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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