Bob 20 30 40 50 20 $160, $160 $140, $210 $120. $240 $100, $250 30 $210. ? Alan $180, $180 $150. ? $120. ? 40 $240. $120 ?, $150 $160, $160 $120. $150 50 2. $100 $200. $120 $150, $120 b. Suppose that Alan and Bob agree to collude and restrict their combined output to maximize their joint profits. They agree to divide production and profits equally. Referring to the payoff matrix above, how many gallons will they agree to produce in total? How many gallons of the total market supply will each supply? How much profit will each earn? c. Does Alan have any incentive to cheat on this collusive agreement? Does Bob? If so, how will such cheating manifest itself? d. What is the Nash in this game? Is the Nash an ideal outcome for our two water producers?1. In a dry, dusty desert town, only two people (Alan and Bob) have water wells. Each day. they begin their morning by pumping water, which they can bring to the town square to sell. Pumping water costs them essentially nothing, but time is such that each can afford to make only one trip to the town center, which means that they must decide how much to pump at the start of each day. The townsfolk's demand for water is given in the table below: Price 12 11 10 9 8 7 6 5 3 2 0 Q (gallons) 0 10 20 30 40 50 60 70 80 90 100 110 120 Suppose for simplicity that Alan and Bob are limited to pumping either 20. 30, 40, or 50 gallons of water each. a. For the table below find the missing values. Bob 20 30 40 50 20 $160, $160 $140. $210 $120. $240 $100, $250 30 $210. ? $180, $180 $150, ? $120, ? Alan 40 $240. $120 ?. $150 $160, $160 $120, $150 50 ?. $100 $200. $120 $150, $120 2