Definition. $G_{1} \wedge G_{2}$ is the simple game with $N=N_{1} \cup N_{2}$ and $S \in \mathscr{W}$ if and only if $S \cap N_{1} \in W_{1}$ and $S \cap N_{2} \in W_{2}$.
Definition. $G_{1} \vee G_{2}$ is the simple game with $N=N_{1} \cup N_{2}$ and $S \in \mathscr{W}$ if and only if $S \cap N_{1} \in \mathscr{W}{1}$ or $S \cap N{2} \in \mathscr{W}_{2}$.
Thus to win in $G_{1} \wedge G_{2}$ a coalition must win in both $G_{1}$ and $G_{2}$, whereas to win in $G_{1} \vee G_{2}$ it must win either in $G_{1}$ or $G_{2}$.
Consider the following axioms for a power index $K$ :
Axiom 1. $K_{i}(G)=0$ if and only if $i$ is a dummy in $G$.
5QQMB205 COURSE NOTES ：
$$
c=\int \frac{u(x)}{u^{\prime}(x)}
$$
and call $c$ the tax credit. Also let
$$
\eta(t)=\frac{u_{t}^{\prime}(x(t))}{u_{t}(x(t))} x(t) .
$$
Then one can calculate
$$
x(t)=\frac{\eta(t)}{1+\eta(t)}[c+e(t)] .
$$