Eco514|Game Theory
Problem Set 3,Due Thursday,October 28
1,Asymmetric Auctions
Consider an interdependent-values auction with two bidders,each of whom observes an i.i.d.
uniform signal si2[0;1],Bidder i’s valuation for the object is equal to vi(si;s i) = isi+s i,
where i > 1 but in general 1 6= 2.
(a) Construct a Bayesian Nash equilibrium of the second-price auction in this environ-
ment,Is the outcome e cient?
(b) Now construct a Bayesian Nash equilibrium of the rst-price auction in this environ-
ment,Is the outcome e cient? Does revenue equivalence hold?
2,Auctions with a reserve price
In the setting of the previous exercise,suppose that the seller decides to set a positive reserve
price r > 0,that is,all bids below the reserve price are discarded (so,in particular,it may
be the case that both bids are discarded),Assume that the value of r is publicly announced
before the auction begins,so it is commonly known.
Construct an equilibrium of the second-price auction in this environment,and express
the expected revenues to the seller as a function of r,Does setting r = 0 maximize the
seller’s expected revenues?
3,From OR,99.1,101.3,108.1
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