# Question: 2 price competition uber eats vs menulog this exercise studies...

###### Question details

2. Price Competition: Uber Eats vs Menulog

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 **N**** ^{M}** denote the number of restaurants that sign up to Menulog, and

**N**

**the number of restaurants that sign up to Uber Eats. Assume**

^{U}**N**

**is determined by the following function:**

^{M}

**N**** ^{M}**(

**C**

^{M}**; C**

**) = 100 - 190**

^{U}**C**

**+ 40**

^{M}**C**

^{U}**;**

where **C**** ^{M}** is the commission rate charged by Menulog, and

**C**

**is the commission rate charged by Uber Eats. Similarly,**

^{U}**N**

**is determined by the following function**

^{U}

**N**** ^{U}**(

**C**

^{M}**; C**

**) = 100 - 190**

^{U}**C**

**+ 40**

^{U}**C**

^{M}**:**

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: **MC**** ^{M}** =

**MC**

**= 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%.**

^{U}

(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 firms 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

**N**^{U}** **(**C**^{M}** ; C**^{U}** **) = 100 - 190**C**** ^{U}** + 40

**C**

**to**

^{M}**N**

**(**

^{U}**C**

^{M}**; C**

**) = 150-190**

^{U}**C**

**+ 40**

^{U}**C**

^{M}**;**

and shrink Menulog’s restaurant base from

**N**^{M}** **(**C**^{M}** ; C**^{U}** **) = 100-190**C**** ^{M}** + 40

**C**

**to**

^{U}**N**

**(**

^{M}**C**

^{M}**; C**

**) = 80-190**

^{U}**C**

**+ 40**

^{M}**C**

^{U}**:**

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 **N**** ^{M}** and

**N**

**:**

^{U}

**N**** ^{M}**(

**C**

^{M}**; C**

**) = 100 - 224**

^{U}**C**

**+ 40**

^{M}**C**

^{U}**N**** ^{U}**(

**C**

^{M}**; C**

**) = 100- 224**

^{U}**C**

**+ 40**

^{U}**C**

^{M}Redo (a) and (b).