Oligopoly and Game Theory

Oligopoly and Game Theory

Topic 3.3.9


Topic 3.3.9

Students should be able to:• Use simple game theory to illustrate the interdependence that

exists in oligopolistic markets• Understanding the Prisoners’ Dilemma and a simple two

firm/two outcome model. • Students should analyse the advantages/disadvantages of being a

first mover• Students will not be expected to have an understanding of the

Nash Equilibrium

Game Theory and Oligopoly

Game theory is the study of how people and businesses behave in strategic situations (i.e. when they must consider the effect of other people’s responses to their own actions).

A game consists of:1. Players2. Strategies3. Payoffs4. It might also involve some

form of pre-commitment

Oligopoly theory often makes heavy use of game theory to model the actual behaviour of businesses in concentrated markets

Different Types of Games

• Simultaneous Games– When players effectively make decisions at the same time– They don’t know the choices of other players when making

their choices– Examples:

• The Prisoners’ Dilemma• A game of Rock, Paper, Scissors• Split or Steal in Golden Balls• Individual plays in a game of American Football• Penalty shoot-outs in soccer matches• Serving and receiving in Tennis• Speed dating• Closed bid auctions• Athletes choosing to dope or not to dope

Different Types of Games

• Sequential games– A sequential game is one in which the players take

alternate turns to make their choices.– Examples:• A game of chess• Open-outcry auctions with sequential bidding• Salary negotiations between employer and employee• Haggling with a trader to buy a second hand car • Making offers on a property

– It is important to know who is going to move first in a sequential game as their may be a first mover advantage, or even a first mover disadvantage

Repeated versus One-Shot Games

• One-Shot Games– This is a game that is played only once– The pay-off may be such that a game might be

impossible to play twice– E.g. mutually assured nuclear destruction– Slightly different with tactical / conventional warfare– In one-shot interaction, people often have an

incentive to behave opportunistically / selfishly – Consider a one shot Prisoners’ Dilemma game where

an individual wants to minimise their own sentence

Repeated versus One-Shot Games

• Repeated games – a game played more than once– A feature of applied business – e.g. decisions on:

• Pricing (Established supermarkets versus the Deep Discounters)• The size of marketing budgets (Coca Cola v Pepsi)• Research and development spend (Samsung v Apple v Huawei)• Capital investment and supply capacity forecasts (Cruise ships)

– There is more scope for co-operative strategies to emerge – Credible threat power – history of past behaviours– Agents “learn by doing” – if someone continually serves to your

backhand in tennis, your backhand will improve– Repeated games – crucial point is the reaction to a defective

strategy by another player• Tit for Tat Strategy – if you defect, I defect in the next round• Grim Strategy – if you defect, I will defect in all future rounds

Valuing the future in repeated games

• If you get punished tomorrow for bad behaviour today and you value the future sufficiently highly, it is probably in your own self-interest to behave well today!

• Application:– Fines applied to price fixing and other anti-

competitive cartels– After a cartel fine … how likely is the cartel to reform?– Are students who have taken an Economics degree

less likely to behave cooperatively in their adult lives?

Game Theory – Prisoners’ Dilemma

Prisoner B

Silent Betray

Prisoner A

Silent (6M,6M) (10Y,0)

Betray (0,10Y) (5Y,5Y)

Comment on the best strategies for each player and the likely outcome in this game

Game Theory – Prisoners’ Dilemma

Prisoner B

Silent Betray

Prisoner A



Comment on the best strategies for each player and the likely outcome in this game

• The prisoners' dilemma is a particular game that illustrated why it is difficult to cooperate, even when it is in the best interest of both parties.

• Both players are assumed to select their own dominant strategies for short-sighted personal gain / self-interest.

• Eventually, they reach an equilibrium in which they are both worse off than they would have been, if they could both agree to select an alternative (non-dominant) strategy.

Prisoners’ Dilemma – Decision TreesPrisoner B

Silent Betray

Prisoner A



Nash Equilibrium

• Nash Equilibrium is an important idea in game theory

• It describes any situation where all of the participants in a game are pursuing their best possible strategy given the strategies of all of the other participants.

• In a Nash Equilibrium, the outcome of a game that occurs is when player A takes the best possible action given the action of player B, and player B takes the best possible action given the action of player A

Game Theory: A Simple Pricing Game

Firm B (right hand figures below)

Expected Profit ($bn) High Prices Low Prices

Firm A

High Prices $3bn; $3bn $0bn, $5bn

Low Prices $5bn; $0bn $1bn, $1bn

In this two firm game, they have to decide whether to set high or low pricesThe table shows the profits (pay-offs) that results from each set of choices

The grid above shows a pay-off matrix – it shows a simple pricing game between firm A and firm B. They are assumed to choose their prices at the same time

A Simple Pricing Game

Firm B (right hand figures below)

Expected Profit ($bn) High Prices Low Prices

Firm A

High Prices $3bn; $3bn $0bn, $5bn


To understand the game we isolate one firm and assume that Firm B makes the first decision. Assume that each firm is a profit maximiser.


A Simple Pricing Game

B

Profit $bn High Prices Low Prices

A

High Prices $3bn; $3bn $0 bn, $5bn


In this game, regardless of what the other firm decides to do, the best response of the other firm is to charge a lower price – they may settle at this low price


Pricing Game – Incentives to Collude

B

Profit $bn High Prices Low Prices

A

High Prices $3bn; $3bn $0 bn, $5bn


If these firms got together and decided to collude by both setting a high price, then both of them would earn higher total profits – this would be pareto optimal


First Mover AdvantageTwo players A and B take turns choosing a number between 1 and 10 (inclusive)

A goes first

The cumulative number of ALL of the numbers chosen is calculated as the game progresses

The winner is the player whose choice of number TAKES THE TOTAL to 100 or more

Does this game have first mover advantage?

First Mover Advantage – 0 to 100 Game

• For Player A to win, he/she must a number that takes the total to 100 or more

• The only way this can happen is Player B to leave me a number of 90 or more

• Player A needs to ensure Player B is left with 89

• Player B knows this too• Player A needs to leave Player B with 78• Use backward-induction to work towards

the solution• 100 – 89 – 78 – 67 – 56 – 45 – 34 – 23 – 12• Player A can ensure he/she wins by going

first and choosing 1

Examples of First Mover Advantage

Just Eat Golden Leaf Holdings

Oculus Rift Spotify

Amazon Web Services

Infrastructure Investment Banks

AWS has become the biggest technology infrastructure provider in the world — and it is also the fastest growing and most profitable part of Amazon

Evaluating First Mover Advantage

Advantages of being the first mover• A business first into the market can develop a significant

competitive advantage through learning by doing - making it difficult and costly for new firms/rivals to enter

• They can exploit internal economies of scale (leading to lower LRAC) and also build brand loyalty/ repeat demand

• Consumer behaviour can become habitual – hard to eat into!

Critical evaluation points• Employees from first mover may leave to set up challenge brands –

taking some of the intellectual capital with them• First movers are often unprofitable, the failure rate can be high• Second-movers can learn much from first mover mistakes• First scaler advantage may be more important than first mover

Game Theory: The Stag Hunt

• Two hunters• Within range is one stag

and two hares• Both hunters must chase

the stag to catch it and share the meat

• The two hares can be caught individually

• The meat from one stag > the meat from two hares

The Stag Hunt

Pay-offs from hunting in terms of units of meat

Player 2

Stag Hare

Player 1

Stag (3 , 3) (0, 2)

Hare (2, 0) (1, 1)

The Ultimatum Game

• In the basic ultimatum game:1. The first player (the proposer) receives a sum of

money and proposes how to divide the sum between the proposer and the other player

2. The second player (the responder) chooses to either accept or reject this proposal

3. If the second player accepts, the money is split according to the proposal

4. If the second player rejects, neither player receives any money

5. The ultimatum game is often played once – what is the equilibrium choice for Player 1?

The Ultimatum Game - Tweaked

• The first player (the proposer) receives a sum of money and proposes how to divide the sum between the proposer and the other player

• The second player (the responder) chooses to either accept or reject this proposal

• If the second player accepts, the money is split according to the proposal

• The second player can• Reject the offer and end the game• Propose a counter-offer

Discussing the Ultimatum Game

• People value things other than money!• They care about fairness (equity)• The size of the bargaining pie will shape people’s

willingness to accept a seemingly inequitable offer• Repeated games / options to make counter-offers

may change the behaviour of players• Are players maximisers or satisficers?• Professionally trained economists nearly always

offer less than “normal” people!

Rock Paper Scissors – Nash Equilibrium?

In the famous Rock, Paper, Scissors game: Rock > Scissors, Paper > Rock and Scissors > Paper. Is there an optimum strategy when playing this game?

Rock Paper Scissors

Rock ( 0, 0) (-1 , 1) (1, -1)

Paper (1, -1) (0, 0) (-1, 1)

Scissors (-1, 1) (1, -1) (0, 0)

Rock Paper Scissors – Random Strategy

Rock Paper Scissors

Rock ( 0, 0) (-1 , 1) (1, -1)

Paper (1, -1) (0, 0) (-1, 1)

Scissors (-1, 1) (1, -1) (0, 0)

In this game matter what both players choose, at least one of them can always improve their payoff by switching to a different choice. If one of them wins the game, the loser can improve their payoff by switching. If it's a tie, either player can improve their payoff by switching to a different choice.

Key Concepts – Game Theory

Cooperative outcome An equilibrium in a game where the players agree to cooperate

Dominant strategyA dominant strategy is one where a single strategy is best for a player regardless of what strategy other players in the game decide to use

Nash equilibriumAny situation where all participants in a game are pursuing their best possible strategy given the strategies of all of the other participants

Tacit collusionWhere firms undertake actions that are likely to minimize a competitive response, e.g. avoiding price-cutting or not attacking each other’s market

Whistle blowing When one or more agents in a collusive agreement report it to the authorities

Zero sum game An economic transaction in which whatever is gained by one party must be lost by the other.

Applications of Game Theory

• Interdependent pricing in an oligopoly– Price wars in concentrated markets

• Decisions on– Research and development– Marketing budgets– New product launches– Output decisions

• Co-operative behaviour and collaboration between businesses (requires trust and recognition of mutually beneficial outcomes)


Topic 3.3.9

Oligopoly and Game Theory

Economy & Finance

Transcript of Oligopoly and Game Theory