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Battle of The Sexes
Two friends hope to spend an evening together. However, they have different preferences. The first person prefers watching Netflix, while the second person prefers a dinner. Both prefer an activity together instead of separate activities. They cannot communicate beforehand. The payoff matrix shows their payoffs (the first number in the bracket is the payoff of player 1).
The Payoff Matrix
| Player 1 \ Player 2 | watch Netflix | have dinner |
|---|---|---|
| watch Netflix | ( 7, 2 ) | ( 1, 1 ) |
| have dinner | ( 0, 0 ) | ( 2, 7 ) |
Solution
This game is called “Battle of the Sexes”. It has two Nash-Equilibria: Either both watch Netflix together or they both have dinner. The game is interesting since both Nash-Equilibra are somewhat unfair for one person. A solution could be to flip a coin and randomize between the equilibra. You’ll find a lot more information about this game online: https://en.wikipedia.org/wiki/Battle_of_the_sexes_(game_theory)