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Can anybody explain what's the most rational decision?

I believe that you should always call "steal". On average (assuming you don't know what the other person will choose) you get more money (1.0 if you steal versus 0.5 if you split) and you can never be betrayed.

More than that: each player decides whether the other player takes any money or not. However since the players decisions are independent it doesn't make sense to say 'split'.

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Yeah, stealing would be the most rational thing to do (in the strict sense, disregarding any feelings of guilt a person might have).

This game really illustrates the importance of repeated games and quid pro quo in human relationships. What makes human society function is that we can actually create binding contracts, and that we increase trust with people over time, on the basis of mutual give and take.

“Yeah, stealing would be the most rational thing to do.”

But only if your utility (roughly) corresponds to the money involved. The sums of money might just be big enough for that to be (roughly) true.

Right.

If they split, you are best off stealing.

If they steal, you are best off stealing.

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