Exam 16: Game Theory and Oligopoly

A particular market is served by two firms. The market demand curve is given by p = 200 - y. Each firm incurs a constant cost per unit of $50. The Cournot profit function for firm 1 in this market is given by:

Suppose the demand function in the industry is p = 100 - y and each firm has a constant marginal cost of $40. Suppose there is a monopoly firm and a potential entrant with a fixed cost of $100. The limit output is:

A Bertrand model of oligopoly is one in which competing firms:

Explain why a collusive equilibrium in a sequential game requires an infinite life.

The Cournot model of oligopoly is one in which competing firms:

A best response function:

The difference between Bertrand and Cournot models is that:

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If one firm honors the cartel agreement while the other firm defects, the output produced by the defecting firm is:

As the number of firms in a Cournot industry increases:

A self enforcing agreement is:

There are only two souvenir vendors at the Super Bowl. They choose their quantities simultaneously. They will not sell in the same market again. Are they likely to collude or not? Why?

When modeling an oligopoly as a prisoners dilemma problem the Nash equilibrium

A particular market is served by three firms. The market demand curve is given by p = 200 - y. Each firm incurs a constant cost per unit of $40. Firm 3's Cournot reaction function is given by:

Two firms produce a homogenous product. Let p denote the product's price. The output level of firm 1 is denoted by q₁, and the output level of firm 2 by q₂. The aggregate industry output is denoted by Q with Q = q₁ +q₂. The aggregate industry (inverse)demand is given by p = 10 - Q. The cost functions of the two firms are c₁(q₁)= 4q₁ and c₂(q₂)= 4q₂. i)Assume that the firms choose their output levels simultaneously (i.e., we have Cournot competition). What are the equilibrium output levels and profits of each firm in this case? ii)Suppose that firm 2 finds a cheaper way to produce the same product. The new cost function of firm 2 is c₂(q₂)= q₂. Assuming that the firms choose their output levels simultaneously, find the equilibrium output levels and profits of each firm.

Suppose the demand function in the industry is p = 100 - y and each firm has a constant marginal cost of $40. Suppose there is a monopoly firm and a potential entrant. The residual demand is given by:

The generalized no- entry condition is that potential entrants will enter as long as the inducement to entry is:

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If one firm honors the cartel agreement while the other firm defects, the profits to the defecting firm are:

The collusive solution is:

When modeling an oligopoly as a prisoners dilemma problem the optimal strategy

When modeling an oligopoly as a prisoners dilemma problem an agreement is a Nash equilibrium if