maps types to
an outcome X - knowing ϴ assures best outcome
Aim is to design a mechanism (g), (spectrum auction) to implement as
an equilibrium the social choice
function f(ϴ) via bids M (messages)
Bidders with WTP £10 or £20, social choice function is £20
What is a vickery auction?
Describe the auction format, decision rule and dominant stratgey - CORRECT ANSWER
Otherwise known as a second-price auction
Same result as English auctions
/Auction format/:
all n bidders submit one bid in an envelope strategy set for each bidder is bi εR
/Decision Rule/:
highest bidder wins paying a price equal to the *second-highest bid*
If there is a tie, winner selected randomly and pays the bid value
/Weakly dominant strategy/:
play true valuation
/Explained/:
Bidder Susie, and has valuation v.
Suppose the highest competing bid is p.
If v > p, then Susie wins the item and earns v-p if she bids her own value v.
No other bids can give Susie better earning.
If Susie's value v < p, then the best Susie can do is to bid below p and earn zero.
_If bj > vi_ (someone else bids higher)
bi>bj will mean player i wins the auction but ends up paying bj>vi
It follows player i is no worse off by bidding
bi=vi
_If bj < vi_ (someone else bids lower)
bi>bj will mean bidder i will win the object and obtain a payoff vi -max bj
so bi=vi weakly dominates
Vickrey-Clarke-Groves (VCG) mechanism - CORRECT ANSWER /Auction format/:
sealed bids are submitted *simultaneously*
/Decision rule/:
Winning bid *combination max value V* = sum of winning bids*
Winners pay second-price calculated by reference to *opp cost*
Gets bidders to bid truthfully
A= V* -b*a (value excluding bidder a's winning bid)
B=V' (the value of the winning combination without bidder a)
B - A is the min bid to win
Example
V* =1,000, b*a= 100, V' = 950
implies bidder a pays 50 = opp cost
A=900, V'=950 implies bidder a has an opp cost of 50 on all the other bidders [Show Less]