Game Theory 7 – chap11. Hold-up problem exercies

EXAMPLE 3.19 (EXERCISE 8 ON PAGE 288). An interaction between two players who are considering a possible business partnership

(1) The players simultaneously choose whether to make an investment; investment entails a personal cost of 3; not investing costs nothing

(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

8 if neither invested

(2-2) If they decide not to work together, each player obtains x – 3 if invested, and zero otherwise

player1player2PS
C1Ii5, 5x-3, x-3
C2In3, 6x-3, 0
C3Ni6, 30, x-3
C4Nn4, 40, 0

in x > 6, equilibrium is (I, i)

1 \ 2in
I5, 5x-3, 0
N0, x-34, 4

in x < 6

1 \ 2in
I5, 53, 6
N6, 34, 4

(a) What outcome maximizes the joint value?

(b) Describe conditions on x such that there is an eqbm in which both players invest.

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

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