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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

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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, 3 rd Edition, Norton –Rasmusen, E. 2007. Games and Information, Blackwell. Chapter 1 –Carmichael, F. 2004. A Guide to Game Theory, Pearson. Chapters 1-3

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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)

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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

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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

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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

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YOU-stars 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 doesnt launch its new product as well – in which case you prefer to make the offer

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YOU-stars 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

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Your payoffs in a matrix X-Cup launches new product X-Cup makes offer Your decision New product -510 Make offer 1-10 Your payoffs depend on what firm X does You dont have an automatically best choice Your decision depends on what you think firm X will do

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X-Cups 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 firms strategy rather than go it alone

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X-Cups 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

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X-Cups payoffs X-Cups choice New product Make offer You launch a new product 20 -100 You make the offer 5 1 X-Cups payoffs depend on what you do but X-Cup always prefers to launch a new product – whatever you do The new product is Xs dominant strategy – a best choice whatever you do

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Predicting the outcome As you dont have a dominant strategy there cant 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

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Step 1: Put both sets of payoff in the same matrix X-Cup New productMake offer You New product You:-5, X:20You:10, X: -100 Make offer You:1, X: 5You:-10, X:1

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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

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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: -100 Make offer You:1, X: 5 You:-10, X:1 Your best strategy is to make the offer

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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: -100 Make offerYou:1, X: 5 You:-10, X:1 Your best strategy is to launch the product

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Step 4: identify X-Cups best strategies X-Cup New product Make offer You New product You:-5, X:20You:10, X: -100 Make offer You:1, X: 5 You:-10, X:1 We already know that Xs best strategy is always to go for the new product

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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 doesnt deviate) X-Cup New product Make offer You New product You:-5, X:20You:10, X: -100 Make offer You:1, X: 5 You:-10, X:1

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Summary When agents 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

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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-cups best outcome is to make the offer with you –X-cups 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?

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Revised game Fill in X-Cups payoffs and find the Nash equilibrium –Use the following numbers to represent X-Cups payoffs: -100, 20, 1, 5, X-Cup New product Make offer You New product You:-5 X:?You:10 X:? Make offer You:1 X:?You:-10 X:?

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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 product You:-5 X:1You:10 X:5 Make offer You:1 X:-100You:-10 X:20

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Investment game Oligopolist 2 Invest Dont Invest Oligopolist 1 Invest200, 150350, -10 Dont Invest-5, 5000, 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?

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Investment game Oligopolist 2 Invest Dont Invest Oligopolist 1 Invest200, 150350, -10 Dont Invest-5, 5000, 0 Investment: The Nash equilibrium is a dominant strategy equilibrium and therefore the predicted outcome is more convincing? What do you think?

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Chicken James and Son Ltd Full speed ahead Detour Dean and Daughter Ltd Full speed ahead -100, -100300, 0 Detour0, 30010, 10 Use the underlying method to predict the outcome.

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Chicken James and Son Ltd Full speed ahead Detour Dean and Daughter Ltd Full speed ahead -100, -100300, 0 Detour0, 30010, 10 There are two NE. What will be the outcome? How can the firms coordinate their actions?

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Battle of the sexes; coordination? Jane Golf clubTennis club John Gold club200, 15010, 10 Tennis club-10, -10150, 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.

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Battle of the sexes; coordination? Jane Golf clubTennis club John Golf club200, 15010, 10 Tennis club-10, -10150, 200 Interpret the scenario and predict the outcome. How could the managers coordinate?

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Games of pure conflict Industrial spy for firm 2 Steal documents Dont steal documents Security manager of firm 1 Expensive surveillance 200, -5-10, 0 No surveillance -100, 50050, 0 Industrial espionage: In this example use the underlying method so see if there is a Nash equilibrium.

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Games of pure conflict Industrial spy for firm 2 Steal documents Dont steal documents Security manager of firm 1 Expensive surveillance 200, -5-10, 0 No surveillance -100, 50050, 0 What outcome do you predict?

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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

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Principles of Game Theory

Principles of Game Theory

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