Strategic competition among the few

– Strategic competition is analysed using game theory• Need to revise 2 person simultaneous move

games and Nash equilibrium

Strategic competition among the few: using game theory to analyse strategic situations involved 2

players making simultaneous/hidden moves

• Suggested reading– Allen et al. 2009. Managerial Economics. Norton.

Chapter 11 – Kreps, D. M. 2004. Microeconomics for Managers.

Norton. Chapter 21– Frank, R. H. 2008. Microeconomics and behaviour.

McGraw Hill. Chapter 13– Wall,S., Minocha, S. and Rees, B. 2010.

International Business, Pearson. Chapter 7– Dixit, A., Reiley, D. H. and Skeath, S. 2009. Games

of Strategy, 3rd Edition , Norton– Rasmusen, E. 2007. Games and Information,

Blackwell. Chapter 1– Carmichael, F. 2004. A Guide to Game Theory,

Pearson. Chapters 1-3

Strategic competition among the few: using game theory to analyse strategic situations involving 2

players making simultaneous/hidden moves

• Interdependency between oligopolists implies strategic decision making – they make secret moves, try to outguess

each other and respond to each others actions• Moves in secret are analysed as if moving

simultaneously and to predict the outcome solve for the Nash equilibrium

– And if there is one, a dominant strategy equilibrium (since all dominant strategy equilibria are also Nash equilibria)

What is a Nash equilibrium?

• A pair of strategy choices that are at least ‘best’ responses to each other (if not all the possible choices of the other player)

• No incentive for either player to deviate

– In a Nash equilibrium of a game played between X and Y:• Y will be satisfied with her choice given

whatever X is doing and X will be satisfied with his choice given whatever you have decided to do

• Participants = 2 coffee shop chains (the players):– Your own coffee chain called YOU-Star and a

competitor, X-Cup.• Your company wants to be different from X-Cup in

order to gain market share because of uniqueness.• X-Cup is a smaller firm and for security wants to do

what ever you do – a copy cat strategy

• Both of you have two choices which you make simultaneously in secret:– Launch a new product– Make a special offer

Example: The Copy Cat Coffee Shop

The possible outcomes

1. YOU-star (You) and X-Cup both launch a new product

2. You launch a new product and X-Cup makes the offer

3. You make the offer and X-Cup launches a new product

4. You and X-Cup both make the offer

YOU-star’s payoffs• The profit level that results from your choice is

your payoff– You really want to choose a different strategy from

firm X – your coffee shop chain really wants to differentiate itself from firm X

• Whatever strategy you chose, if firm X chooses the same strategy as you, your profits will be lower

– But launching a new product is less costly and potentially more profitable than making the offer - you have already done the R&D and the market research - launching the new product gives you your highest profits ……………as long as X-Cup doesn’t launch its new product as well – in which case you prefer to make the offer

YOU-star’s payoffs

• Highest payoff = 10 (e.g. $10 million): You launch the new product and X-Cup makes the offer

• Second best payoff = 1: You make the offer and X-Cup launches a new product

• Third best payoff = -5 : You and X-Cup both launch new products

• Lowest payoff = -10: You and X-Cup both make the offer

Your payoffs in a matrix

X-Cup launches new product

X-Cup makes offer

Your decision

New product

-5 10

Make offer

1 -10

•Your payoffs depend on what firm X does•You don’t have an automatically best choice•Your decision depends on what you think firm X will do

X-Cup’s payoffs

• Like you X-Cup would really prefer to launch the new product– making an offer is extremely costly

for X-Cup

• But firm X is small and also would prefer to follow your firm’s strategy rather than go it alone

X-Cup’s payoffs

• Highest payoff = 20: You both launch a new product

• Second best payoff = 5: X-Cup has the new product and you make the offer

• Third best payoff = 1: You and X-Cup both make the offer

• Lowest payoff = -100: X-Cup makes the offer and you launch a new product

X-Cup’s payoffs

X-Cup’s choice

New product

Make offer

You launch a new product

20 -100

You make the offer

5 1

•X-Cup’s payoffs depend on what you do but X-Cup always prefers to launch a new product – whatever you do

•The new product is X’s dominant strategy – a best choice whatever you do

Predicting the outcome• As you don’t have a dominant strategy

there can’t be a dominant strategy equilibrium(DSE); in a DSE both players choose their dominant strategies

• We need to find the next best thing to a DSE - a Nash equilibrium– A pair of strategy choices that are at least

‘best’ responses to each other (even if not best responses to all the possible choices of the other player)

– In a Nash equilibrium of the game there is no incentive for either of you to deviate as:

• You will be satisfied with your choice given whatever X is doing and X-Cup will be satisfied with their choice given whatever you have decided to do

Step 1: Put both sets of payoff

in the same matrix

X-CupNew product Make offer

You

New produ

ct

You:-5, X:20 You:10, X: -100

Make offer

You:1, X: 5 You:-10, X:1

Finding the Nash equilibrium

•To find the Nash Equilibrium (NE) underline payoffs corresponding to best responses–A cell with 2 underlined payoffs implies the corresponding strategies are best responses to each other so they will constitute a Nash equilibrium

Step 2: Identify Your best strategies if X launches a new product

X-CupNew

product

Make offer

You

New product

You:-5, X:20 You:10, X: -100

Make offer

You:1, X: 5 You:-10, X:1

Your best strategy is to make the offer

Step 3: Identify Your best strategies if X goes makes the

offerfirm X

New product Make offer

YouNew

product

You:-5, X:20 You:10, X: -100

Make offer You:1, X: 5 You:-10, X:1

Your best strategy is to launch the product

Step 4: identify X-Cup’s best strategies

X-CupNew

productMake offer

YouNew

product

You:-5, X:20

You:10, X: -100

Make offer

You:1, X: 5 You:-10, X:1

We already know that X’s best strategy is always to go for the new product

Identifying the Nash equilibrium

The Nash equilibrium is {You: make the offer, X: new product}This is the only strategy combination in which neither of you will want to deviate (if the other doesn’t deviate)

X-CupNew

productMake offer

YouNew

productYou:-5, X:20

You:10, X: -100

Make offer

You:1, X: 5

You:-10, X:1

Summary• When agent’s payoffs depend on what other

agents do, we need to look at all possible choices and outcomes

• The predicted strategies are ones that are:– best responses to each other– i.e. they constitute a Nash equilibrium

• if we are lucky they will also constitute a dominant strategy equilibrium

• In the example the Nash equilibrium is for you to go to make the offer and firm X to launch a new product– you are OK with this and X is as well – this is the

best either of you can do

Practise• In a payoff matrix write payoffs for a version

of the game in which your payoffs are unchanged but although X-Cup still wants to copy you, X-cup now strongly prefers to make the offer instead of launch the new product– X-cup’s best outcome is to make the offer with you – X-cup’s worst case scenario is to launch the new

product while you make the offer– But X-cup would rather make the offer without you

than go for the new product with you

• What will this game look like and what will be the Nash equilibrium?

Revised game

• Fill in X-Cup’s payoffs and find the Nash equilibrium – Use the following numbers to

represent X-Cup’s payoffs: -100, 20, 1, 5,

X-Cup

New product Make offer

YouNew

product

You:-5 X:? You:10 X:?

Make offer

You:1 X:? You:-10 X:?

Revised game: X always strongly prefers to make the

offer

The Nash equilibrium is {You: New product, X: make offer}

X-Cup

New product Make offer

You

New produ

ct

You:-5 X:1 You:10 X:5

Make offer

You:1 X:-100 You:-10 X:20

Investment game

Oligopolist 2

Invest Don’t Invest

Oligopolist 1

Invest 200, 150 350, -10

Don’t Invest

-5, 500 0, 0

Two oligopolists choose between investing in new technology or not. Interpret the game (describe the scenario) and use the underlying method so see if there is a Nash equilibrium and if there is whether this is also a dominant strategy equilibrium?

Investment game

Oligopolist 2

Invest Don’t Invest

Oligopolist 1

Invest 200, 150 350, -10

Don’t Invest

-5, 500 0, 0

Investment: The Nash equilibrium is a dominant strategy equilibrium and therefore the predicted outcome is more convincing? What do you think?

Chicken

James and Son Ltd

Full speed ahead

Detour

Dean and Daughter Ltd

Full speed ahead

-100, -100 300, 0

Detour 0, 300 10, 10

Use the underlying method to predict the outcome.

Chicken

James and Son Ltd

Full speed ahead

Detour

Dean and Daughter Ltd

Full speed ahead

-100, -100 300, 0

Detour 0, 300 10, 10

There are two NE. What will be the outcome? How can the firms coordinate their actions?

Battle of the sexes; coordination?

Jane

Golf club Tennis club

John Gold club 200, 150 10, 10

Tennis club -10, -10 150, 200

These two managers of two different firms want to meet up for various reasons. There are two possible locations where they might meet. Each has a preference. Interpret the scenario and predict the outcome.

Battle of the sexes; coordination?

Jane

Golf club Tennis club

JohnGolf club 200, 150 10, 10

Tennis club -10, -10 150, 200

Interpret the scenario and predict the outcome. How could the managers coordinate?

Games of pure conflict

Industrial spy for firm 2

Steal documents

Don’t steal documents

Security manager of firm 1

Expensive surveillance

200, -5 -10, 0

No surveillance

-100, 500 50, 0

Industrial espionage: In this example use the underlying method so see if there is a Nash equilibrium.

Games of pure conflict

Industrial spy for firm 2

Steal documents

Don’t steal documents

Security manager of firm 1

Expensive surveillance

200, -5 -10, 0

No surveillance

-100, 500 50, 0

What outcome do you predict?

Summary• In the strategic competition between

oligopolists predications need to take account of the interdependence between the firms.

• Game theory can do this– e.g. discrete decisions between strategies

in simultaneous move games• And also continuous strategies about output

and price (e.g. Cournot, Stackelberg, Bertrand) where the predicted out is also a Nash equilibrium