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Big Match with a Clock and a Bit of Memory, The | The Federmann Center for the Study of Rationality

Big Match with a Clock and a Bit of Memory, The

Citation:

Kristoffer Arnsfelt Hansen, Rasmus Ibsen-Jensen, Abraham Neyman . “Big Match With A Clock And A Bit Of Memory, The”. Discussion Papers 2018. Web.

Abstract:

The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage.Blackwell and Ferguson (1968) give an $varepsilon$-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless.The present paper proves that there is such a strategy that is $varepsilon$-optimal. In fact, we show that just two states of memory are sufficient.

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