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In this paper, we present a computing theory and its analysis for collaborative and transparent decision making under temporary constraint, i.e., cost of time pressure which decision makers face in negotiation. We have formulated the proposed computing theory based on game theory and information economics, and checked its feasibility in its applications to a case study. A general heuristics tells that the critical point of selection of proper strategies between collaboration and competition is the half time of the maximum acceptable time for negotiation. The proposed theory shows that the true critical point is the one-third of the maximum acceptable time for negotiation so that conventional decision support systems should be re-designed to select the strategy of collaboration at the much earlier stage.