Hi i am not sure how to do thesequestion

The double auction is a mechanism designed to nd a price at which the quantity demanded equals the quantity offered and is. therefore. closely related to the standard economic analysis of equilibrium in competitive markets [where supply equals demand]. For instance. treasury auctions in the US are an example of a double auction. with the specific Feature that there is just one seller on the supply side of the market. Your task: In what follows. you will be asked to characterise the Nash equilibria of the simplest possible version of the double auction with just one good. one seller and one buyer. This special case of a double auction is also often referred to as bilateral trade or bilateral bargaining. The details of this strategic interaction are as follows: the buyer yalues the good for sale at n3. while the seller values it at eye. Suppose that y a: mg. The buyer can submit bid prices E] {which are nonnegative real numbers} and the seller can submit ask prices s {also nonnegative real numbers]. There is an auctioneer who determines the price 33: according to the following rule: If s :e fr then no trade occurs as the seller asks for more money than the buyer is willing to ear: If s :3 l: then trade occurs at price p = {fl + .sjy'r. The buyer's net payoff is [I if no trade occurs. and try.- p when trade occurs. Likewise. the seller's net payoff is [J if no trade occurs. and p eg- when trade occurs. [a] Set up the normalform game that captures the strategic interaction described abuse. [15 marks] (b) Deriue separately for each player {i.e., the buyer and the seller] the way her payoff yaries with her bid in order to identify her payoffmaximizing bids. [25 marks] {c} In a esdiagram. depict graphically both players' best responses {similar to what we've done during the IPT on auctions in Iil'lleek Id] and then highlight and interpret your results. Are any of the Nash equilibria you found inefficient? Explain! [35 marks]