2.Price Competition: Uber Eats vs Menulog

MENULOG UBER EATS This exercise studies the price competition between two online food ordering and delivery plat- forms: Uber Eats and Menulog. Both firms adopt the same platform-to-consumer business model: Available restaurants close to the customer's proximity are listed on a website or a mobile app, and consumers can then order from these partner restaurants and have the food delivered. Let NM denote the number of restaurants that sign up to Menulog, and NO the number of restaurants that sign up to Uber Eats. Assume NM is determined by the following function: NM (CM, CU) = 100 - 190CM + 40CU where C is the commission rate charged by Menulog, and CO is the commission rate charged by Uber Eats. Similarly, N is determined by the following function NU(CM, CV) = 100 - 190CU + 40CM. Suppose on average each restaurant can generate 100 orders and each order is worth $20. The marginal cost is constant at $2 for each order and for each firm: MCM = MCV = 2. There is no fixed costs. To simplify the analysis, assume that each firm only considers setting the commission rate at one of the following three values: 35%, 30%, and 25%. (a) (2 marks) Derive the profit function for each firm. (b) (4 marks) Construct a 3x3 payoff matrix for the pricing game between Menulog and Uber Eats and find the Nash equilibrium of the game. Calculate each firm's profits and market share, and the Herfindahl Index in equilibrium. The following questions are independent to each other. (c) (4 marks) Suppose the firms move sequentially instead of simultaneously: Menulog sets its commission rate first. After observing the commission rate set by Menulog, Uber Eats then sets its commission rate accordingly. Construct a game tree for this sequential-move game and find the SPNE of the game. Make sure you specify each firm's strategy properly. (d) (5 marks) Suppose Uber Eats is considering whether to make an investment to improve its user interface design on the platform and gain competitive advantage over Menulog. The investment will cost Uber Eats F dollars, and it will expand its restaurant base from NU (CM, CV) = 100 - 190C + 40CM to NU (CM, CV) = 150 - 190C + 40CM,and shrink Menulog's restaurant base from NM(CM, CV) = 100 - 190CM + 40CV to NM(CM, CV) = 80 - 190CM + 40CU. Other things remain unchanged. Consider the following two-stage game: In the first stage, Uber Eats decides whether to make the investment or not. In the second stage, the two firms set their commission rates simultaneously. Find the SPNE of this two-stage game and determine the cut-off value of F, F*, such that Uber Eats will make the investment if and only if F