# (Solved): P1. For theory of game and decision (Cooperative games ) (In each problem explain what and why you ...

P1. For theory of game and decision (Cooperative games ) (In each problem explain what and why you do. State necessary definitions.) Consider the following cooperative game:

`[[(15,7),(2,3),(4,1),(2,0)],[(-2,-1),(1,1),(-2,3),(0,2)],[(4,1),(7,15),(2,3),(2,0)]]`

a) On the Cartesian plane draw the payoff region. b) Write down the equations of the line segments, the Pareto-optimal-boundary consists of. c) Under the assumption, that the status quo point is

`(2,4)`

find the bargaining set. Write down its equations. d) Find the Nash solution for such a bargaining problem P2.(Cooperative games. In each problem explain what and why you do. State necessary definitions.) Consider the following cooperative game:

`[[(5,3),(7,4),(1,10)],[(1,1),(9,-2),(5,1)]]`

Find the Nash solution for the bargaining problem under the assumption, that the status quo point is given by the safety levels of the players.

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