What is the expected payoff to each type of bidder

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Reference no: EM132174175

Question - Discrete Auctions with Continuous Types

Consider an auction for a single good, with two bidders, each with a private value drawn independently from the uniform distribution on [0, 100]. The seller decides to hold a first- price sealed-bid auction, but bids are constrained to be taken from the set {0, 25, 50, 75}. If both bid 0, nobody will be awarded the object; if they bid the same, the winner will be chosen at random (with equal probabilities).

(a) Show that in any equilibrium, neither bidder bids higher than own value.

(b) Show that in any equilibrium nobody bids 75.

(d) Assuming that the bidding strategy is non-decreasing in type, calculate the unique symmetric equilibrium of this auction. (Hint: We need to establish the value at which bidders stop bidding 25 and start bidding 50.)

(e) Now suppose that bids are instead constrained to be taken from the set {0, 50}, with the same rules. What are equilibrium strategies?

(f) Calculate the sellers expected revenue in part e. How does this compare to the expected revenue in a standard first-price (e.g. FPSB) auction?

(g) What is the expected payoff to each type of bidder? Is there any type that prefers this (constrained) auction to an ordinary first-price auction?

Reference no: EM132174175

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