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Game Theory 4x4 Tables

Game Theory 4x4 Tables
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2015-08-09 10:35
Probability & StatisticsMatrixOptimization
This example demonstrates the normal form representation of 4x4 bi-matrices in Game Theory, visualizing calculations for pure strategy outcomes. Core concepts include matrices, probability & statistics, and optimization. GeoGebra commands used are Polygon, Max, If to construct the table, find maxima, and display conditional text. Suitable for high school students and learners interested in game theory and matrix applications.

GeoGebra Commands & Parameters

  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