## Answers

The answer to Q 3:

1. The Laplace Principle:

Step 1: Calculate P for each row.

n= 3 (Three alternatives) | |||||

P= 1/3(P1+P2+P3) | |||||

State of Nature | |||||

S1 | S2 | S3 | Expected Payoff | ||

A1 | 50 | 80 | 80 | 1/3(50+80+80) | |

A2 | 60 | 70 | 20 | 1/3(60+70+20) | |

A3 | 90 | 30 | 60 | 1/3(90+30+60) | |

Step 2: Select the maximum Pay off from the expected payoff

State of Nature | ||||

S1 | S2 | S3 | Expected Payoff | |

A1 | 50 | 80 | 80 | 70 |

A2 | 60 | 70 | 20 | 50 |

A3 | 90 | 30 | 60 | 60 |

Chosen Alternative A1.

2. The Maxi-max Rule:

Step 1: Find the maximum of each row.

State of Nature | ||||

S1 | S2 | S3 | Maximum Payoff | |

A1 | 50 | 80 | 80 | 80 |

A2 | 60 | 70 | 20 | 70 |

A3 | 90 | 30 | 60 | 90 |

Step 2: Select the maximum from the column of maximum pay off.

State of Nature | ||||

S1 | S2 | S3 | Maximum | |

A1 | 50 | 80 | 80 | 80 |

A2 | 60 | 70 | 20 | 70 |

A3 | 90 | 30 | 60 | 90 |

Chosen alternative: A3 S1.

3. The Hurwicz Rule:

Step 1: Identify the maximum and minimum of each row:

State of Nature | |||||

S1 | S2 | S3 | Maximum | Minimum | |

A1 | 50 | 80 | 80 | 80 | 50 |

A2 | 60 | 70 | 20 | 70 | 20 |

A3 | 90 | 30 | 60 | 90 | 30 |

Step 2: Calculate P for each alternative.

State of Nature | ||||||

S1 | S2 | S3 | Maximum | Minimum | H | |

A1 | 50 | 80 | 80 | 80 | 50 | 72.5 |

A2 | 60 | 70 | 20 | 70 | 20 | 57.5 |

A3 | 90 | 30 | 60 | 90 | 30 | 75 |

p= α*maximum+(1-α)*Minimum |

For A1, P=0.75*80+(1-0.75)*50 |

For A2, P = 0.75*70+(1-0.75)*20 |

For A3, P = 0.75*90+(1-0.75)*30 |

Step 3: Select the maximum payoff from column H

The highest payoff is with alternative A3.

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