Paradoxes and Game Theory

One of my favourite paradoxes is the unexpected hanging paradox. I'll quote the paradox from Wikipedia http://en.wikipedia.org/wiki/Unexpected_hanging_paradox

Quote

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.
Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that if the hanging were on Friday then it would not be a surprise, since he would know by Thursday night that he was to be hanged the following day, as it would be the only day left (in that week). Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.
He then reasons that the hanging cannot be on Thursday either, because that day would also not be a surprise. On Wednesday night he would know that, with two days left (one of which he already knows cannot be execution day), the hanging should be expected on the following day.
By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.
The next week, the executioner knocks on the prisoner's door at noon on Wednesday — an utter surprise to him. Everything the judge said has come true.

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This is still a paradox which is highly debated and nobody has any conclusive answer as to where the problem in the reasoning is.
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But today when I was re-reading this paradox in Wikipedia, I found a game which almost mirrored the reasoning of the prisoner. It is called the Centipede game. Again I'll quote from Wikipedia the rules of the game. http://en.wikipedia.org/wiki/Centipede_game

Quote

Consider two players Alice and Bob. At the start of the game, Alice has two piles of coins in front of her: one pile contains two coins and the other pile is empty. Alice moves first. Each player has two moves available: either take the larger pile of coins and give the smaller pile to the other player or push both piles across the table to the other player. Each time the piles of coins pass across the table, one coin is added to each pile. For example, on his first move, Bob can take the pile of 3 coins and give 1 coin to Alice, or he can pass the two piles back across the table again to Alice, increasing the size of the piles to 4 and 2 coins. The game continues for a fixed number of rounds or until a player decides to end the game by pocketing a pile of coins.

If we notice carefully the rational decision in the game is made in the same way, backward induction, like the prisoner in the previous case. And if two humans play the game they are always better at it than if two perfectly rational computers play.

Update: And if two humans play the game they are better but never worse at it than if two perfectly rational computers play.