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Objectives: Find the value for 2 x n games and analyse strategies. To understand and apply dominance to reduce pay-off matrices. To graphically.

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Presentation on theme: "Objectives: Find the value for 2 x n games and analyse strategies. To understand and apply dominance to reduce pay-off matrices. To graphically."— Presentation transcript:

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5 Objectives: Find the value for 2 x n games and analyse strategies. To understand and apply dominance to reduce pay-off matrices. To graphically represent pay-offs for 2 x n games. Mixed Strategies A Beautiful Mind

6 Survival 3 men are on a hill, only 1 can come down alive. They are armed with pistols and honourable. They will take it in turns to shoot at 1 of their adversaries or fire into the air. The 1 st man has a 1/6 probability of shooting and killing. The 2 nd man a ½ probability. The 3 rd man a 5/6 probability. Q1) Who would you prefer to be? Q2) Who is most likely to die first? Q3)Who is most likely to remain alive? Q4) If you were the 1 st man what would your tactics be? Q5) Would you like to change your choice for Q1? Bilborough College Maths – Decision 2 game theory : mixed strategies (Adrian) 19/04/13

7 A less risky version Model the survival game using a six-faced die numbered 1, 2, 3, 4, 5, 6. Player A needs 6 to kill. Player B needs ≥ 4 to kill. Player C needs ≥ 2 to kill. Players have option of throwing or passing each time their turn comes around. Play in groups of 3 and tally results.

8 GamePlayer A : 1,2,SPlayer B: 1,2,SPlayer C: 1,2,S 1 2 3 4 5 6 7 8 9 10 11 12 TOTAL1=, 2=, S=

9 GamePlayer A : 1,2,SPlayer B: 1,2,SPlayer C: 1,2,S 1 2 3 4 5 6 7 8 9 10 11 12 TOTAL1=, 2=, S=

10 Objectives: Find the value for 2 x n games and analyse strategies. To understand and apply dominance to reduce pay-off matrices. To graphically represent pay-offs for 2 x 2 games. Mixed Strategies A Beautiful Mind

11 Pay-off matrix for player A 2 -1 3 0 2 -2

12 A’s expected pay-off

13 Finding the value 2-3p = 5p -2 Value (v) = (-1) x + 2 x (1 - ) = v = 3 x + (-2) x (1 - ) = P = V =

14 Activity Exercise 5B Pages 86-87 Q1,3,4 Nash Equilibrium Golden Balls

15 Activity Finish Multi guess worksheet

16 Pay-off matrix for player A 2 -1 3 0 2 -2 2-3p = 5p -2 Value (v) = (-1) x + 2 x (1 - ) = v = 3 x + (-2) x (1 - ) = P = V = Player B 2 -1 3 0 2 -2 -1 3 2 -2

17 How can we find the value of the game with pay-off matrix -2 0 ? 1 -2 -3 2

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