Question

There is a new media streaming company "N" which is considering entry to a new market where incumbent company "B" is the only major firm in the business. If N chooses OUT, then payoffs are (X,9) where X is some unknown payoff value for company N. If N chooses ENTER, then B must choose IGNORE or ADAPT, and N will then choose OLD or NEW in response to B’s choice. With IGNORE chosen by B, the payoffs from OLD are (2,2) and payoffs from NEW are (7,0). With ADAPT chosen by B, the payoffs from OLD are (0,1) and the payoffs from NEW are (4,3). Also note that this is a "single shot" game, meaning it is not repeated – equivalently, you can think of these payoff values as a total discounted stream of all future profits if that is more intuitive than "utility".

A) Find the Nash Equilibrium outcome in this game.

B) Briefly explain what X represents conceptually and what might affect this value. Now suppose incumbent company B can pay $b to challenger company N to stay out of the market:

C) What is the most that B be willing to pay N (the maximum b) to stay out of the market?

D) What is the lowest possible value for X where a payment can be made to stay out?

E) If X=0, find the exact range of possible values for b.

F) If X=0, find the optimal value b* that B should offer to N

Answer 1

The Nash Equilibrium outcome in this game would be for company N to choose ENTER and for company B to choose ADAPT. X represents the unknown payoff value for company N, and it represents the potential profits N could earn if it enters the new market. The maximum amount B would be willing to pay N to stay out of the market would depend on the potential profits B could earn if N enters the market. If X=0, the lowest possible value for X where a payment can be made to stay out, the exact range of possible values for b would depend on the calculations and potential profits involved. The optimal value b* that B should offer to N would also depend on the specific circumstances and calculations based on potential profits.

Step-by-step explanation:

The Nash Equilibrium outcome in this game would be for company N to choose ENTER and for company B to choose ADAPT. This is because the payoffs for N are higher when B chooses ADAPT, with payoffs of (4,3) for N compared to (2,2) for N if B chooses IGNORE. X represents the unknown payoff value for company N, and it represents the potential profits N could earn if it enters the new market. Factors that might affect X include the size of the market, the level of competition, and the demand for the product or service.

If company B can pay N to stay out of the market, the maximum amount B would be willing to pay (b) would depend on the potential profits B could earn if N enters the market. B would want to pay N an amount that is less than the potential profits it could earn from the market, but enough to incentivize N to stay out. The most that B would be willing to pay N would depend on the specific circumstances and calculations based on potential profits.

If X=0, the lowest possible value for X where a payment can be made to stay out, the exact range of possible values for b would depend on the calculations and potential profits involved. It would be a value greater than 0 and less than the potential profits B could earn if N enters the market. The optimal value b* that B should offer to N would also depend on the specific circumstances and calculations based on potential profits.