Static strategic interaction

Question 1

What is game theory?

Answer 1

The study of strategic interactions among two or more economic actors.

Question 2

What is a strategic decision?

Answer 2

An action made based on the anticipation of others’ actions.

Question 3

What is a simultaneous game?

Answer 3

A game in which participants choose their actions simultaneously without knowing their opponents strategies. Examples includes Cournot and Bertrand models, in which firms choose quantities or prices simultaneously.

Question 4

1. What are the three common elements of an economic game?

Answer 4

All economic games have three common elements:

a. Players, or the decision makers in a game
b. Strategies, or a player’s plan of action in a game. Generally, the strategy a player chooses to pursue depends on the anticipated actions of the other players.
c. Payoffs, or the outcome of a game

Question 5

2. What differentiates game theory from single-agent problems?

Answer 5

Unlike single-agent problems (only the player’s own choices affect her payoffs), game theory is concerned with situations in which a player’s actions affect her opponents’ choices and payoffs, and not just her own. A monopolist choosing an output level given the demand and marginal cost curves it faces, or the consumers’ utility-maximization problem are examples of sing-agent problems.

Question 6

What is the optimal strategy?

Answer 6

Predicting behaviour in games is about finding a player’s optimal strategy - the action that has the highest expected payoff. This can be difficult because a particular strategy may be optimal for a player if her opponent chooses one action, but not optimal if her opponent chooses another action. I.e. the optimal strategy must be a best response to the other player’s chosen strategy.

Question 7

What is a dominant strategy and a dominated strategy?

Answer 7

Dominant strategy: a winning strategy for a player, regardless of her opponents’ strategies. A strategy that is always the best thing for a player to do.
Dominated strategy: a losing strategy regardless of her opponents’ strategies. Strategies that are never the right thing to do.
When one strategy is dominant, all other strategies must be dominated.

Question 8

What is a payoff matrix?

Answer 8

A table that lists the players, strategies, and payoffs of an economic game. It gives game in normal form.

Question 9

3. How does the existence of multiple Nash equilibria complicate the solution to an economic game?

Answer 9

In games with multiple Nash equilibria, just as with all games with Nash equilibria, firms’ best responses depend on competitor firms’ decisions. As a result, we can narrow down the possible outcomes but cannot determine the final outcome of the game prior to its being played.

Question 10

4. How can a payoff matrix be used to find a player’s optimal strategy?

Answer 10

The payoff matrix incorporates information about all three elements of a game-its players, their possible strategies, and the associated payoffs-and therefore can be used to eliminate dominant strategies as possible equilibrium outcomes and to find the players’ mutual best responses or the strategy that will lead to the Nash equilibrium or equilibria.

Question 11

What is a pure strategy and what is a mixed strategy?

Answer 11

Pure strategy: a strategy in which the player chooses a particular action with certainty
Mixed strategy: a strategy in which the player randomizes her actions

Question 12

5. Why might a player pursue a mixed strategy?

Answer 12

In some situations, it may be best for the player to choose actions randomly from the set of available pure strategies and therefore to pursue a mixed strategy. One example would be in a game in which a pure strategy does not lead to a mutual best response (i.e., no box with two checks using the check-box method). No set of strategies exists such that both players simultaneously choose the best response to the other’s choice.

Question 13

How can we arrive at a mixed strategy equilibrium?

Answer 13

To arrive at a mixed strategy equilibrium, each player needs to pick the probability of taking each action so that the player’s opponent is indifferent between her own actions.

Question 14

6. Why is the maximin strategy considered a conservative strategy?

Answer 14

A player using a maximin strategy is not going for the greatest payoff, but rather is choosing the conservative strategy of minimizing her losses. Therefore, maximum can be useful in games in which one or more of the players might be irrational.

Question 15

What is oligopoly?

Answer 15

A market structure characterised by competition among a small number of firms.

Question 16

What is monopolistic competition?

Answer 16

A type of imperfect competition with a large number of firms in which each firm has some market power but makes zero economic profit in the long run.

Question 17

1. Name some different forms of imperfect competition.

Answer 17

Imperfectly competitive markets have characteristics between those of perfectly competitive and monopolistic markets. Oligopolies and monopolistic competition are two examples of imperfectly competitive markets.

Question 18

2. Define Nash equilibrium. Why do firms in oligopoly situations reach Nash equilibria?

Answer 18

Nash equilibrium is an equilibrium in which each firm does the best it can conditional on the actions its competitors take. Since oligopolies are in a stable equilibrium where no firm wants to change its behaviour when it learns of its competitors’ market behaviour, we say that oligopolies reach a Nash equilibrium.

Question 19

What is a prisoner’s dilemma?

Answer 19

A situation in which the Nash equilibrium outcome is worse for all involved than another (unstable) outcome.

Question 20

What is Bertrand competition?

Answer 20

Oligopoly model in which each firm chooses the price of its product. Firms sell the same product, consumers compare prices and chooses the product with the lowest price.

Question 21

What are the three assumptions for Bertrand competition with identical goods?

Answer 21

Firms sell identical products. The firms compete by choosing the price at which they sell their products. The firms set their prices simultaneously.

Question 22

4. What is the market equilibrium in Bertrand competition with identical goods?

Answer 22

The market outcome of Bertrand competition is identical to that of perfect competition: At equilibrium, price equals marginal cost and quantity equals the competitive market quantity. This is because all firms have a strong incentive to continue to cut prices to gain more of the market. Firms will continue to slash prices until all firms charge a price equal to the marginal cost of production. (If firms have different marginal costs, the equilibrium is for the lowest-cost firm(s) to charge a price just under the second-lowest cost in the market)

Question 23

Why do firms in the Bertrand competition model face a demand that is perfectly elastic?

Answer 23

Because consumers only care about the price of the good, each firm faces a demand that is perfectly elastic. Any increase in a firm’s price results in it losing all of its market share.

Question 24

What are the assumptions for Cournot competition with identical goods?

Answer 24

Firms sell identical products. Firms compete by choosing a quantity to produce. All goods sell for the same price - the market price, which is determined by the sum of the quantities produced by all the firms in the market. Firms choose quantities simultaneously.

Question 25

What is Cournot competition?

Answer 25

Oligopoly model in which each firm chooses its production quantity. Individual firms do not control the price of their goods. First, all firms in the industry decide how much they will product; then based on the quantity produced by all firms, the market demand curve determines the price at which all firms’ output will sell.

Question 26

5. Contrast Bertrand and Cournot competition. Why do they reach different market equilibria?

Answer 26

Firms in Bertrand competition set their prices simultaneously. In contrast, firms in Coumot competition choose quantities simultaneously, and sell their products at the same market price. As a result, the equilibrium in Bertrand competition is the result of price cutting; as we saw in Question 4, this outcome is equivalent to the perfectly competitive equilibrium. The Coumot equilibrium is based on quantity decisions, and firms in Cournot competition are in equilibrium at the point where their reaction curves intersect.

Question 27

How can we find the equilibrium in a Cournot oligopoly?

Answer 27

The market quantity Q is the sum of the quantities produced in the firms.
First, we find each producer’s marginal revenue curve, and then find the quantity at which marginal revenue equals marginal cost.
The firm produces the quantity at which its residual marginal revenue equals its marginal cost.

Question 28

6. What does the residual demand curve tell us about a firm’s output in Cournot competition?

Answer 28

The residual demand curve gives the demand remaining for a firm’s output given its competitor firms’ outputs.

Question 29

What is a reaction curve?

Answer 29

A function that relates a firm’s best response to its competitor’s possible actions. In Cournot competition, this is the firm’s best production response to its competitor’s possible quantity choices. Because both reaction curves are downward-sloping, a firm’s optimal output falls as the other producer’s output rises.

Question 30

7. How can reaction curves be used to find a firm’s equilibrium in Cournot competition?

Answer 30

In Cournot competition, the reaction curve shows a firm’s best production response to its competitor’s possible quantity choices. The Cournot equilibrium occurs at the intersection of the two firms’ reaction curves. To solve for equilibrium, we need to substitute one firm’s reaction curve into the reaction curve for the other firm.

Question 31

How can we find a company’s reaction curve?

Answer 31

Substitute the function for Q (probably q_1+q_2+⋯+q_k) into the market inverse demand curve. Then derive each firm’s marginal revenue curve. Each firm will set its marginal revenue equal to its marginal cost to maximize profit. From this, we can obtain each firm’s reaction curve.

Question 32

What happens if there are more than two firms in a Cournot Oligopoly?

Answer 32

If there are more than two firms in a Cournot oligopoly, the total quantity, profit and price remain between the monopoly and perfectly competitive extremes. However, the more firms there are, the closer these outcomes get to the perfectly competitive case, with price equalling marginal cost and economic profits being zero. Having more competitors means than any single firm’s supply decision becomes a smaller and smaller part of the total market - hence, with very large number of firms the producer essentially becomes a price taker. Thus, more firms in a Cournot oligopoly lead to lower prices, higher total output and lower average firm profits.

Question 33

When can the Cournot model be a good predictor of market outcomes even if firms choose their prices in the short run?

Answer 33

In industries in which there are large costs of investing in capacity, so that firms don’t change their capacity very often e.g. apartments.

Question 34

What is an important similarity between perfect competition and monopoly?

Answer 34

No strategic interaction

Question 35

What are the steps to determine the Nash equilibrium?

Answer 35

Step 1: Firm 1’s best reply
Step 2: Best reply for firm 2 - interaction of firms
Equilibrium: pair of prices such that no firm can increase profit by unilaterally changing
price (no-one wants to change) Intersection of best replies!