econ100_winter2010_lecture18_topost

Bonnie if clyde confesses i am better off confessing

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What should each player do? Bonnie: If Clyde confesses, I am better off confessing (-5 vs. 10) If Clyde denies: I am better off confessing ( -1 vs. - 2) So, no matter what happens, it is best for me to confess
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Clyde’s reasoning goes exactly the same way BOTH players are better off confessing, regardless of what the other player does Example of a DOMINANT STRATEGY
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Dominant Strategy A dominant strategy exists when a player has a best response, regardless of what the other player does Game will have an equilibrium in dominant strategies if there is a pair of strategies that represents a dominant strategy for both players
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(weakly dominant strategy player has a response that makes him at least as well off as alternative strategies, regardless of what the other player does)
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Equil. in Dominant Strategy from player’s perspective I’m doing the best I can, no matter what YOU do, AND You’re doing the best you can no matter what I do
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Finally, back to oligopoly Consider a market in which 2 firms produce a product These firms could attempt to work together (COLLUDE) and behave as if they were a monopolist (Charge High P, limit output) Or, could compete with one another (Charge P = MC, produce more)
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Game: Compete or Collude FIRM 2 FIRM 1 P monop P<P monop P<P monop P monop 10,10 16,0 0,16 8,8
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Each firm has an incentive NOT to collude If set monopoly price, will be worse off, REGARDLESS of what your opponent does So, P< P monop is a dominant strategy for both firms, and there is an equilibrium in these dominant strategies
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Because competing is a dominant strategy, collusion is very difficult to maintain Note: in this case, “rules” of the game that we have imposed make some sense
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Many games will NOT have a solution in dominant strategies, so we need to consider alternative solution concepts Nash Equilibrium
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Consider the game below… 5,5 10,10 10,10 5,5 Player 1 Player 2 S1 S2 S1 S2
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