Matching - Consider a matching game between 3 females (x1, x2, x3) and 3 males (y1, y2, y3), where the players' preferences are given in Table 2. Answer the following questions:

(a) Consider a matching ? where ? (x1) = {y1}, ? (x2) = {y2} and ? (x3) = {y3}. Is this matching stable (in the core)? Justify your answer.

(b) Find a stable matching using the Deferred Acceptance Procedure (DAP) where the y's propose to the x's.

(c) Find a stable matching using the DAP where the x's propose to the y's.

(d) Come up with an example of a matching game with three men and three women and the stable matchings you get from DAP with men proposing and from DAP with women proposing are not the same. Verify it by performing DAP letting men and women propose respectively.

TABLE 2. Matching 20 2 C 3 y1 y2 y3 1st y1 y1 y3 20 2 C 2 1 2nd y3 y2 y2 20 2 3rd y3 y1 3