Game theory typically describes games using a matrix like the one above. In this game, you and your opponent each choose to say “yes” or “no.” The first number shows the amount you’d win and the second number shows the amount your opponent would win. If you are both playing rationally, game theory would recommend that you say “yes” (and get 6 points) and your opponent says “no” (and gets 1 point), because neither of you can get more points by changing your own move without changing your partner’s move. If you alone switched, your payoff would go from 6 to 4, and if your opponent alone switched, his payoff would go from 1 to 0. A play like this is called a “Nash Equilibrium.”
Credit: Adapted from a graphic by David H. Wolpert
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