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Cournot’s model of oligopoly - page 37 / 38

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Property of all equilibria

In all equilibria the object is obtained by the player who values it most highly (player 1)

Argument:

  • If player i = 1 obtains the object then we must have bi > b1.

  • But there is no equilibrium in which bi > b1:

    • if bi > v2 then i’s payoff is negative, so she can do better by reducing her bid to 0

    • if bi v2 then player 1 can increase her payoff from 0 to v1 bi by bidding bi.

Another equilibrium

(v1, v1, v3, . . . , vn) Outcome: player 1 obtains the object at the price v1.

As before, player 2’s action may seem “risky”: if there is any chance that player 1 submits a bid less than v1 then there is a chance that player 2’s payoff is negative.

37

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