Of course, the alluring aspect of the ultimatum game is that player's don't act rationally. If they followed the blackboard, you'd see nothing but the smallest offers from Player 1-- a single penny-- and have them be immediately accepted by Player 2. Should Player 1, after viewing the latest Victoria's Secret catalogue, decide to accept $2.50 of $10 as opposed to $3, is he acting any more rationally? He's accepted an offer closer to the accepted rational outcome, but he's still acting irrationally according to the definitions of the situation. I'm not sure there are degrees of rationality here-- not when you've solved the problem beforehand and are looking for a specific result.
Nonetheless, the next time I'm playing poker against a particularly aggressive adversary, I'll make sure to bring the latest in pictorial bliss-- I may be able to steal a hand or two.
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