Question 1

Ice cream stall game

There are ice cream sellers (illustrated in the figure above) on Orchard road. For simplicity, let us assume that all sellers sell the same type of ice cream and that each tourist on Orchard Road would buy one ice cream and would choose the nearest stall to buy.

The ice cream sellers are free to choose their location, but they aim to choose a location to attract most tourists. They consider the number of tourists attracted to his/her stall as the only concern. The number of the attracted tourists will be evenly shared if the sellers choose a same location.

Given the above information, discuss the following questions:

(a) Assume that only 2 sellers are allowed to carry out their business on Orchard Road.

Consider the game of location selection between these two sellers and fill in the following table for the classifications of the game.

(b) Now we consider a game with some assumptions. The assumptions of the scenario are

• Only 2 sellers (Player A and Player B) are allowed on the Road and the locations to be selected are only 3 pits (i.e. the leftmost pit (L), the middle pit (M) and the rightmost pit (R).

• Assume that every day, there are 100 tourists that are evenly distributed on the road from the leftmost point to the rightmost point.

• Player A always shows up earlier to start the business.

Answer the following questions:

(i) Interpret the first interaction of location selection at the beginning of the day as a game (i.e. identify the key attributes of the game). (Word limit – 250 words)

(ii) Use Gambit to present and solve the game in (i).

(iii) Assume now, instead of the 3-pits limitation, that any point on the road may be selected to be a suitable location. Player A suggests that they could each choose the location at ¼ and ¾ of the Road (assuming that the leftmost point is 0 and rightmost point is 1) respectively to share the market. Appraise this suggestion.

Question 2

Sun Tzu said: The good fighters of old first put themselves beyond the possibility of defeat, and then waited for an opportunity of defeating the enemy.1 Under the framework of a complete and perfect information game, do you agree with Sun Tzu’s saying above? Write a short essay to discuss.

Note: The marking will be subjectively given according to your presentation and your views.