  We introduce the study of sequential information elicitation in strategic
multi-agent systems. In an information elicitation setup a center attempts to
compute the value of a function based on private information (a-k-a secrets)
accessible to a set of agents. We consider the classical multi-party
computation setup where each agent is interested in knowing the result of the
function. However, in our setting each agent is strategic,and since acquiring
information is costly, an agent may be tempted not spending the efforts of
obtaining the information, free-riding on other agents' computations. A
mechanism which elicits agents' secrets and performs the desired computation
defines a game. A mechanism is 'appropriate' if there exists an equilibrium in
which it is able to elicit (sufficiently many) agents' secrets and perform the
computation, for all possible secret vectors.We characterize a general
efficient procedure for determining an appropriate mechanism, if such mechanism
exists. Moreover, we also address the existence problem, providing a polynomial
algorithm for verifying the existence of an appropriate mechanism.
