AQA D2 2007 January — Question 4

Exam BoardAQA
ModuleD2 (Decision Mathematics 2)
Year2007
SessionJanuary
TopicDynamic Programming
4
  1. Two people, Ros and Col, play a zero-sum game. The game is represented by the following pay-off matrix for Ros.
    \multirow{2}{*}{}\multirow[b]{2}{*}{Strategy}Col
    XYZ
    \multirow{3}{*}{Ros}I-4-30
    II5-22
    III1-13
    1. Show that this game has a stable solution.
    2. Find the play-safe strategy for each player and state the value of the game.
  2. Ros and Col play a different zero-sum game for which there is no stable solution. The game is represented by the following pay-off matrix for Ros.
    \cline { 2 - 5 } \multicolumn{1}{c|}{}Col
    \cline { 2 - 5 } \multicolumn{1}{c|}{}Strategy\(\mathbf { C } _ { \mathbf { 1 } }\)\(\mathbf { C } _ { \mathbf { 2 } }\)\(\mathbf { C } _ { \mathbf { 3 } }\)
    \multirow{2}{*}{Ros}\(\mathbf { R } _ { \mathbf { 1 } }\)321
    \cline { 2 - 5 }\(\mathbf { R } _ { \mathbf { 2 } }\)- 2- 12
    1. Find the optimal mixed strategy for Ros.
    2. Calculate the value of the game.
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