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博弈论4x4表格

博弈论4x4表格
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2015-08-09 10:35
概率统计矩阵最值优化
①本范例演示了博弈论中4x4双矩阵的正则形式表示，通过可视化计算纯策略下的博弈结果；②涉及核心数学概念包括矩阵、概率统计、最值优化；③构造要点：使用Polygon（多边形）、Max（最大值）、If（条件判断）等GeoGebra命令绘制表格、计算最大值并显示条件文本；④适合高中及以上学生及对博弈论、矩阵应用感兴趣的学习者。

GeoGebra 命令及参数

  1. Polygon(O, O1, O2, O3) → poly1, o, o1, o2, o3
  2. Max(aL) → amax
  3. Max(bL) → bmax
  4. Max(cL) → cmax
  5. Max(dL) → dmax
  6. Max(AU) → Amax
  7. Max(BU) → Bmax
  8. Max(CU) → Cmax
  9. Max(DU) → Dmax
  10. If(AaL ≟ amax, 1, 0) → ColourAaL
  11. If(BaL ≟ amax, 1, 0) → ColourBaL
  12. If(CaL ≟ amax, 1, 0) → ColourCaL
  13. If(DaL ≟ amax, 1, 0) → ColourDaL
  14. If(AbL ≟ bmax, 1, 0) → ColourAbL
  15. If(BbL ≟ bmax, 1, 0) → ColourBbL
  16. If(CbL ≟ bmax, 1, 0) → ColourCbL
  17. If(DbL ≟ bmax, 1, 0) → ColourDbL
  18. If(AcL ≟ cmax, 1, 0) → ColourAcL
  19. If(BcL ≟ cmax, 1, 0) → ColourBcL
  20. If(CcL ≟ cmax, 1, 0) → ColourCcL
  21. If(DcL ≟ cmax, 1, 0) → ColourDcL
  22. If(AdL ≟ dmax, 1, 0) → ColourAdL
  23. If(BdL ≟ dmax, 1, 0) → ColourBdL
  24. If(CdL ≟ dmax, 1, 0) → ColourCdL
  25. If(DdL ≟ dmax, 1, 0) → ColourDdL
  26. If(AaU ≟ Amax, 0.8, 0) → ColourAaU
  27. If(AbU ≟ Amax, 0.8, 0) → ColourAbU
  28. If(AcU ≟ Amax, 0.8, 0) → ColourAcU
  29. If(AdU ≟ Amax, 0.8, 0) → ColourAdU
  30. If(BaU ≟ Bmax, 0.8, 0) → ColourBaU
  31. If(BbU ≟ Bmax, 0.8, 0) → ColourBbU
  32. If(BcU ≟ Bmax, 0.8, 0) → ColourBcU
  33. If(BdU ≟ Bmax, 0.8, 0) → ColourBdU
  34. If(CaU ≟ Cmax, 0.8, 0) → ColourCaU
  35. If(CbU ≟ Cmax, 0.8, 0) → ColourCbU
  36. If(CcU ≟ Cmax, 0.8, 0) → ColourCcU
  37. If(CdU ≟ Cmax, 0.8, 0) → ColourCdU
  38. If(DaU ≟ Dmax, 0.8, 0) → ColourDaU
  39. If(DbU ≟ Dmax, 0.8, 0) → ColourDbU
  40. If(DcU ≟ Dmax, 0.8, 0) → ColourDcU
  41. If(DdU ≟ Dmax, 0.8, 0) → ColourDdU
  42. If(AaL ≟ amax ∧ AaU ≟ Amax, 1, 0) → ColourAa
  43. If(BaL ≟ amax ∧ BaU ≟ Bmax, 1, 0) → ColourBa
  44. If(CaL ≟ amax ∧ CaU ≟ Cmax, 1, 0) → ColourCa
  45. If(DaL ≟ amax ∧ DaU ≟ Dmax, 1, 0) → ColourDa
  46. If(AbL ≟ bmax ∧ AbU ≟ Amax, 1, 0) → ColourAb
  47. If(BbL ≟ bmax ∧ BbU ≟ Bmax, 1, 0) → ColourBb
  48. If(CbL ≟ bmax ∧ CbU ≟ Cmax, 1, 0) → ColourCb
  49. If(DbL ≟ bmax ∧ DbU ≟ Dmax, 1, 0) → ColourDb
  50. If(AcL ≟ cmax ∧ AcU ≟ Amax, 1, 0) → ColourAc
  51. If(BcL ≟ cmax ∧ BcU ≟ Bmax, 1, 0) → ColourBc
  52. If(CcL ≟ cmax ∧ CcU ≟ Cmax, 1, 0) → ColourCc
  53. If(DcL ≟ cmax ∧ DcU ≟ Dmax, 1, 0) → ColourDc
  54. If(AdL ≟ dmax ∧ AdU ≟ Amax, 1, 0) → ColourAd
  55. If(BdL ≟ dmax ∧ BdU ≟ Bmax, 1, 0) → ColourBd
  56. If(CdL ≟ dmax ∧ CdU ≟ Cmax, 1, 0) → ColourCd
  57. If(DdL ≟ dmax ∧ DdU ≟ Dmax, 1, 0) → ColourDd
  58. Polygon(A, B, 4) → poly2, c, d, e, f, C, D
  59. Polygon(E, D, 4) → poly3, g, h, i, j, F, G
  60. If(AaL ≟ amax ∧ AbL ≟ bmax ∧ AcL ≟ cmax ∧ AdL ≟ dmax, true, false) → DomA
  61. If(BaL ≟ amax ∧ BbL ≟ bmax ∧ BcL ≟ cmax ∧ BdL ≟ dmax, true, false) → DomB
  62. If(CaL ≟ amax ∧ CbL ≟ bmax ∧ CcL ≟ cmax ∧ CdL ≟ dmax, true, false) → DomC
  63. If(DaL ≟ amax ∧ DbL ≟ bmax ∧ DcL ≟ cmax ∧ DdL ≟ dmax, true, false) → DomD
  64. If(AaU ≟ Amax ∧ BaU ≟ Bmax ∧ CaU ≟ Cmax ∧ DaU ≟ Dmax, true, false) → Doma
  65. If(AbU ≟ Amax ∧ BbU ≟ Bmax ∧ CbU ≟ Cmax ∧ DbU ≟ Dmax, true, false) → Domb
  66. If(AcU ≟ Amax ∧ BcU ≟ Bmax ∧ CcU ≟ Cmax ∧ DcU ≟ Dmax, true, false) → Domc
  67. If(AdU ≟ Amax ∧ BdU ≟ Bmax ∧ CdU ≟ Cmax ∧ DdU ≟ Dmax, true, false) → Domd
  68. Polygon(H, I, J, K) → poly4, h_1, i_1, j_1, k
  69. Polygon(L, M, N, P) → poly5, l, m, n, p
  70. Polygon(Q, R, S, T) → poly6, q_1, r_1, s, t
  71. If(ELLEFT1 ≟ false, Append[U1U, C2]) → list1
  72. If(ELLEFT2 ≟ false, Append[U1U, C4]) → list2
  73. If(ELLEFT3 ≟ false, Append[U1U, C6]) → list3
  74. If(ELLEFT4 ≟ false, Append[U1U, C8]) → list4
  75. If(ELLEFT1 ≟ false, Append[U1U, C2]) → list5
  76. If(ELLEFT2 ≟ false, Append[U1U, C4]) → list6
  77. If(ELLEFT3 ≟ false, Append[U1U, C6]) → list7
  78. If(ELLEFT4 ≟ false, Append[U1U, C8]) → list8