Firms Alpha and Beta serve the same market. They have constant average costs of $2 per unit. The firms can choose either a high price ($10) or a low price ($5) for their output. When both firms set a high price, total demand = 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 18,000, which is again split evenly. If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units, the high priced firm only 2,000 units.Analyze the pricing decisions of the two firms as a non-co-operative game. 1. In the normal from representation, construct the pay-off matrix, where the elements of each cell of the matrix are the two firms' profits. 2. Derive the equilibrium set of strategies. 3. Explain why this is an example of the prisoners' dilemma game