Question

Consider an industry that consists of two firms, Alpha and Beta, that produce identical products. Suppose that Alpha seeks to preempt Beta by making its capacity decision a year before Beta’s. Thus, by the time Beta makes its decision, it will have observed Alpha’s choice and must adjust its decision making accordingly. We will assume that each firm always produces at full capacity. Thus, expansion of capacity entails a trade-off. The firm may achieve a larger share of the market, but it may also put downward pressure on the market price. The consequences of each firm’s choices are described in the game tree below. Each firm chooses among three options: no expansion of current capacity, a small expansion, or a large expansion. What is the branch sequence that represents the clear (continuous) path of equilibrium of this game?

D stands for Do not Expand, S stands for Small, and L stands for Large.

	Alpha selects L and Beta does not expand.
		Alpha selects L and Beta selects S.
		Alpha selects S and Beta does not expand.
		Alpha and Beta do not expand.

Answer 1

Hi .

The answer of the following question is given below as follows :

So according to me the Most likely result = ($ 18, $ 9)

Reason: This situation has the advantage of being the first to move. Alpha will check Beta's response to each of his moves and choose the move that is most profitable for him.
If you move D, Beta will respond with S as it gives Beta the maximum reward (20). If Alpha moves S, Beta will respond with S, again the highest reward (16). If Aplha moves L, Beta will respond with D (payoff 9).
Among these three Beta responses, the most profitable for Alpha would be the last, since he, Alpha, gets the highest reward of the three responses.
So Alpha will move L and, as predicted, Beta will follow with D.
So the result will be (L, D) with payment ($ 18, $ 9).
In other words, Alpha will have a great capacity; and Beta will not expand for fear of lowering the price.

I hope I have served the purpose well.

THANKS.