The Big Match with a clock and a bit of memory



Hansen, Kristoffer Arnsfelt, Ibsen-Jensen, Rasmus and Neyman, Abraham
(2019) The Big Match with a clock and a bit of memory. Mathematics of Operations Research.

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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. The undiscounted Big Match has been much-studied. Blackwell and Ferguson (1968) give an ε-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 on just the clock or just a finite memory is worthless (i.e., cannot guarantee strictly more than the least reward). The long-standing natural open problem has been whether every strategy that depends on just the clock and a finite memory is worthless. The present paper proves that there is such a strategy that is ε-optimal. In fact, we show that just two states of memory are sufficient.

Item Type: Article
Depositing User: Symplectic Admin
Date Deposited: 17 Dec 2019 09:15
Last Modified: 09 Jan 2021 02:39
URI: https://livrepository.liverpool.ac.uk/id/eprint/3066682