Consider the following parlor game to be played between two players. Each player beginswith 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, thefollowing 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 playsher one remaining chip, resulting in the third and final payoff.Winning Chip Payoff ($)Red beats white 250White beats blue 100Blue beats red 50Matching colors 0(a) Formulate the payoff matrix for the game and identify possible saddle points.(b) Construct a linear programming model for each player in this game.(c) Produce an appropriate code to solve the linear programming model for this game.(d) Solve the game for both players using the linear programming model.[Hint: Each player has the same strategy set. A strategy must specify the first chipchosen, the second and third chips chosen. Denote the white, red and blue chips by W,R and B respectively. For example, a strategy “WRB” indicates first choosing the whiteand then choosing the red, before choosing blue at the end.]
Consider the following parlor game to be played between two players. Each player begins
with three chips: one red, one white, and one blue. Each chip can be used only once.
To begin, each player selects one of her chips and places it on the table, concealed.
Both players then uncover the chips and determine the payoff to the winning player.
In particular, if both players play the same kind of chip, it is a draw; otherwise, the
following table indicates the winner and how much she receives from the other player.
Next, each player selects one of her two remaining chips and repeats the procedure,
resulting in another payoff according to the following table. Finally, each player plays
her one remaining chip, resulting in the third and final payoff.
Winning Chip Payoff ($)
Red beats white 250
White beats blue 100
Blue beats red 50
Matching colors 0
(a) Formulate the payoff matrix for the game and identify possible saddle points.
(b) Construct a linear programming model for each player in this game.
(c) Produce an appropriate code to solve the linear programming model for this game.
(d) Solve the game for both players using the linear programming model.
[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.]
Step by step
Solved in 2 steps with 2 images
