Game Theory : Eliminating weakly dominated strategies

Question

I have a question in game theory. Let's suppose we have two players A and B, let's say that A is a Girl, and B is a Boy. Both of them are in the same class.

Let's suppose that anyone of them can choose from two strategies : to love or like the other player(L), or reject (or not like : O).

• If both players like each others, then each of them will get 4 points : 2 points for being "loved", and 2 points for starting a relationship.

• If one player likes and the other rejects, the one who is "loved" will get 2 points, and the one who is rejected will lose 2 points : -2, for having his heart broken.

• If both players reject (none likes the other), then nothing changes : 0 points.

Question : What is the best response for, say : Player B ? How to eliminate weakly dominated strategies in this game?

Thanks,

Answer 1

There is no dominated strategy because there is no strategy that has less utility across all the other player's strategies. For example, for player B, $U_B (L) = (4,-2)$ is not better or worse than $U_B (O) = (2,0)$.