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Part B [5 marks] Consider that management and unions are negotiating a wage increase. Management is looking at three potential wage increases: $10 an hour, $3 an hour, and $1 an hour. Successful negotiations will lead to $600 million in profits which will be split between management and the union based on the agreed upon wage increase. If they agree on a $1 an hour increase, the split in profits is 500/100 in favour of management. A $3 increase results in a 300/300 split in profit sharing. Lastly, a $10 increase results in a 500/100 split in favour of the union. Failure to reach an agreement results in a loss to the firm of $100 million and a union loss of $3 million. This is a sequential game in that management makes an offer and the union can accept or decline. This is a one-shot deal in that if the union declines, there is no agreement. a. Construct the game's payoffs in extensive form. What is the sub-game perfect Nash equilibrium? b. What if the game was reversed in that the union makes the first offer, does the result change? Explain your finding.Part A [5 marks Consider the scheduling of sales by retailers. Some sales are scheduled predictably (e.g. those that occur on holidays or end of season) while others are not as predictable (weekly sales for produce). In general, a consumer's shopping schedule is difficult to predict. Given this information, the following table summarizes the shopping payoffs to the seller and buyer. Consumer Shop Today Shop Tomorrow Sale Today 5, 10 8, 4 Seller Sale Tomorrow 10, 5 4, 8 Find the Nash equilibrium (pure or mixed) for this game. If mixed, explain why a pure strategy is not possible