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

Kristoffer Arnsfelt Hansen, Rasmus Ibsen-Jensen and Abraham Neyman

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.

Pages: 15 pages
Date: 2018-02
New Economics Papers: this item is included in nep-gth and nep-mic
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