Given a fixed set of players N, each coalition T N determines a unanimity game uT (example 1.48) defined by 1. For each coalition S

Given a fixed set of players N, each coalition T Š‚ N determines a unanimity game uT (example 1.48) defined by

1. For each coalition S c N, recursively define the marginal value of a coalition by

(Recall that T Š‚ S means that T is a proper subset of S, i.e., T Š‚ S but T ‰  S.) Show that

(Recall that T Š‚ S means that T is a proper subset of S, i.e., T Š‚ S but T ‰  S.) Show that

2. Show that

for every coalition SJN.
A subset S of a linear space X is a subspace of X if for every x and y in S, the combination ax + βy belongs to S, that is,
ax + βy ˆˆ S for every x; y ˆˆ S and a, b ˆˆ R

0 otherwise TES = w(i) x,-w(S) for every S N e(S) #7.11 r.(S) TEN