## Competing Costume Companies and Saddle Points

Suppose two costume companies, A and B,s each make clown, skeleton and space costumes. The total costume market is fixed. Experience indicates the following payoff matrix, which shows the sales of each costume by each company:

A\B | Clown | Skeleton | Space |

Clown | -2 | 0 | 4 |

Skeleton | 0 | 2 | 1 |

Space | -1 | -4 | 0 |

The table can be interpreted in this way. If both companies make clown costumes, then for every 20 sold, company A will lose two sames to company B. If company A makes clown costumes and B makes space costumes, then for every twenty costumes sold, company A will sell 4 more than company B. Company A can quickly decide not to make space costumes, because it will sell more skeleton costumes whatever company B make, since every entry in row 2 is greater than the corresponding entry in row 3. Hence we can ignore row 3 to give the matrix below. Row 2 is said to dominate row 3.

indicates the following payoff matrix, which shows the sales of each costume by each company:

A\B | Clown | Skeleton | Space |

Clown | -2 | 0 | 4 |

Skeleton | 0 | 2 | 1 |

Similarly company B will decide not to make space costumes, because the loss of sales to company A will be greater if company B makes space costumes than if it makes clown costumes. Hence company B will never make space costumes, and we can eliminate column 3. Column 1 is said to dominate column 3.

A\B | Clown | Skeleton |

Clown | -2 | 0 |

Skeleton | 0 | 2 |

Now it is easy to see that company A will sell most costumes by only making skeleton costumes, and company B will sell most costumes by only making clown costumes.

The entry in the second row, first column is a saddle point and the value of the game is 0.