if the best response of firm 1: p1 = R1(p2) = (a - p2 - k) / 4 and the best response of firm 2: p2 = R2(p1) = (a - p1 - k) / 4. When subsitituting in a=8 and k=1 how do you solve this step by step to produce a best response functions simultaneously which will = 3.5

QUESTION (3) P1 R L P2 U P1 P1 R' L' R' L' (a) Find subgame perfect Nash equilibria of the game above. (b) Find all perfect Bayesian Nash equilibria and sequential equilibria of the game above.

Two firms bid for a contract to build a university building. Their construction costs are independent and uniformly drawn from [0,1]: Both bidders submit their bids si- multaneously. The winner is the bidder who submits a lowest bid. Tie-breaking rule is random. This kind of bidding game is called i'reverse auction' because the bidders bid for the right to provide a service and the winner is paid for the service. The FCC in 2017 has adopted similar auctions designed to repurpose spectrum for new uses. (a)  In the first auction, the winner gets paid the loser's bid. For example, if the winner's cost is 0.5, his bid is 0.56, and the loserís bid is 0.6, then the winner gets the contract and the university pays the winner 0.6. The winner's net profit from the contract is 0.6-0.5 = 0.1. Solve for a Bayesian Nash equilibrium of this auction. What is the equilibrium bid of a firm bid if his cost is actually 0.5? (b)  In the second auction, the winner gets paid the his/her own winning…

Two firms, A and B, know that holder of a telecom license will make a profit of either £0 or £4m with equal probabilities. They bid simultaneously either £0 or £1m for this license. The highest bidder wins the license (with probability ½ if both bidders submit the same bid) and pays its bid.                                            a)    Represent the game in normal and extensive form.                                                                                                                                 b)    Solve the game with the relevant solution concept(s).   c)    Represent the game in normal and extensive form when, before bidding, firm A learns the actual profit (£0 or £4m) of the license holder.                                                                                                                                     d)    Solve the game in c) with the relevant solution concept(s). Does firm A benefit from learning the actual profit?