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Cournot’s model of oligopoly - page 35 / 38

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Distinguishing between equilibria

For each player i the action vi weakly dominates all her other actions

That is: player i can do no better than bid vi no matter what the other players bid.

Argument:

  • If the highest of the other players’ bids is at least vi, then

    • if player i bids vi her payoff is 0

    • if player i bids x = vi her payoff is either zero or negative.

  • If the highest of the other players’ bids is b < vi, then

    • if player i bids vi her payoff is vi b (she obtains the object at the price b)

    • if player i submits some other bid then she either obtains the good and gets the same payoff, or does not obtain the good and gets the payoff of zero.

Summary

Second-price auction has many Nash equilibria, but the equilibrium (b1, . . . , bn) = (v1, . . . , vn) is the only one in which every players’ action weakly dominates all her other actions.

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