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Solutions to Nash Equilibrium Exercises

Solutions to Nash Equilibrium Exercises. NOTE: I have coloured payoffs green if they are the best response rather than underlining. A Nash equilibrium is therefore a square with two green payoffs. If you want to discuss these solutions, email me or see me in my office hour. GAME 1.

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Solutions to Nash Equilibrium Exercises

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  1. Solutions to Nash Equilibrium Exercises NOTE: I have coloured payoffs green if they are the best response rather than underlining. A Nash equilibrium is therefore a square with two green payoffs. If you want to discuss these solutions, email me or see me in my office hour.

  2. GAME 1 PLAYER TWO a b Nash Equilibrium at 1b2a. A is dominant strategy for 2. a 0 , 5 5 , 0 PLAYER ONE 4 , 4 1 , 1 b Confused? Click here for an animated explanation.

  3. GAME 2 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. No dominant strategy. a 2 , 1 0 , 0 PLAYER ONE 0 , 0 1 , 2 b

  4. GAME 3 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. A is weakly dominant strategy for 1. a 1 , 1 0 , 0 PLAYER ONE 0 , 1 0 , 2 b

  5. GAME 4 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. No dominant strategy. a 2 , 1 0 , 0 PLAYER ONE 0 , 0 1 , 2 b

  6. GAME 5 PLAYER TWO a b Nash Equilibrium at 1b2a. B is dominant strategy for 1; A is dominant strategy for 2. a 5 , 9 5 , 4 PLAYER ONE 8 , 8 6 , 7 b

  7. GAME 6 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. No dominant strategy. a 14 , 10 0 , 1 PLAYER ONE 2 , 1 1 , 2 b

  8. GAME 7 PLAYER TWO a b Nash Equilibriua at 1a2a and 1b2b. A is weakly dominant strategy for 1. a 1 , 3 0 , 2 PLAYER ONE 0 , 2 0 , 3 b

  9. GAME 8 PLAYER TWO a b Nash Equilibrium at 1b2b. B is dominant strategy for 2. a 5 , 0 1 , 1 PLAYER ONE 1 , 2 2 , 3 b

  10. GAME 9 PLAYER TWO a b Nash Equilibrium at 1b2a. A is dominant strategy for 2; B is dominant strategy for 1. a 17 , 40 20 , 30 PLAYER ONE 18 , 23 91 , 21 b

  11. GAME 10 PLAYER TWO a b Nash Equilibrium at 1b2b. B is dominant strategy for both 1 and 2. a 1 , 1 -1 , 4 PLAYER ONE 2 , 2 0 , 3 b

  12. GAME 1 PLAYER TWO a b LET’S BE PLAYER TWO. IF PLAYER ONE PLAYS “A” WE CAN EITHER PLAY “A” AND GET 5 OR WE CAN PLAY “B” AND GET 0 SO WE PLAY “A” a 0 , 5 0 , 5 5 , 0 PLAYER ONE 4 , 4 1 , 1 b

  13. GAME 1 PLAYER TWO a b WE’RE STILL PLAYER TWO, BUT... THIS TIME, IF PLAYER ONE PLAYS “B” WE CAN EITHER PLAY “A” AND GET 4 OR WE CAN PLAY “B” AND GET 1 SO WE PLAY “A” a 0 , 5 5 , 0 PLAYER ONE 4, 4 4 , 4 1 , 1 b

  14. GAME 1 PLAYER TWO a b NOW LET’S BE PLAYER ONE. IF PLAYER TWO PLAYS “A” WE CAN EITHER PLAY “A” AND GET 0 OR WE CAN PLAY “B” AND GET 4 SO WE PLAY “B” a 0 , 5 5 , 0 PLAYER ONE 4 , 4 4 , 4 1 , 1 b

  15. GAME 1 PLAYER TWO a b FINALLY, IF PLAYER TWO PLAYS “B” WE CAN EITHER PLAY “A” AND GET 5 OR WE CAN PLAY “B” AND GET 1 SO WE PLAY “A” a 0 , 5 5 , 0 5 , 0 PLAYER ONE 4 , 4 1 , 1 b

  16. GAME 1 A Nash Equilibrium is easy to spot – it’s where a square has two green payoffs. In this case, then, it is 1b2a. Is there a dominant strategy? Yes. If 1 plays “A”, 2 plays “A” And if 1 plays “B”, 2 plays “A” So A is a dominant strategy for 2. PLAYER TWO a b a 0 , 5 5 , 0 PLAYER ONE 4 , 4 1 , 1 b

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