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50p+10(1-p)

50p+10(1-p). 20p+80(1-p). CC better for Navratilova. DL better for Navratilova. Evert’s BR p(q). Navratilova’s BR q(p). If p=0.7, Navratilova is indiff between q=0 or q=1 or anything in the middle. Evert’s BR p(q). Navratilova’s BR q(p).

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50p+10(1-p)

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  1. Game Theory ECO4400

  2. Game Theory ECO4400

  3. 50p+10(1-p) 20p+80(1-p) Game Theory ECO4400

  4. CC better for Navratilova DL better for Navratilova Game Theory ECO4400

  5. Game Theory ECO4400

  6. Evert’s BR p(q) Navratilova’s BR q(p) If p=0.7, Navratilova is indiff between q=0 or q=1 or anything in the middle Game Theory ECO4400

  7. Evert’s BR p(q) Navratilova’s BR q(p) Reflected across the 45degrees line (switch p and q) Game Theory ECO4400

  8. Different values Game Theory ECO4400

  9. Game Theory ECO4400

  10. Min=62 if p=0.7 Game Theory ECO4400

  11. 80p+20(1-p) 50p+90(1-p) Game Theory ECO4400

  12. Navratilova picks CC if p<0.7 to minimize Evert’s payoff (zero-sum game) Navratilova picks DL if p>0.7 Game Theory ECO4400

  13. New Game Theory ECO4400

  14. Game Theory ECO4400

  15. 50q+80(1-q) 70q+60(1-q) 90q+20(1-q) Game Theory ECO4400

  16. 65 Game Theory ECO4400

  17. Not a unique q for Navratilova if Lob (horizontal line) gives payoffs of 70 and 70 to Evert 1/3 5/7 Game Theory ECO4400

  18. 4.c) Domination by a mixed strategy Was 70 Was 60 Game Theory ECO4400

  19. 4.c) Domination by a mixed strategy Game Theory ECO4400

  20. 4.c) Domination by a mixed strategy Orange line: Mix of DL and CC For p=1 Game Theory ECO4400

  21. 4.c) Domination by a mixed strategy Orange line: Mix of DL and CC For p<1 Game Theory ECO4400

  22. 4.c) Domination by a mixed strategy Orange line: Mix of DL and CC For p smaller Game Theory ECO4400

  23. 4.c) Domination by a mixed strategy Orange line: Mix of DL and CC For p smaller! Game Theory ECO4400

  24. 4.c) Domination by a mixed strategy Orange line: Mix of DL and CC For p=0.25: Mix line Game Theory ECO4400

  25. 4.c) Domination by a mixed strategy Orange line: Mix of DL and CC For p going to 0 (almost CC line) Game Theory ECO4400

  26. qL qR qC=1-qL-qR pL pC=1-pL-pR pR Game Theory ECO4400

  27. For Goalie: 55qL+10qC+10qR For Kicker: 45pL+85pC+95pR Game Theory ECO4400

  28. 5.b) Some strategies unused Was 85 Was 85 Game Theory ECO4400

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