Find the set of rationalizable strategies find all pure and

Question

Assignemnt

1. For the following game:

(i) Find the set of rationalizable strategies.

(ii) Find all pure and mixed-strategy Nash Equilibria.

2. Let us go back to the Cournot duopoly model where firms 1 and 2 select their production levels q₁ and q₂, respectively. So far, we have assumed that both firms have the same production cost. Let us relax this assumption in this exercise and consider an asymmetric Cournot duopoly game where the two firms have different production costs. Suppose the cost for firm 1 of producing q₁ units is 2 • q₁, while the cost for firm 2 of producing q₂ units is 4 • q₂. Suppose that the market price is given by p = 12 - q₁ - q₂. Answer the following:

(i) Write down the payoff functions u₁(q₁, q₂) and u₂(q₁, q₂).

(ii) Calculate the firms' best response functions BR₁(q₂) and BR₂(q₁).

(iii) Find the pure-strategy Nash equilibrium (q₁*, q₂*) in this game.

3. Take the following extensive game.

(i) Write the game in Normal Form.

(ii) Look for all Nash Equilibria (in pure and mixed-strategies).