Three friends have houses, which each values differently, as shown in the table above. The friends decide to play the house trading game, in which any coalition of players can get together and reallocate the houses belonging to those players among the members of the coalition (with no money changing hands).

a. Is this game cohesive? Does it have transferable payoffs?

b. If initially Sven owns the green house, Olaf owns the blue house, and Hans owns the yellow house, what allocations will be in the core of this game?

c. Is the core always nonempty in this game for any initial allocation of houses? Is the core always the same for any initial allocation of houses? ONLY ANSWER IF YOU ARE CERTAIN!

Sven's value Olaf's value Hans's value Blue house Yellow house Green house 80 100 50 100 90 80 70 50 70