Try to find the Nash-Equilibrium/Equilibra.
A mother baked two cakes for their two kids. However, one of the cakes got bigger than the other. The mother tells the kids they should clarify between themselves how they share it. However, if they start fighting, they will receive no cake at all! If they both are peaceful, they find an agreement and share the cakes evenly. If only one fights, the fighting kid will receive the large cake. 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 | fight | be peaceful |
---|---|---|
fight | ( 0, 0 ) | ( 10, 2 ) |
be peaceful | ( 2, 10 ) | ( 8, 8 ) |