Consider the horizontal quality model on the unit interval from 0 to 1. There are Consumers located uniformly along with the interval. There are two firms, with zero marginal costs, initially located at 0 to 1. Consumers will buy one unit of the good from the lowest cost retailer as long as the effective price is below V. They have transportation costs of t getting from their location to the store and back.
1. If both firms locate together in the middle, what is the equilibrium price?
2. Show that firm 1 has a profitable deviation from locating in the middle with the other firm.
3. Show that if firm 1 moves away from firm 2, firm 2 will want to deviate as well.
4. Explain why there is no pure-strategy Nash equilibrium in this game.
5. In principle, what objects must on solve to find the mixed strategy equilibrium?
Consider the horizontal quality model on the unit interval from 0 to 1. There are Consumers located uniformly along with the interval. There are two firms, with zero marginal costs, initially located at 0 to 1. Consumers will buy one unit of the good from the lowest cost retailer as long as the effective price is below V. They have transportation costs of t getting from their location to the store and back.
1. If both firms locate together in the middle, what is the equilibrium price?
2. Show that firm 1 has a profitable deviation from locating in the middle with the other firm.
3. Show that if firm 1 moves away from firm 2, firm 2 will want to deviate as well.
4. Explain why there is no pure-strategy Nash equilibrium in this game.
5. In principle, what objects must on solve to find the mixed strategy equilibrium?
