Imagine a one-shot, three-player, sequential game between two firms in an oligop

Question

Imagine a one-shot, three-player, sequential game between two firms in an oligopoly market and a third fim which is considering joining the market. The first fim can choose to set a low,medium, or high price. The second firm observes the pricing decision of the first fim and has the same three strategies available for their price.Then, based on the price set by first two firms, the third fim decides to either enter and not enter this market This game is reprsemted by the gametee below Enter 300 300 400 500 500 0 250 350 350 400 600 0 200 400 150 300 700 0 350 250 350 600 400 0 300 300 200 375 375 0 200 500 -50 50 650 0 400 100 150 Dont Medum 3 nter Dont Enter Dont Enter Dont Low Enter Medium 3Ehiler Don't Medium2 Enter Dont Enter Dont Enter Don't Enter Dont Low 3 700 300 0 500 200 -50 650 150 0 200 200 -100 250 250 0 Medium3 oW a Given first-mover advantage, what strategy should fim 1 choose to maximize profit? b. Based on the strategy selacted by firm 1 in part a, what strategy should fim 2 choose to maximize profit? c. Based on the choices of firm 1 and 2, will fim 3 choose to enter this market or not? d Could fim 1 and 2 increase profits by collusion/agreeing to each set the high price?

Explanation / Answer

Firm 1 takes into account the actions of other players:

From backward induction:

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