Consider an economy with \(L \times S\) future markets open at time \(t=0\), for every contingent good \((l, s)\), for all \(l=1, \ldots, L\) and \(s=1, \ldots, S\), as considered at the beginning of Sect. 4.2. Prove that, in correspondence of an Arrow-Debreu equilibrium allocation, there cannot be incentives to trade at date \(t=1\) after the state of the world has been revealed.