Strategic competitions using game theory, Slides of Public Relations

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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-

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

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

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

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-Cup

New product Make offer

You

New

product

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

Make

offer

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

Step 2: Identify Your best strategies if

X launches a new product

X-Cup

New product Make offer

You

New product

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

Make offer

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

Your best strategy is to make the offer

Step 3: Identify Your best

strategies if X goes makes the offer

firm X New product

Make offer

You

New product

You:-5, X:20 (^) You:10 , X: -

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

Your best strategy is to launch the 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-Cup

New product

Make offer

You

New product

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

Make offer

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

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