Previous analyses of market structures characterized by gradual information dissemination presume the equilibrium price existing after all market participants are informed is independent of the order of information dissemination. In these papers, final market clearing price, given the investors' posterior beliefs, is known a priori and is assumed to equal the price that would exist if data were disseminated simultaneously. We demonstrate that final equilibrium price is dependent, in general, on the order of information dissemination. This implies that, if the dissemination sequence is stochastic, price is unknown prior to the complete dissemination of information, even if the investors' posterior beliefs given the information event are known. We derive a necessary and sufficient condition for equilibrium price to be independent of the dissemination sequence in our economy. Our analysis highlights the importance of the wealth redistribution dynamics inherent in the information dissemination process.