? EXERCISE 263.1 (Strategic behavior under a deferred acceptance procedure) Con- sider the preferences in Figure 263.1. Find the matchings produced by the deferred acceptance procedures, and show that the core contains no other matchings. Con- sider the strategic game described in the previous paragraph that is induced by the procedure with proposals by X’s. Take as given that each X’s naming her true
ranking is a dominant strategy. Show that the game has a Nash equilibrium in which y1 names the ranking (x1 , x2, x3) and every other player names her true ranking.
Figure 263.1 The players’ preferences in the game in Exercise 263.1.