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Consider a TU-game (N,v) such that v(S)=f(s) for each S∈ 2

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Ex.1

Consider a TU-game ({1,2,3,4},w) such that w(S)=0 is S∈{{1},{4},{1,4}}; w(S)=1 for each other non empty coalition S. Calculate the Shapley value of w (without using the formula!) and say whether the Shapley value is in the core of the game w.

EX.2

Consider a TU-game (N,v) such that v(S)=f(s) for each S∈ 2

N

\{∅} where s is the cardinality of S and f(s) is a real-valued function. 1) Is v a superadditive game? 2) The Shapley value of v gives f(n)/n to each player in N? 3) Find conditions on f such that the core of v is non-empty.

Ex.3

Find the Nash and Kalai-Smorodinsky solution for the following bargaining games (in both cases the

disagreement point is (0,0). What can you say if the disagreement point was (1,1)?

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