# In the “symmetric” Cournot Game with two players, Player 1 chooses any nonnegative x

November 24, 2016

. In the “symmetric” Cournot Game with two players, Player 1 chooses any nonnegative x; Player 2 chooses any nonnegative y, realizing unit cost 10 and unit price equal to 110-(x+y) and therefore the payoffs P1(x; y) = x(100- x-y);P2(x; y) = y(100- x-y).

(i) Show that, for Player 1, any x > 50 is strictly dominated by x = 50.

(ii) Show that, if x is less than or equal to 50, then for Player 2, any y x’ is strictly dominated by x = x’:

Does this game have an “iteratively dominant strategy equilibrium” ?

2. (i) What is the Nash Equilibrium of the symmetric Cournot game with three players ?

(ii) What is the maximum Player 1 would be willing to offer to Player 3 to “buy” Player 3 before the game is played ? (Explanation : If Player 1 buys Player 3 then the game becomes a two player symmetric Cournot game between Players 1 and 2.) Would Player 3 be willing to accept this amount ?

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