The 2-Period Exchange Economy

• $I$ traders live for two periods; $t=0,1$.
• State $s\in S$ is revealed at the beginning of the second period.
• $L$ physical commodities available at date 0 and states 1 through $S$. The consumption set for each trader is $\R^{L(S+1)}_+$.
• Each trader has a strictly positive vector $\omega^i\gg 0$ in $\R^{L(S+1)}_+$.
• Each trader has beliefs $\pi^i$ and concave and increasing date $t$ payoff functions $u^i_t:\R^L_+\to\R$.

\begin{equation*} U^i(x^i)=u^i(x^i_0)+\sum_{s=1}^S\pi^i_su^i_1(x^i_s) \end{equation*}