Posted on Categories:Game theory , 博弈论, 经济代写

# 经济代写|博弈论代考Game theory代写|ECON3050 Optimal auctions

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## 经济代写|博弈论代考Game theory代写|Optimal auctions

Alice wants to sell her house, which is worth nothing to her if a buyer can’t be found. The only potential buyers are Bob and Carol. What auction design should Alice use?
Alice’s problem is similar to King Solomon’s. She doesn’t know Bob and Carol’s valuations for her house. If she knew their valuations, she would simply make a take-it-or-leave-it offer of one penny less than the higher of the two valuations. It would then be rational for the bidder with the higher valuation to accept, because a profit of one penny is better than nothing. This analysis depends heavily on Alice having the power to make an irrevocable commitment to the rules of the Ultimatum Game. Mechanism design doesn’t work at all if the agents don’t believe that the principal will stick by the rules of the game she invents for them to play.

Since Alice doesn’t know Bob and Carol’s valuations, she follows Harsanyi’s methodology by modelling her uncertainty about their valuations with the help of a chance move. In the simplest case, this chance move assigns valuations to Bob and Carol independently – so that nothing you may learn about one agent’s valuation tells you anything new about the valuation of the other agent. Where it is necessary to be specific, I shall assume that each agent’s valuation for Alice’s splendid house is equally likely to be anything between zero and 36 million dollars.

Most people are surprised to discover that all the auction designs surveyed in the previous section are optimal for Alice if everybody is trying to maximize their average profit in dollars. Alice should set a reserve price of 18 million dollars and then use whichever of the designs takes her fancy, because they all yield the same average profit of 15 million dollars.

## 经济代写|博弈论代考Game theory代写|Reserve prices

Notice that Bob won’t bid at all half the time, because his valuation will be less than Alice’s reserve price. Since the same is true of Carol, Alice won’t sell her house at all one time in every four. If this happens, she mustn’t cheat on her own rules by auctioning the house again with a lower reserve price – unless she doesn’t care whether the agents will believe her in the future when she acts as a principal again!

I have given advice to many governments on designing big-money auctions, but I have never had any success in persuading the responsible officials to set as high a reserve price as I wished. Nor have I ever had any confidence that the officials understood that they mustn’t put the object for sale back on the market immediately if it didn’t reach its reserve price. But my efforts on this front aren’t entirely wasted, since they provide an excuse for looking only at the case of a zero reserve price in what follows. All the auction designs we have considered so far raise the same revenue on average whatever the reserve price, but it is easiest to explain why in the case when all the potential buyers can be counted on to make a bid.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Reserve prices

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