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Based on bargaining problems in the form that J. Nash originally formulated, a two-person bargaining process is modelled as an infinite game in extensive form. In this game, both bargainers make their proposals in terms of the utility pair resulting from possible agreement, and express approval or disapproval, alternatively changing roles. The existence and the uniqueness of subgame-perfect pure-strategy Nash equilibrium are explored. Limiting results when the time between bargaining sessions becomes shorter and shorter are connected with one of the conventional bargaining theories. Throughout this note, time-preference modelled by constant discounting plays an important role.