Suppose G is a two player game. The strategies x, y, and z are all in Player 1’s strategy set S1. The size of S1 is unspecified and may be infinite. The strategies a and b are both in Player 2’s strategy set S2. The size of S2 is also unspecified and
may be infinite.
Write out the mathematical definition for each of the following statements, using our notation.
(a) Player 1’s strategy y is strictly dominated by Player 1’s strategy z.
(b) Player 1’s strategy y is weakly dominated by Player 1’s strategy z.
(c) For player 1, x is a best response to a
(d) For player 2, b is a best response to x.
(e) For player 2, b is not a best response to z.