AQA D2 2010 January — Question 3

Exam BoardAQA
ModuleD2 (Decision Mathematics 2)
Year2010
SessionJanuary
TopicDynamic Programming
3
  1. Two people, Ann and Bill, play a zero-sum game. The game is represented by the following pay-off matrix for Ann.
    \multirow{5}{*}{Ann}Bill
    Strategy\(\mathbf { B } _ { \mathbf { 1 } }\)\(\mathbf { B } _ { \mathbf { 2 } }\)\(\mathbf { B } _ { \mathbf { 3 } }\)
    \(\mathbf { A } _ { \mathbf { 1 } }\)-10-2
    \(\mathbf { A } _ { \mathbf { 2 } }\)4-2-3
    \(\mathbf { A } _ { \mathbf { 3 } }\)-4-5-3
    Show that this game has a stable solution and state the play-safe strategies for Ann and Bill.
  2. Russ and Carlos play a different zero-sum game, which does not have a stable solution. The game is represented by the following pay-off matrix for Russ.
    Carlos
    \cline { 2 - 5 }Strategy\(\mathbf { C } _ { \mathbf { 1 } }\)\(\mathbf { C } _ { \mathbf { 2 } }\)\(\mathbf { C } _ { \mathbf { 3 } }\)
    \cline { 2 - 5 } Russ\(\mathbf { R } _ { \mathbf { 1 } }\)- 47- 3
    \cline { 2 - 5 }\(\mathbf { R } _ { \mathbf { 2 } }\)2- 11
    1. Find the optimal mixed strategy for Russ.
    2. Find the value of the game.
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