Question

I would like to know the detailed solution process and the answer to question number 1 a,b. Please explain it.

1. Samsung and Sony have to decide whether they will increase the spending on Research and Development (R&D) Department in order to improve the features of their products which are sold worldwide. If they both increase the spending, the gains of doing so are zero for both. If only one of them increases the R&D budget while the other doesn’t, the gain of the improved features is equal to the loss of the other company. If both of them do not change R&D spending, their customers will switch to other brand from the U.S., both will equally make huge losses.

a) Construct the pay-off matrix for the game. Is this a zero-sum game? Why or why not

b) Is there a dominant strategy equilibrium? If so, what is it?

Answer 1

The possible states:

1 - Both increase spending, gain 0

2 - Samsung increases spending, gain = Sony's loss

3 - Sony increases spending, gain = Samsung's loss

4 - No increase in spending, huge losses for both

a.Pay-off matrix:

   Samsung

Sony	Increases	Doesnt increase
Increases	0,0	x,-x
Doesn't increase	-x,x	Huge losses

No it is not a zero sum game. It is not a zero sum game, because the all the states are not equal and opposite. For it to be a zeo sum game between two players, the profits of one player leads to equal losses of the second player, which is not the case when both companies increase investments or do not increase investment.

b. There is a dominant strategy equilirium, which is where both the companies increase investment. This is because, if both companies dont increase investment, they stand to make huge losses. If only one increases, the other company makes equal loss, so those states are unstable. The onle possible stable state is when both increase investment.