3. Consider the following game. Two brothers have inherited two iden- tical pieces of antique, which both of them consider worthless. Now a potential buyer wants to buy one, and only one piece from them. As- sume that the brothers know that it is worth 10 dollars to the buyer, but the buyer does not know it. The buyer sets the following rule: (1) each brother has to simultaneously name an integer price between 0 and 20; (2) the brother who names the lower price sells his piece to the buyer and is paid the price he names and the other one gets nothing; (3) if the two brothers name the same price, then the buyer gets suspicious and walks away. (a) Use the notation we had in class to describe what N, {8,}ieN, and {wheN are. (b) Are there strategies that are strictly dominated? Demonstrate your reasoning. What are the resulting strategies after iterated elimination of dominated strategies? (c) Find the best responses (correspondence) for each player. That is, nd the strategies that maximize a player's payoff given what the other player does. (d) Find the pure strategy Nash equilibria of the game