301lec24

301lec24 - Summary Strategic Behavior Imperfectly...

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Slide 1 Summary: Strategic Behavior Imperfectly competitive markets are characterized by interdependence and interaction. Strategic decisions: (i) when interdependence and interaction are present. (ii) take into account competitors’ likely behavior by putting oneself in the competitor’s shoes. Game theory is a tool for understanding strategic behavior and finding the optimal strategy.
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Slide 2 Nash Equilibrium Definition of Nash equilibrium. A collection of strategies (one per player) which constitute best responses to each other. Every player is using her best response to other players’ strategies. -“I’m doing the best I can given what you are doing.” -“You’re doing the best you can given what I am doing.”
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Slide 3 Nash Equilibrium Illustration The Lockhorns
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Slide 4 Nash equilibrium The best response terminology: Strategy X is a best response by player A to strategy Y by player B if strategy X gives A the highest payoff when B plays strategy Y. A Nash equilibrium is a collection of players’ strategies , such that each player’s strategy is a best response to the others’ strategies in this collection.
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Slide 5 Lockhorns’ Game Two Equilibria. Leroy- Drink, Loretta- Drive. Why is this equilibrium played, rather than the other? Loretta Drive Drink Leroy Drive 5 , 5 3 , 10 Drink 10 , 3 1 , -1
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Slide 6 Finding an Equilibrium – Cell-by-Cell Inspection A low-tech method, which works for all 2 player games. Check each cell in the matrix to see if any player has a profitable deviation. A profitable deviation is where by changing his strategy (leaving the rival’s choice fixed) a player can improve his or her payoff. If no player has a profitable deviation, then we have a Nash equilibrium. This method finds all equilibria in a given game. But it’s time consuming for more complicated games. Next method: matching best responses.
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Slide 7 Game Table – Row Analysis Low Medium High Low 25, 25 25, 50 25, 75 Medium 50, 25 50, 50 0, 0 High 75, 25 0, 0 0, 0 Suppose that Column player plays Low For row player: High is a best response to Low
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Slide 8 Game Table – Row’s Best Responses Low Medium High Low 25, 25 25, 50 25, 75 Medium 50, 25 50, 50 0, 0 High 75, 25 0, 0 0, 0
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Slide 9 Game Table – Column Analysis Low Medium High Low 25, 25 25, 50 25, 75 Medium 50, 25 50, 50 0, 0 High 75, 25 0, 0 0, 0 Suppose that row player plays Low. For column player: High is a best response to Low
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Slide 10 Game Table – Column’s Best Responses Low Medium High Low 25, 25 25, 50 25, 75 Medium 50, 25 50, 50 0, 0 High 75, 25 0, 0 0, 0
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Slide 11 Equilibria are where best responese match Low Medium High Low 25, 25 25, 50 25, 75 Medium 50, 25 50, 50 0, 0 High 75, 25 0, 0 0, 0
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Slide 12 Summary In this game, there are three pairs of mutual best responses So there are three different Nash equilibria.
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301lec24 - Summary Strategic Behavior Imperfectly...

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