Maybe there's an obvious answer here I'm missing but I've wracked by brain for an hour trying to find the answer to this on my homework and when it turns abstract I have no idea what to do.
The question is: "Consider the following situation: Two people are playing a game. They each have to choose a (whole) number from 0 to 100. If they both choose the same number, then they both win that number of dollars If they choose different numbers, then: – The player who chose the smaller number wins that number +2 dollars – The player who chose the larger number wins the SMALLER number minus the difference between the two numbers (note, this means that they might actually end up loosing money) For example, if Player 1 chooses 10 and Player 2 chooses 15, then: Payoff for Player 1 = 10 + 2 = 12 Payoff for Player 2 = 10 − (15 − 10) = 10 − 5 = 5. What is the rational outcome of this game?"
My inclination is both choose the same number, 100, 100 but I don't have any logic behind that.