Question

Tourists in Bintan island, a 45-minute ferry ride from Singapore, are demanding the latest espresso drinks from a familiar brand but their small number means demand can only sustain one new coffee shop. You and another popular chain, Starbucks, are considering making the considerable investment necessary to set up a shop in Bintan. Analyse the interaction between the two firms using game theory. Present a payoff matrix to model the situation and analyse it for Nash equilibrium. What can you do to make your best outcome more likely?

Answer 1

And: There are two players in the game- us and the starbucks.

Also, there are two strategies for each player- 1) Invest or 2) Do not Invest.

Payoff's for different strategies-

When we invest and starbucks don't = 3

When both of us don't invest = 2. (Reason- when both of us don't invest we both are practically losing out nothing except for the profits)

When both of us invest = 1. (reason- when both of us invest, we both will not be able to sustain, hence we don't get profits and we lose our investments as well)

When we do not invest but starbucks does = 0 (all the profits will be available to starbucks as we didn't even enter the market).

The rows represent strategies for us and the columns represent the strategies for starbucks.

	Invest	do not invest
Invest	(1,1)	(3,0)
Do not invest	(0,3)	(2,2)

Pure strategy nash equilibrium will be (invest,invest).

Reasons -

When we choose invest, starbucks choose invest and when we choose do not invest, starbucks then also chooses to invest.

Similarly, when starbucks chooses to invest, we choose to invest as well and when starbucks chooses do not invest, we then also choose to invest.

Therefore, invest is the dominant strategy for both the players and hence (invest,invest) is the dominant strategy nash equilibrium.