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# A seller has a single indivisible unit of a good that is of interest to a buyer. The seller decides on a price p to set for the good.

A seller has a single indivisible unit of a good that is of interest to a buyer. The seller decides on a price p to set for the good. She posts this price in her storefront, and this

announcement is observed by the buyer, who lives nearby. A single unit of this good is also being sold on Ebay at a price q > 0. After observing the seller’s price, the buyer decides whether to buy the good held by the seller or the good sold on Ebay. Buying the good on Ebay also entails paying a shipping fee of c∈(0,q). The buyer derives value v > q+c from consuming either sellers’ good, and the seller derives no benet from retaining the good.

(a) Formulate the interaction between the seller and the buyer as a game in strategic form.

(b) Find a Nash equilibrium of this game in which the buyer does not visit the seller.

(c) Find a Nash equilibrium of this game in which the buyer visits the seller.

(d) Using your answer from (c), what can you say about the possible prices that the buyer pays in any Nash equilibrium in which the buyer visits the seller?

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