# Question: consider the finite 2 player game representing price competition in...

###### Question details

Consider the finite 2 player game, representing price competition in a market where al costumers buy from the seller with the lowest price. Both sellers simultaneously choose price, p1 and p2, where pi is in P = {0,1,2,3,4}. The profits to each seller are given in the payoff bi-matrix below, where seller 1 chooses row and seller 2 column.

Firm 2

p=0 | p=1 | p=2 | p=3 | p=4 | |
---|---|---|---|---|---|

p=0 | -5,-5 | -10,0 | -10,0 | -10,0 | -10,0 |

p=1 | 0,-10 | 0,0 | 0,0 | 0,0 | 0,0 |

p=2 | 0,-10 | 0,0 | 3,3 | 6,0 | 6,0 |

p=3 | 0,-10 | 0,0 | 0,6 | 4,4 | 8,0 |

p=4 | 0,-10 | 0,0 | 0,6 | 0,8 | 3,3 |

Firm 1

a.) Find and describe all strictly dominated pure strategies for Firm 1

b.) Find and describe all weakly dominated pure strategies for Firm 1

c.) Find and describe all pure strategy Nash equilibria