The Big Match with a Clock and a Bit of Memory

Hansen, KA ORCID: 0000-0002-1155-8072, Ibsen-Jensen, R ORCID: 0000-0003-4783-0389 and Neyman, A (2023) The Big Match with a Clock and a Bit of Memory Mathematics of Operations Research, 48 (1). pp. 419-432. ISSN 0364-765X, 1526-5471

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Abstract

The Big Match is a multistage 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; 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
Uncontrolled Keywords:	stochastic games, Markov strategies, bounded memory
Depositing User:	Symplectic Admin
Date Deposited:	17 Dec 2019 09:15
Last Modified:	01 Mar 2026 12:04
DOI:	10.1287/moor.2022.1267
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3066682
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