? E XERCISE 263.1 (Strategic behavior under a deferred acceptance procedure) Con- sider the…

? 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.

 

x1 y2

x2 y1

x3 y1

y1 x1

y2 x3

y3 x1

y1

y3

y2

x3

x1

x3

y3

y2

y3

x2

x2

x2

Figure 263.1 The players’ preferences in the game in Exercise 263.1.

 

 

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