AQA D2 2011 June — Question 3

Exam BoardAQA
ModuleD2 (Decision Mathematics 2)
Year2011
SessionJune
TopicGroups
3
  1. Two people, Tom and Jerry, play a zero-sum game. The game is represented by the following pay-off matrix for Tom.
    Jerry
    \cline { 2 - 5 }StrategyABC
    TomI- 45- 3
    \cline { 2 - 5 }II- 3- 28
    \cline { 2 - 5 }III- 76- 2
    Show that this game has a stable solution and state the play-safe strategy for each player.
  2. Rohan and Carla play a different zero-sum game for which there is no stable solution. The game is represented by the following pay-off matrix for Rohan. \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{Carla} Rohan
    Strategy\(\mathbf { C } _ { \mathbf { 1 } }\)\(\mathbf { C } _ { \mathbf { 2 } }\)\(\mathbf { C } _ { \mathbf { 3 } }\)
    \(\mathbf { R } _ { \mathbf { 1 } }\)35- 1
    \(\mathbf { R } _ { \mathbf { 2 } }\)1- 24
    \end{table}
    1. Find the optimal mixed strategy for Rohan and show that the value of the game is \(\frac { 3 } { 2 }\).
    2. Carla plays strategy \(\mathrm { C } _ { 1 }\) with probability \(p\), and strategy \(\mathrm { C } _ { 2 }\) with probability \(q\). Find the values of \(p\) and \(q\) and hence find the optimal mixed strategy for Carla.
      (4 marks)
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      \includegraphics[max width=\textwidth, alt={}]{1aca4e91-d1b3-4a78-8880-e42a4fbf3ddb-11_2486_1714_221_153}
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