Question

Imagine you and your friends have created a new prototype of an electric car and you are discussing the possibility of opening a start-up to produce and sell it. Your big shot is represented by the US! Even though it is still a market niche, US electric car demand is high enough to allow you high returns to your investments. To this extent, you start gathering information to be able to draw a production plan. Yet, there is a big problem...the US niche is monopolized by Tesla which, of course, would not be happy about your entry into the market. Luckily you have an advantage: electric cars’ buyers are not yet expert enough and cannot distinguish between your car and Tesla’s one, which implies: 

• that you can compete for the same demand but brands make no difference; 

• that the prices at which you and Tesla sell your cars are the same; 

• that you and Tesla compete over quantities of cars sold on the market. 

After a market research you discover that the US demand for electric cars is given by Q = 100 − P, where Q is the whole quantity demanded and P is the price for each vehicle on that niche - hence the price at which you and Tesla sell your cars. Moreover, you also discover that both you and Tesla happen to have the same cost structure, as the total costs for producing Q cars equal toTC = 40Q for both of you. At the same time, you also know that Tesla has come to know you are deciding whether to enter the US market and has the same knowledge you have about the whole situation. Provided that, you now have two decisions to make: 

• whether to enter or not the market;

• how many cars to produce. 

As to the timing, these decisions are not contemporaneous. As a matter of fact, if you decide to enter you know that (i) Tesla will set its own quantity before you are able to set yours; (ii) you will observe Tesla’s move before setting your quantity. 

Finally, both you and Tesla want to maximize your own profits π -needless to say that, if you decide not to enter the market your profits equal zero. To this extent: 

(a) draw the extensive form of the game. For simplicity assume that you and Tesla have only 3 possible quantities to choose from - say q1 (Tesla) = 5, q2 (Tesla)  = 15, q3 (Tesla) = 25, q1 (You) = 5, q2 (You) = 15, q3 (You)  = 25 (note: you have to compute and write the payoffs in each possible outcome of the game); 

(b) how many subgames are there in this game-tree? 

(c) solve the game by backward induction: do you decide to enter or not? 

(d) how would the game-tree change if you and Tesla decide at the same time the quantities to produce? Draw the new extensive form and indicate how many subgames there are in this case; 

(e) going back to the sequential case, focus only on the part of the game involving the decisions on the quantities to be sold on the market and consider all the possible strategies that you and Tesla can implement (that are way more than 3): write down the strategy spaces and motivate your answer; 

(f) find the subgame perfect Nash equilibrium of this game (note: explain the logic behind your computations); 

(g) by assuming that you and Tesla decide at the same time the quantities to produce, find the Nash Equilibrium of the game and compare it with the outcome of the sequential case...what can you say about the two situations? (note: underlined words should ring you a bell...).