Yet Another Matching Problem: Strategic Behavior Consider the matching problem with three men, three women, and preferences as in Table 10.6. (a) Compute the two matchings produced by the deferred...

Yet Another Matching Problem: Strategic Behavior

Consider the matching problem with three men, three women, and preferences as in Table 10.6.

(a) Compute the two matchings produced by the deferred acceptance procedure with the men and with the women proposing.

(b) Are there any other stable matchings

Now consider the following noncooperative game. The players are w1, w2, and w3. The strategy set of a player is simply the set of all possible preferences over the men. (Thus, each player has 16 different strategies.) The outcomes of the game are the matchings produced by the deferred acceptance procedure with the men proposing, assuming that each man uses his true preference given in Table 10.6.

(c) Show that the following preferences form a Nash equilibrium: w2 and w3 use their true preferences, as given in Table 10.6; w1 uses the preference .m1; m2; m3/. Conclude that sometimes it may pay off to lie about one’s true preference. (Hint: in a Nash equilibrium, no player can gain by deviating.)