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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,

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

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  • $\begingroup$ 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 $\endgroup$
    – Darvvin
    Mar 7, 2018 at 18:45
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    $\begingroup$ 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. $\endgroup$ Mar 7, 2018 at 19:10
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    $\begingroup$ 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 $B$. $\endgroup$
    – yassem
    Mar 9, 2018 at 18:12
  • $\begingroup$ @dbx thank you so much, I see ... thanks for the reference, I will look into nash mixed strategy equilibrium. Best $\endgroup$
    – Darvvin
    Aug 29, 2019 at 14:21
  • $\begingroup$ @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 ! $\endgroup$
    – Darvvin
    Aug 29, 2019 at 14:24

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