Question 1209230: Consider the following parlour game to be played between two players. Each player begins
with three chips: one red, one white, and one blue. Each chip can be used only once. To
begin, each player selects one of her chips and places it on the table, concealed. Both players
then uncover the chips and determine the payoff to the winning player. In particular, if both
players play the same kind of chip, it is a draw; otherwise, the following table indicates the
winner and how much she receives from the other player. Next, each player selects one of her
two remaining chips and repeats the procedure, resulting in another payoff according to the
following table. Finally, each player plays her one remaining chip, resulting in the third and
final payoff.
winning chip - payoff ($)
red beats white - 50
white beats blue -20
blue beats red - 10
matching colours - 0
(a) Formulate the payoff matrix for the game and identify possible saddle points.
[10 Marks]
(b) Construct a linear programming model for each player in this game.
[10 Marks]
(c) Produce an appropriate code to solve the linear programming model for this game.
[10 Marks]
(d) Solve the game for both players using the linear programming model and interpret your
solution in 3-5 sentences.
[10 Marks]
[Hint: Each player has the same strategy set. A strategy must specify the first chip chosen,
the second and third chips chosen. Denote the white, red and blue chips by W, R and B
respectively. For example, a strategy “WRB” indicates first choosing the white and then
choosing the red, before choosing blue at the end.]
Answer by ikleyn(52884)   (Show Source):
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