Motivation
Everyone has some relationship with other people, whether it be with family members, friends, or a romantic partner. We would have some interactions with them that would either improve the relationship or break it altogether. How do we know what to do in order to have the best outcome for ourselves? Is there a best option that would be easy for us to see?
Analysis
There are two situations that I can think of that game theory that would affect certain aspects of a relationship.
Let’s say that you are currently in a romantic relationship, and have yet to take the step to say “I love you”. Why is it so hard to do so? Consider the following payoff matrix:

Both you and your partner saying “I love you” would be the best situation, but you run the risk of being rejected depending on the strategy your partner plays. But, saying nothing will protect you from the feeling of rejection, regardless of your partner’s choice. Therefore, you and your partner saying nothing would be the best course of action.
But it always isn’t as black and white as the payoff matrix. Usually, you would be able to tell if your partner would reciprocate those feelings before deciding to say the big words. There would be other factors to consider that affect your decision other than the two choices in the matrix.
Let us consider a general situation in any relationship between family, friends, or a romantic partner. Consider doing chores or anything that requires some sort of assistance. Giver would be someone who would help, while Taker would be someone who is freeloading off of the other person doing the work.

Your parents are cleaning the house; they are giving to the family by doing house chores to keep the house clean. You have the choice to either help as well (“give”) or to let them do it on their own (“take”).
It could be that because you don’t do chores, they are forced to become a “taker” and do it themselves. They might see that you’re doing the chores and decide not to do it with you. Or, both of you decide not to do any cleaning and wait for the other to do so. In all three of these cases, there would be a negative impact on the relationship between you and your parents. “Why aren’t they helping me clean? They live here as well.” So the real best situation, in this case, would be if both of you help to clean the house.
Becoming familiar with a person would change how the payoff matrix would look – it is no longer as black or white as it would be like years in jail for the prisoner’s dilemma. It would help us make smarter choices in our strategy to benefit everyone involved.
Conclusion
Game theory has a lot of real-life impact on us; we essentially play 4D chess every day in our relationships to keep ourselves and everyone else happy. Because in the end, there being sad would affect us too since we care for our friends and family. There is the best choice that would be beneficial for both parties given the situation, and a lot of trust and selfless acts would need to be involved.
References
Jain, Nishant. “Dating, Mating and Mathematics: The Game (Theory) of Love.” LinkedIn, LinkedIn, Jan. 12, 2022, https://www.linkedin.com/pulse/dating-mating-mathematics-game-theory-love-nishant-jain/.
LiveReal Agent Grace. “How Game Theory Can Help You Be Smart About Relationships.” LiveReal, LiveReal, https://www.livereal.com/relationships/game-theory-relationships/.