Game Theory Lecture Jan 18

Game Theory Lecture Jan 18 - Ex 58.2 (Cournot) Two firms,...

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Game Theory Lecture Jan 18
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In Bertrand’s model of oligopoly A) Each firm chooses its quantity as the best response to the quantity chosen by the other(s). B) Each firm chooses its price as the best response to the price chosen by the other(s). C) The firms set quantities sequentially. The second firm’s quantity is the best response to the first firm’s quantity.
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Ex 42.2 (a joint project) Two players, choose effort levels x1 and x2 between 0 and 1. Cost of effort to player i is xi2 Part a) Total output is 3x1x2. They divide output equally. Payoff to Player 1 is:
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Find Player 1’s best response Maximize
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Player 1’s reaction function
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The two reaction functions
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Reaction Function Graph
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Part b Total output is 4x1x2 and is split between two players. Cost of effort xi is c(xi)=xi Payoff to player 1 is:
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Find Player 1’s best response function Take derivative: What does it tell us?
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Unformatted text preview: Ex 58.2 (Cournot) Two firms, linear inverse demand function P=a-Q=a-q1-q2. Firms have constant marginal costs, c1 and c2 Profit function for firm 1 is: Reaction Functions Graph reaction functions Algebra Ex 59.1 (Cournot 2) Linear inverse demand P=a-Q Quadratic Cost function: C(qi)=qi2 What is profit function for firm 1? Bertrand model Each player does best response to others price. Constant marginal cost Buyers will purchase only from seller with lowest price. If prices are equal, demands are split. What can be an equilibrium? Ex 69.1 Bertrand with fixed costs Mixed Strategies Matching pennies Player 2s best response If Player 1 plays heads with probability p>1/2, what is Player 2s best response? What if p<1/2? What if p=1/2 Both players best responses Hide and seek game...
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Game Theory Lecture Jan 18 - Ex 58.2 (Cournot) Two firms,...

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