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This exercise studies the price competition between two online food ordering and delivery platforms:

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 NU 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 CM is the commission rate charged by Menulog, and CU is the commission rate charged by Uber Eats. Similarly, NU is determined by the following function

NU(CM, CU) = 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 = MCU = 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 33 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, CU) = 100 190CU + 40CM to NU(CM, CU) = 150 190CU + 40CM,

and shrink Menulog's restaurant base from

NM(CM, CU) = 100 190CM + 40CU to NM(CM, CU) = 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 F. Calculate the Herfindahl Index in equilibrium. You don't need to draw a game tree here.

(e) (5 marks) Suppose the COVID-19 pandemic brings the following two changes to the business environment facing online delivery platforms: (i) A surge in demand for online food ordering services, and (ii) Restaurants become more price-sensitive and actively look for a platform that brings the best benefits to its business. Due to those changes, assume that the number of orders each restaurant can generate increases from 100 to 200, and we have the following new functions for NM and NU :

NM(CM, CU) = 100 224CM + 40CU

NU(CM, CU) = 100 224CU + 40CM

Redo (a) and (b).

(f) (2 marks) First go over this news article. Based on our simple model and your answers in (b) and (e), can you give an explanation why Uber Eats cut its commission rate in May 2020? Is your explanation consistent with that provided in the article?

(g) (3 marks) Recently several cities in the US, including New York, San Francisco, Seattle and Washington, D.C., imposed a temporary cap of 15% on commission charged by third-party delivery platforms. Suppose the Australian government is also considering to impose a 15% cap on commission charged by third-party delivery platforms. Based on your answers in (e), discuss how this government intervention will affect

(i) the profits of Menulog and Uber Eats,

and (ii) the number of restaurant signups to each platform. Do you think the government

should intervene to see restaurants through the pandemic? Justify your answers.

(h) (5 marks) So far we have assumed that each firm can only set its commission rate at 35%, 30%, or 25%, which is an unrealistic assumption. Assume now Menulog and Uber Eats can set its commission rate at any non-negative value; i.e., CM 0 and CU 0. Find the Nash equilibrium in this general pricing game in the following two scenarios: Before The Pandemic. We have

NM(CM, CU) = 100 190CM + 40CU

NU(CM, CU) = 100 190CU + 40CM

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 = MCU = 2. Amidst The Pandemic. We have

NM(CM, CU) = 100 224CM + 40CU

NU(CM, CU) = 100 224CU + 40CM