$3.($Bargaining with alternating offers$)$ A buyer and a seller are bargaining over the price of a house. The buyer is willing to pay up to $$250,000$ and the seller is willing to accept no less than$$150,000,$ so potential gains from trade are M $=$ $$100,000.$ Disagreement payoffs are equal tozero. This information is common knowledge.The two parties have agreed that there would be at most three rounds of alternating offers.If an agreement is not reached by the end of the third round, then the house is not sold and both parties get nothing out of the negotiations $($each party receives its disagreement payoff of zero$).$Suppose a coin flip has determined that the buyer would make the first offer $($then the seller may accept or make a counteroffer, which the buyer can accept or respond to with a counteroffer$).($a$)(5$ points$)$ Use backward induction to determine how the gains from trade will be shared in equilibrium. What is the price of the house in equilibrium? Explain.