Two companies, TopSport and XActive, serve the same niche market for a piece of gym equipment. They have constant averag

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Two companies, TopSport and XActive, serve the same niche marketfor a piece of gym equipment. They have constant average costs of£200 per unit. The companies can choose either a high price (£1000)or a low price (£500) for their piece of equipment. When both firmsset a high price, total demand = 5,000 units which is split evenlybetween the two firms. When both set a low price, total demand is9,000, which is again split evenly. If one firm sets a low priceand the second a high price, the low-priced firm sells 7,500 units,the high-priced firm only 1,000 units. Analyse the pricingdecisions of the two firms as a non-cooperative game.
a. Construct a pay-off matrix, in the normal form, where theelements of each cell of the matrix are the two companies’ profits.(10 marks)
b. Derive and report the equilibrium set of strategies. Commenton the consequences of competition between the two companies. (10marks)
c. Examine and report on the sensitivity of the solution in (b)to the assumption of a 7,500:1,000 sales split when one companysets a low price and the other company a high price.