Mutual Mate Choice Problem with Arrivals

In this paper mutual choice problem is considered. The individuals from two groups want to choose the partner from the other group. We present the multistage game, where free individuals from different groups randomly match with each other at each stage. The individuals choose each other by the quality. The distributions of the qualities at the first stage are uniform on $[0, 1]$. If they accept each other, they create a couple and leave the game. In this case each receives the partner's quality as a payoff. The remained players go to the next stage. At each stage the groups are reinforced by new individuals. At the last stage the individuals accept the partners lest remain alone. Each player aims to maximize her expected payoff. In this paper the optimal strategies are obtained. Also the statement in which the payoff of the player is equal to the arithmetic mean of the qualities of the couple is considered.