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Dollar auction game by game theory pioneer Martin Shubik

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The dollar auction is a non-zero sum sequential game designed by economist Martin Shubik, a pioneer of game theory,  to illustrate a paradox brought about by traditional rational choice theory in which players are compelled to make an ultimately irrational decision based completely on a sequence of apparently rational choices made throughout the game, also known as "escalation of commitment"
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A one dollar bill is put up for auction with the following rule: the bill goes to the winner, however the second bidder also loses the amount that he bids.

The winner can get a dollar for a mere 5 cents, but only if no one else enters into the bidding war. The second-highest bidder is the biggest loser by paying the top amount they bid without getting anything back. The game begins with one of the players bidding 5 cents (the minimum), hoping to make a 95-cent profit. They can be outbid by another player bidding 10 cents, as a 90-cent profit is still desirable. Similarly, anoth…