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Cournot’s model of oligopoly - page 34 / 38

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Another Nash equilibrium

(v2, v1, 0, . . . , 0) is also a Nash equilibrium: Outcome: player 2 gets object at price v2; all payoffs 0. Reason:

  • Player 1:

    • if she raises her bid to x < v1 she still loses

    • if she raises her bid to x v1 she wins, and gets a payoff of 0

  • Player 2

    • if she raises her bid or lowers it to x > v2, outcome remains same

    • if she lowers her bid to x v2 she loses and gets 0

  • Players 3, . . . , n:

    • if she raises her bid to x v1 she still loses

    • if she raises her bid above v1 she wins, but gets a negative payoff vi v1.

Player 2’s may seem “risky”—but isn’t if the other players adhere to their equilibrium actions.

N a s h e q u i l i b r i u m r e q u i r e s o n l y t h a t e a c h p l a y e r s a c t i o n b optimal, given the other players’ actions. e

In a dynamic setting, player 2’s bid isn’t credible (why would she keep bidding above v2?) [Will study this issue later.]

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