# Game Theory : Eliminating weakly dominated strategies

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,

## 1 Answer

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 $U_B (O) = (2,0)$.

• Thank you so much, I just started learning Game Theory, and I wondered what would be the best response in this kind of games, where there is no better strategy to choose. +1 Mar 7, 2018 at 18:45
• There isn't one best play, but there are several frameworks that prescribe (potentially) different strategies. The most famous of these would be the Nash mixed strategy equilibrium. Mar 7, 2018 at 19:10
• The usual way to answer questions like this is to look for Nash equilibria, which in this case are $(L,L)$ and $(O,O)$. In a simple game like this, where you can present the payoffs in a 2D table you find those by looking at such cells, that the $A$ player cannot improve his payoff by switching to another strategy ($B$ still playing the same), and $B$ cannot improve by switching ($A$ playing the same). You can see how e.g. at $(L,L)$ by switching his strategy $A$ would lose $2$, and so would $B$. Mar 9, 2018 at 18:12
• @dbx thank you so much, I see ... thanks for the reference, I will look into nash mixed strategy equilibrium. Best Aug 29, 2019 at 14:21
• @yassem , Yes, You are right, this game has 2 Nash equilibria, there is no way to look for dominant strategies as the game is symmetric (same options for A and B). Thanks : Best ! Aug 29, 2019 at 14:24