Question: Two builders, A and B, are competing for a contract to construct a new office block. Each can bid either £3.5 million or £4 million for the job. The builder with the lower bid will win the contract and will be paid the value of their bid once the building is finished. If both bids are equal, a fair coin is tossed to decide who should win the contract. Builder A reckons that his real cost of completing the job is £2 million, whereas builder B reckons it will cost him 2.5 million to complete it.They decide to discuss their bids.
(i) Construct the table of pay-offs (i.e the expected profits) to the two builders and find the maximum profit each can reasonably expect to get.
(ii) Deter-mine the Shapley solution.