ECON 230 Study Guide - Nash Equilibrium, Cooperative Game Theory, Strategic Dominance

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11 Mar 2014

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Strategic decisions result in payoffs for the players. Cooperative game: game in which participants can negotiate binding contracts that allow them to plan joint strategies. We focus on non-cooperative games, where it is essential to understand your opponents point of view and to deduce his likely response to your actions. Dominant strategy: strategy that is optimal no matter what an opponent does. Firm a does better if it does a certain move than it would in both options of the other move, so it must do the first move. When both players have a dominant strategy, we call it equilibrium in dominant strategies. If there is no dominant strategy, the firm without the strategy must put themselves in the other firms shoes and see if they have a dominant strategy, and what they would do, to decide what we would do.

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1. Which of the following statements about oligopolies is not correct?

a.		Oligopolistic firms always charge the monopoly price.
b.		Oligopolistic firms are interdependent in a way that firms in perfect competition are not.
c.		An oligopolistic market has only a few sellers.
d.		The actions of any one seller can have a large impact on the profits of all other sellers.

2. Which is true of an oligopoly market that reaches a Nash equilibrium?

a.		The firms will not have behaved as profit maximizers.
b.		A firm will have chosen its best strategy, given the strategies chosen by other firms in the market.
c.		A firm will not take into account the strategies of competing firms.
d.		The market price will be different for each firm.

3. In game theory, what is a dominant strategy?

a.		the best strategy for a player to follow, regardless of the what strategies other players use
b.		a strategy that makes every player better off
c.		a strategy that must appear in every game
d.		the best strategy for a player to follow only if other players are cooperative

4. Which of the following situations produces the largest profits for oligopolists?

a.		The firms reach a Nash equilibrium.
b.		The firms combine to produce the monopoly output level.
c.		The firms set prices equal to marginal cost.
d.		The firms produce a quantity of output that lies between the competitive outcome and the monopoly outcome.

1. Which of the following statements about oligopolies is not correct?

a.		Oligopolistic firms always charge the monopoly price.
b.		Oligopolistic firms are interdependent in a way that firms in perfect competition are not.
c.		An oligopolistic market has only a few sellers.
d.		The actions of any one seller can have a large impact on the profits of all other sellers.

2. Which is true of an oligopoly market that reaches a Nash equilibrium?

a.		The firms will not have behaved as profit maximizers.
b.		A firm will have chosen its best strategy, given the strategies chosen by other firms in the market.
c.		A firm will not take into account the strategies of competing firms.
d.		The market price will be different for each firm.

3. In game theory, what is a dominant strategy?

a.		the best strategy for a player to follow, regardless of the what strategies other players use
b.		a strategy that makes every player better off
c.		a strategy that must appear in every game
d.		the best strategy for a player to follow only if other players are cooperative

4. Which of the following situations produces the largest profits for oligopolists?

a.		The firms reach a Nash equilibrium.
b.		The firms combine to produce the monopoly output level.
c.		The firms set prices equal to marginal cost.
d.		The firms produce a quantity of output that lies between the competitive outcome and the monopoly outcome.

Glassworks and Clearsmooth compete in the local market for windshield repairs. The market size (total available profits) is $10 million per year. Each firm can choose whether to advertise on local television. If a firm chooses to advertise in a given year, it costs that firm $3 million. If one firm advertises and the other does not, then the former captures the whole market. If both firms advertise, they split the market 50:50. Even if both do not advertise, they split the market 50:50.
a) Suppose the two windshield-repair firms know they will compete for just one year. Write down the payoff matrix for this game. Find the Nash equilibrium strategies.
b) Suppose the firms play this game for five years in a row, and they know that at the end of five years, both firms plan to go out of business. What is the sub game-perfect equilibrium for this five-period game? Explain.
c) What would be a tit-for-tat strategy in the game described in part b?
d) Suppose that the firms play this game repeatedly forever, and suppose that future profits are discounted with an interest rate of 20% per period. Can you find a sub game-perfect equilibrium that involves higher annual payoffs than the equilibrium in part (b)? If so, explain what strategies are involved. If no, explain why not.

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ECON 230 Study Guide - Nash Equilibrium, Cooperative Game Theory, Strategic Dominance

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