{"id":1155,"date":"2023-06-02T12:36:14","date_gmt":"2023-06-02T03:36:14","guid":{"rendered":"https:\/\/saraheee.com\/?p=1155"},"modified":"2023-07-03T23:11:07","modified_gmt":"2023-07-03T14:11:07","slug":"game-theory-7-chap11-hold-up-problem-exercies","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2023\/06\/game-theory-7-chap11-hold-up-problem-exercies\/","title":{"rendered":"Game Theory 7 \u2013 chap11. Hold-up problem exercies"},"content":{"rendered":"

EXAMPLE 3.19 (EXERCISE 8 ON PAGE 288)<\/mark>. An interaction between two players who are considering a possible business partnership<\/p>\n\n\n\n

(1) The players simultaneously choose whether to make an investment; investment entails a personal cost of 3; not investing costs nothing<\/p>\n\n\n\n

(2-1) After observing the investment choices, the players jointly decide whether to form a partnership firm and, if so, divide the profit (16 if both invested; 12 if one invested) equally<\/p>\n\n\n\n

8 if neither invested<\/mark><\/p>\n\n\n\n

(2-2) If they decide not to work together, each player obtains x – 3 if invested, and zero otherwise<\/p>\n\n\n\n

<\/td>player1<\/td>player2<\/td>P<\/td>S<\/td><\/tr>
C1<\/td>I<\/td>i<\/td>5, 5<\/td>x-3, x-3<\/td><\/tr>
C2<\/td>I<\/td>n<\/td>3, 6<\/td>x-3, 0<\/td><\/tr>
C3<\/td>N<\/td>i<\/td>6, 3<\/td>0, x-3<\/td><\/tr>
C4<\/td>N<\/td>n<\/td>4, 4<\/td>0, 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

in x > 6, equilibrium is (I, i)<\/mark><\/p>\n\n\n\n

1 \\ 2<\/td>i<\/td>n<\/td><\/tr>
I<\/td>5, 5<\/td>x-3, 0<\/td><\/tr>
N<\/td>0, x-3<\/td>4, 4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

in x < 6<\/mark><\/p>\n\n\n\n

1 \\ 2<\/td>i<\/td>n<\/td><\/tr>
I<\/td>5, 5<\/td>3, 6<\/td><\/tr>
N<\/td>6, 3<\/td>4, 4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

(a) What outcome maximizes the joint value?<\/p>\n\n\n\n

(b) Describe conditions on x such that there is an eqbm in which both players invest.<\/p>\n\n\n\n

(c) Briefly provide some intuition for your answers to (a) and (b) in relation to be “hold-up” problem.<\/p>\n\n\n\n

<\/p>\n\n\n\n