Assignment

1. This problem is related to the discussion of what happens in the Bertrand Competition model once we introduce capacity constraints. Consider a Bertrand, price-competition model between two firms with capacity constraints. Suppose the market consists of 20 consumers, each of which will purchase one unit of the good. Suppose that each consumer is willing to pay at most $2.00 for the good. Suppose that each unit can be produced at a cost of $0.50 (fifty cents) and this cost is the same for both firms. Suppose that each firm can produce at most 15 units of the good (so the capacity constraint is 15 units for each firm).

(i) Is there a pure-strategy Nash equilibrium?

(ii) Find the Nash equilibria in this game.

2. For each of the following games:

i. Determine whether they are strictly competitive games.

ii. Find all the Nash equilibria (in pure and mixed strategies).

iii. Find the security strategies for each player.

3. For each of these games:

i. Determine whether they are strictly competitive games.

ii. Find all the Nash equilibria (in pure and mixed strategies).

iii. Find the security strategies for each player.

4. For each of these games:

(i) Determine whether they are strictly competitive games.

(ii) Find the security strategies for each player and determine whether they are rationalizable.