We consider a two-sided search model in which individuals from two distinct populations would like to form a long-term relationship with a member of the other population. The individual choice is determined by the quality of the partner. Initially the quality of individuals in the population is uniform. At every stage the individuals randomly matched from their populations recognize the quality of the partner. If they accept each other they create a couple and leave the game. The partner's quality is the payoff. Unmatched players go to the next stage. At the last stage the individuals accept any partner. Each player aims to maximize her/his expected payoff. In this paper explicit formulas for Nash equilibrium strategies are derived. Also, the model with incoming individuals is analyzed.
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