econ100_winter2010_lecture19_topost

At a ne neither player would like to change decision

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the game? At a NE, neither player would like to change decision once rival’s action is known (stable outcome)
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Nash Equilibrium from the player’s perspective I’m doing the best I can, given what you are doing AND You’re doing the best you can, given what I am doing
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Some games, as above, will have more than 1 Nash Equilibrium need more advanced solution concepts to predict outcome More advanced game theory: repeated games, reputations, random strategies, …much more
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Back to Oligopoly Applications We can use concepts of game theory to make predictions about many models with just a few (or two) firms But, need to make some additional assumptions about how rivals interact (similar to rules of the game)
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Cournot Model of Duopoly 2 firms producing identical products Each firm believes that its rival will set some level of output, that cannot be changed (in the short run, or after other firm’s actions are revealed) Firm 1 believes that Firm 2 will choose some q2, and then set price to sell that amount
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Firm 1 must choose output level to maximize profits, knowing that firm 2 will produce some level (q2) as well Firm 1 can “solve” profit max. problem for every possible level of q2. At each different level of q2, firm 1 will have an optimal output q1*(q2)
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Cournot Duopolist D--Market P Q q2 D-firm 1 MR-firm 1 MC-firm 1
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Cournot Duopoly Model For any ASSUMED level of q2, firm 1 can find the profit maximizing level of output, q1 *
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