TOPIC 8: OLIGOPOLY AND GAME THEORY

Topic 8 | Part 1 30 May 2013Date

ANTITRUST ECONOMICS 2013David S. EvansUniversity of Chicago, Global Economics Group

Elisa MariscalCIDE, ITAM, CPI

2Overview

Part 1

Role of Oligopolies in the

Economy

Game Theory and Strategic

Behavior

Part 2

Oligopoly Theory: Cournot

and Bertrand

Dynamic Games and Competition

3 Role of Oligopolies in the Economy

4The “rough” spectrum of competition

• Industries appear to be “pretty competitive” with many fewer firms than under atomistic competition; e.g. an industry with 10 firms, each with 10 percent market shares would ordinarily be pretty competitive.

Industries are competitive when there is a large number of firms and none of them is large enough to influence price (atomistic competition) or the threat of entry prevents incumbents from increasing prices beyond the competitive level (contestable markets).

• Industry is effectively a monopoly if there is a single firm that is so large that it can dictate price; its ability to do so requires barriers that prevent the competitive fringe from expanding and new entrants from coming in.

Industries are monopolies when there is a single firm.

• Industry is often said to be an oligopoly when there are a handful of significant firms that have to take each other’s actions into account in deciding on pricing and other business decisions (the lines aren’t firm though).

Industries are oligopolies when there are a few large firms that compete with each other.

5

Firms act largely independently of each other in competition and monopoly but not in oligopoly

A monopoly firm faces no direct competitor and therefore sets its price constraint only based on the level of demand.

A competitive firm cannot affect price because it is too small relative to the market (or because it faces a credible threat of entry). It takes the market price as given.

An oligopoly has to consider the actions and reactions of each of its rivals; as a result an oligopoly’s price depends on its rivals’ prices.

6A small number of firms dominate many industries

Game consoles (Xbox, Sony Playstation, Nintendo)

Large commercial aircraft manufacturing (Airbus and Boeing)

Mobile phone operators (Vodafone, T-Mobile, Orange, O2, ...)

Supermarkets (Tesco, Sainsbury, …)

Stock exchanges (NYSE/Euronext, LSE, Deutsche-Borse, …)

7Concentration in selected US industries

Source: US Economic Census

Industry 4 largest companies

8 largest companies

20 largest companies

Motor Vehicle 82.4% 91.8% 98.8%

Aircraft Manufacturing 62.3% 78.1% 88.0%

Soft Drinks 47.5% 55.6% 77.9%

Breweries 89.7% 93.4% 95.2%

Tobacco 83.4% 93.3% 99%

8Oligopoly industries are ripe for competition issues

Mergers—more likely lead to harm to consumers when industry will become more concentrated and farther from competition and closer to oligopoly

Cartels—may be easier to form cartels when there are fewer players to coordinate.

Abuse—greater ability to engage in strategic behavior targeted to rivals when a firm has more pricing ability.

It is important that competition policy have tools that can help analyze issues in these industries.

9

Economic models of oligopoly account for strategic interactions among firms

Perfect competition—assumes interactions away because firms are too small to matter

Single-firm profit maximization models—monopoly and monopolistic competition—take demand as given including the price of substitutes.

We need a theory which takes interdependencies into account when there is a small number of firms.

10

Modeling interactions among firms and people is tricky

Why don’t you bump into people traveling in the opposite direction when you walk down the sidewalk?

You and a friend agree to meet in Paris but don’t have any way to communicate because of global meltdown of the internet and phones and haven’t agreed where. Will you meet and where?

EasyJet can make more profits through a fare decrease but only if British Air doesn’t follow on competing routes. Should it decrease fares?

Game theory provides a set of tools for thinking through these sorts of questions and provides the basis for analyzing strategic interactions among firms.

11 Game Theory and Strategic Behavior

12

“Game theory” provides insights into many problems involving interactions

Game theory recognizes the mutual interdependence between players and that players take these into account in making decisions.Field established by John von Neumann, a mathematician who is also credited with inventing the modern computer. See Theory of Games and Economic Behavior with Oskar Morgenstern (1944).

Game theory is like statistics: it is a field that is applied in many diverse areas ranging from biology to sociology to political science to law (in the Cold War it was the theoretical foundation of the theory of “mutually assured destruction” (MAD)). It is a mathematical field with heavy influence from economics and psychology.

Major development was the paper by John Nash “Non-Cooperative Games” that established what is now called the “Nash equilibrium” (Nash won the Nobel Prize in Economics shortly after having come out of a 25 year period of being delusional. See A Beautiful Mind by Sylvia Nasar or the movie with Russell Crowe.)

13Basics of game theory

A “game” refers to any situation in which decisions are made in anticipation of decisions made by others.

A game is a stylized model that depicts situations of strategic behavior, where the payoff (the reward at the end of the game) for one agent depends on its own actions as well as on the actions of other agents.

Each “player” forms a “strategy” and hopes to receive a “payoff”.

In a “cooperative” game each player can make side-payments to the other players. A cartel is the result of a cooperative game.

In a “non-cooperative” game players cannot make side-payments. Competition laws generally require that market rivalry be “non-cooperative”.

14Components of games

• A set of players:• Players 1 and 2

• A set of rules, such as who can do what and when: • Play available strategies simultaneously• Player 1 moves first

• A set of strategies:• Choose LEFT, RIGHT, UP, DOWN• Move rook

• A set of payoffs:• If Player 1 plays UP and 2 plays RIGHT player 1 gets 3 and

player 2 gets 6• If I checkmate your King I earn the prize

Games are defined by:

Games are analyzed by examining optimal payoffs for players given the rules of game and the strategies available.

15The “payoff matrix” describes the game

The payoffs of a one-period game are often expressed as a payoff matrix (Player 1, Player 2).

The game is one period because players make simultaneous decisions. It is non-cooperative and we are excluding side payments between players.

Player 2

Player 1

Player 1 gets 6 and Player 2 gets 3 if Player 1 moves Down and Player 2 moves Left

LEFT RIGHT

UP (5,5) (3,6)

DOWN (6,3) (4,4)

(player 1 payoff, player 2 payoff)

16

Optimal strategies with simple one-period non-cooperative game

If P1 played UP P2 would choose RIGHT, and P2 would receive a payoff of 6.

If P1 played DOWN P2 would choose RIGHT, and P2 would receive a payoff of 4.

Therefore, P2 will choose to play RIGHT regardless of what P1’s action is in this case.

Same logic shows, P1 will choose to play DOWN regardless of what P2’s action is.

Player 2

Player 1

LEFT RIGHT

UP (5,5) (3,6)

DOWN (6,3) (4,4)

(player 1 payoff, player 2 payoff)

17The “dominant strategy” is a key concept

• For P1, playing DOWN is a dominant strategy.• For P2, playing RIGHT is a dominant strategy.

A strategy is said to be “dominant” whenever this strategy is strictly better than any other possible strategy, regardless of what the other players’ actions are:

Player 2

Player 1

LEFT RIGHT

UP (5,5) (3,6)

DOWN (6,3) (4,4)

18The dominant strategies point to game equilibrium

Dominant strategies yield an easy solution to the game

Therefore [DOWN, RIGHT] is the equilibrium set of strategies and (4,4) the equilibrium set of payoffs given that the game is non-cooperative.

Player 2

Player 1

LEFT RIGHT

UP (5,5) (3,6)

DOWN (6,3) (4,4)

(player 1 payoff, player 2 payoff)

19The cost of not cooperating

The payoff box considered above demonstrates that “non-cooperative games” results in an equilibrium that is worse for both players than another outcome in total: 8<9<10!

Non-cooperative equilibrium (DOWN,RIGHT) is worse for both players individually than cooperative equilibrium (UP,LEFT) : (5,5) vs. (4,4)

Player 2

Player 1

LEFT RIGHT

UP (10=5,5) (9=3,6)

DOWN (9=6,3) (8=4,4)

20The prisoner’s dilemma game

You and your partner in crime have been busted; police have evidence on minor crime but need confession to convict for major crime.

You are each better off if neither confesses: cooperation (with each other) is the best strategy.But if your partner confesses and you don’t get 40 years; and if you turn in your partner and he doesn’t confess you avoid a long sentence.

It doesn’t take much mistrust for the best strategy to be to confess.

Then, you both get 20 years even though you are both worse off as a result.

Player 2

Player 1Do not

Confess Confess

Do not Confess (1,1) (40,0)

Confess (0,40) (20,20)

Prisoner 2 goes free and prisoner 1 gets 40 years.

(player 1 payoff, player 2 payoff)

21The Nash equilibrium

• The “Nash equilibrium” of a game is the set of actions such that, for each player, the chosen action is the best response to the action of all other players.

• OR• The “Nash equilibrium” of a

game is when no player could change her action, given the chosen actions of all other players, and make herself better off.

The previous examples have used the important concept of the “Nash equilibrium”

John Forbes Nash (1928)

22Games don’t always have just one equilibrium

Another example: The battle of the sexes

You have different preferences over entertainment but want to get together more than anything;

If you don’t coordinate (of course you will!) one of you might be alone at the ballet and your partner at the football match.

He

She

Ballet Football

Ballet (3,2) (1,1)

Football (0,0) (2,3)

(Her Payoff, His Payoff)

23What to do when there are many equilibria?

Focal points (let’s meet in Paris—with no more information where would you meet?)

“Pareto dominance”—you eliminate equilibria where one party is worse off and the other party isn’t better off (you’d rather go to the football match and I’m ok so long as I’m with you)

“Mixed strategies”—this is due to Nash. The idea is that you aren’t certain what the other party will do. Therefore, you randomly choose among your best strategies and so does the other player.

24End Part 1, Next Class Part 2

Part 1

Role of Oligopolies in the

Economy

Game Theory and Strategic

Behavior

Part 2

Oligopoly Theory: Cournot

and Bertrand

Dynamic Games and Competition